sampled_efficientzero.py

import copy
from typing import List, Dict, Any, Tuple, Union

import numpy as np
import torch
import torch.optim as optim
from ding.model import model_wrap
from ding.torch_utils import to_tensor
from ding.utils import POLICY_REGISTRY
from ditk import logging
from torch.distributions import Categorical, Independent, Normal
from torch.nn import L1Loss

from lzero.mcts import SampledEfficientZeroMCTSCtree as MCTSCtree
from lzero.mcts import SampledEfficientZeroMCTSPtree as MCTSPtree
from lzero.model import ImageTransforms
from lzero.policy import scalar_transform, InverseScalarTransform, cross_entropy_loss, phi_transform, \
    DiscreteSupport, to_torch_float_tensor, ez_network_output_unpack, select_action, negative_cosine_similarity, \
    prepare_obs, \
    configure_optimizers
from lzero.policy.muzero import MuZeroPolicy
from .utils import configure_optimizers_nanogpt


@POLICY_REGISTRY.register('sampled_efficientzero')
class SampledEfficientZeroPolicy(MuZeroPolicy):
    """
    Overview:
        The policy class for Sampled EfficientZero proposed in the paper https://arxiv.org/abs/2104.06303.
    """

    # The default_config for Sampled EfficientZero policy.
    config = dict(
        model=dict(
            # (str) The model type. For 1-dimensional vector obs, we use mlp model. For 3-dimensional image obs, we use conv model.
            model_type='conv',  # options={'mlp', 'conv'}
            # (bool) If True, the action space of the environment is continuous, otherwise discrete.
            continuous_action_space=False,
            # (tuple) the stacked obs shape.
            # observation_shape=(1, 96, 96),  # if frame_stack_num=1
            observation_shape=(4, 96, 96),  # if frame_stack_num=4
            # (bool) Whether to use the self-supervised learning loss.
            self_supervised_learning_loss=True,
            # (int) The size of action space. For discrete action space, it is the number of actions.
            # For continuous action space, it is the dimension of action.
            action_space_size=6,
            # (bool) Whether to use discrete support to represent categorical distribution for value/reward/value_prefix.
            categorical_distribution=True,
            # (int) the image channel in image observation.
            image_channel=1,
            # (int) The number of frames to stack together.
            frame_stack_num=1,
            # (int) The scale of supports used in categorical distribution.
            # This variable is only effective when ``categorical_distribution=True``.
            support_scale=300,
            # (int) The number of res blocks in Sampled EfficientZero model.
            num_res_blocks=1,
            # (int) The hidden size in LSTM.
            lstm_hidden_size=512,
            # (str) The type of sigma. options={'conditioned', 'fixed'}
            sigma_type='conditioned',
            # (float) The fixed sigma value. Only effective when ``sigma_type='fixed'``.
            fixed_sigma_value=0.3,
            # (bool) whether to learn bias in the last linear layer in value and policy head.
            bias=True,
            # (str) The type of action encoding. Options are ['one_hot', 'not_one_hot']. Default to 'one_hot'.
            discrete_action_encoding_type='one_hot',
            # (bool) whether to use res connection in dynamics.
            res_connection_in_dynamics=True,
            # (str) The type of normalization in MuZero model. Options are ['BN', 'LN']. Default to 'LN'.
            norm_type='LN',
        ),
        # ****** common ******
        # (bool) Whether to use multi-gpu training.
        multi_gpu=False,
        # (bool) ``sampled_algo=True`` means the policy is sampled-based algorithm (e.g. Sampled EfficientZero), which is used in ``collector``.
        sampled_algo=True,
        # (bool) Whether to enable the gumbel-based algorithm (e.g. Gumbel Muzero)
        gumbel_algo=False,
        # (bool) Whether to use C++ MCTS in policy. If False, use Python implementation.
        mcts_ctree=True,
        # (bool) Whether to use cuda in policy.
        cuda=True,
        # (int) The number of environments used in collecting data.
        collector_env_num=8,
        # (int) The number of environments used in evaluating policy.
        evaluator_env_num=3,
        # (str) The type of environment. The options are ['not_board_games', 'board_games'].
        env_type='not_board_games',
        # (str) The type of action space. Options are ['fixed_action_space', 'varied_action_space'].
        action_type='fixed_action_space',
        # (str) The type of battle mode. The options are ['play_with_bot_mode', 'self_play_mode'].
        battle_mode='play_with_bot_mode',
        # (bool) Whether to monitor extra statistics in tensorboard.
        monitor_extra_statistics=True,
        # (int) The transition number of one ``GameSegment``.
        game_segment_length=200,
        # (bool): Indicates whether to perform an offline evaluation of the checkpoint (ckpt).
        # If set to True, the checkpoint will be evaluated after the training process is complete.
        # IMPORTANT: Setting eval_offline to True requires configuring the saving of checkpoints to align with the evaluation frequency.
        # This is done by setting the parameter learn.learner.hook.save_ckpt_after_iter to the same value as eval_freq in the train_muzero.py automatically.
        eval_offline=False,

        # ****** observation ******
        # (bool) Whether to transform image to string to save memory.
        transform2string=False,
        # (bool) Whether to use gray scale image.
        gray_scale=False,
        # (bool) Whether to use data augmentation.
        use_augmentation=False,
        # (list) The style of augmentation.
        augmentation=['shift', 'intensity'],

        # ****** learn ******
        # (bool) Whether to ignore the done flag in the training data. Typically, this value is set to False.
        # However, for some environments with a fixed episode length, to ensure the accuracy of Q-value calculations,
        # we should set it to True to avoid the influence of the done flag.
        ignore_done=False,
        # (int) How many updates(iterations) to train after collector's one collection.
        # Bigger "update_per_collect" means bigger off-policy.
        # collect data -> update policy-> collect data -> ...
        # For different env, we have different episode_length,
        # we usually set update_per_collect = collector_env_num * episode_length / batch_size * reuse_factor.
        # If we set update_per_collect=None, we will set update_per_collect = collected_transitions_num * cfg.policy.replay_ratio automatically.
        update_per_collect=None,
        # (float) The ratio of the collected data used for training. Only effective when ``update_per_collect`` is not None.
        replay_ratio=0.25,
        # (int) Minibatch size for one gradient descent.
        batch_size=256,
        # (str) Optimizer for training policy network. ['SGD', 'Adam', 'AdamW']
        optim_type='AdamW',
        learning_rate=1e-4,  # init lr for manually decay schedule
        # (float) Weight uniform initialization range in the last output layer
        init_w=3e-3,
        normalize_prob_of_sampled_actions=False,
        policy_loss_type='cross_entropy',  # options={'cross_entropy', 'KL'}
        # (int) Frequency of target network update.
        target_update_freq=100,
        weight_decay=1e-4,
        momentum=0.9,
        grad_clip_value=10,
        # You can use either "n_sample" or "n_episode" in collector.collect.
        # Get "n_episode" episodes per collect.
        n_episode=8,
        # (float) the number of simulations in MCTS.
        num_simulations=50,
        # (float) Discount factor (gamma) for returns.
        discount_factor=0.997,
        # (int) The number of step for calculating target q_value.
        td_steps=5,
        # (int) The number of unroll steps in dynamics network.
        num_unroll_steps=5,
        # (int) reset the hidden states in LSTM every ``lstm_horizon_len`` horizon steps.
        lstm_horizon_len=5,
        # (float) The weight of reward loss.
        reward_loss_weight=1,
        # (float) The weight of value loss.
        value_loss_weight=0.25,
        # (float) The weight of policy loss.
        policy_loss_weight=1,
        # (float) The weight of policy entropy loss.
        policy_entropy_loss_weight=5e-3,
        # (float) The weight of ssl (self-supervised learning) loss.
        ssl_loss_weight=2,
        # (bool) Whether to use the cosine learning rate decay.
        cos_lr_scheduler=False,
        # (bool) Whether to use piecewise constant learning rate decay.
        # i.e. lr: 0.2 -> 0.02 -> 0.002
        lr_piecewise_constant_decay=False,
        # (int) The number of final training iterations to control lr decay, which is only used for manually decay.
        threshold_training_steps_for_final_lr=int(5e4),
        # (int) The number of final training iterations to control temperature, which is only used for manually decay.
        threshold_training_steps_for_final_temperature=int(1e5),
        # (bool) Whether to use manually decayed temperature.
        # i.e. temperature: 1 -> 0.5 -> 0.25
        manual_temperature_decay=False,
        # (float) The fixed temperature value for MCTS action selection, which is used to control the exploration.
        # The larger the value, the more exploration. This value is only used when manual_temperature_decay=False.
        fixed_temperature_value=0.25,
        # (bool) Whether to use the true chance in MCTS in some environments with stochastic dynamics, such as 2048.
        use_ture_chance_label_in_chance_encoder=False,
        # (bool) Whether to add noise to roots during reanalyze process.
        reanalyze_noise=True,

        # ****** Priority ******
        # (bool) Whether to use priority when sampling training data from the buffer.
        use_priority=True,
        # (float) The degree of prioritization to use. A value of 0 means no prioritization,
        # while a value of 1 means full prioritization.
        priority_prob_alpha=0.6,
        # (float) The degree of correction to use. A value of 0 means no correction,
        # while a value of 1 means full correction.
        priority_prob_beta=0.4,

        # ****** UCB ******
        # (float) The alpha value used in the Dirichlet distribution for exploration at the root node of the search tree.
        root_dirichlet_alpha=0.3,
        # (float) The noise weight at the root node of the search tree.
        root_noise_weight=0.25,

        # ****** Explore by random collect ******
        # (int) The number of episodes to collect data randomly before training.
        random_collect_episode_num=0,

        # ****** Explore by eps greedy ******
        eps=dict(
            # (bool) Whether to use eps greedy exploration in collecting data.
            eps_greedy_exploration_in_collect=False,
            # (str) The type of decaying epsilon. Options are 'linear', 'exp'.
            type='linear',
            # (float) The start value of eps.
            start=1.,
            # (float) The end value of eps.
            end=0.05,
            # (int) The decay steps from start to end eps.
            decay=int(1e5),
        ),
    )

    def default_model(self) -> Tuple[str, List[str]]:
        """
        Overview:
            Return this algorithm default model setting.
        Returns:
            - model_info (:obj:`Tuple[str, List[str]]`): model name and model import_names.
                - model_type (:obj:`str`): The model type used in this algorithm, which is registered in ModelRegistry.
                - import_names (:obj:`List[str]`): The model class path list used in this algorithm.

        .. note::
            The user can define and use customized network model but must obey the same interface definition indicated \
            by import_names path. For Sampled EfficientZero, ``lzero.model.sampled_efficientzero_model.SampledEfficientZeroModel``
        """
        if self._cfg.model.model_type == "conv":
            return 'SampledEfficientZeroModel', ['lzero.model.sampled_efficientzero_model']
        elif self._cfg.model.model_type == "mlp":
            return 'SampledEfficientZeroModelMLP', ['lzero.model.sampled_efficientzero_model_mlp']
        else:
            raise ValueError("model type {} is not supported".format(self._cfg.model.model_type))

    def _init_learn(self) -> None:
        """
        Overview:
            Learn mode init method. Called by ``self.__init__``. Initialize the learn model, optimizer and MCTS utils.
        """
        assert self._cfg.optim_type in ['SGD', 'Adam', 'AdamW'], self._cfg.optim_type
        if self._cfg.model.continuous_action_space:
            # Weight Init for the last output layer of gaussian policy head in prediction network.
            init_w = self._cfg.init_w
            self._model.prediction_network.fc_policy_head.mu.weight.data.uniform_(-init_w, init_w)
            self._model.prediction_network.fc_policy_head.mu.bias.data.uniform_(-init_w, init_w)
            try:
                self._model.prediction_network.fc_policy_head.log_sigma_layer.weight.data.uniform_(-init_w, init_w)
                self._model.prediction_network.fc_policy_head.log_sigma_layer.bias.data.uniform_(-init_w, init_w)
            except Exception as exception:
                logging.warning(exception)

        if self._cfg.optim_type == 'SGD':
            self._optimizer = optim.SGD(
                self._model.parameters(),
                lr=self._cfg.learning_rate,
                momentum=self._cfg.momentum,
                weight_decay=self._cfg.weight_decay,
            )

        elif self._cfg.optim_type == 'Adam':
            self._optimizer = optim.Adam(
                self._model.parameters(), lr=self._cfg.learning_rate, weight_decay=self._cfg.weight_decay
            )
        elif self._cfg.optim_type == 'AdamW':
            # NOTE: nanoGPT optimizer
            self._optimizer = configure_optimizers_nanogpt(
                model=self._model,
                learning_rate=self._cfg.learning_rate,
                weight_decay=self._cfg.weight_decay,
                device_type=self._cfg.device,
                betas=(0.9, 0.95),
            )

        if self._cfg.cos_lr_scheduler is True:
            from torch.optim.lr_scheduler import CosineAnnealingLR
            self.lr_scheduler = CosineAnnealingLR(self._optimizer, 1e6, eta_min=0, last_epoch=-1)

        if self._cfg.lr_piecewise_constant_decay:
            from torch.optim.lr_scheduler import LambdaLR
            max_step = self._cfg.threshold_training_steps_for_final_lr
            # NOTE: the 1, 0.1, 0.01 is the decay rate, not the lr.
            lr_lambda = lambda step: 1 if step < max_step * 0.5 else (0.1 if step < max_step else 0.01)  # noqa
            self.lr_scheduler = LambdaLR(self._optimizer, lr_lambda=lr_lambda)

        # use model_wrapper for specialized demands of different modes
        self._target_model = copy.deepcopy(self._model)
        self._target_model = model_wrap(
            self._target_model,
            wrapper_name='target',
            update_type='assign',
            update_kwargs={'freq': self._cfg.target_update_freq}
        )
        self._learn_model = self._model

        if self._cfg.use_augmentation:
            self.image_transforms = ImageTransforms(
                self._cfg.augmentation,
                image_shape=(self._cfg.model.observation_shape[1], self._cfg.model.observation_shape[2])
            )
        self.value_support = DiscreteSupport(-self._cfg.model.support_scale, self._cfg.model.support_scale, delta=1)
        self.reward_support = DiscreteSupport(-self._cfg.model.support_scale, self._cfg.model.support_scale, delta=1)
        self.inverse_scalar_transform_handle = InverseScalarTransform(
            self._cfg.model.support_scale, self._cfg.device, self._cfg.model.categorical_distribution
        )

    def _forward_learn(self, data: torch.Tensor) -> Dict[str, Union[float, int]]:
        """
        Overview:
            The forward function for learning policy in learn mode, which is the core of the learning process.
            The data is sampled from replay buffer.
            The loss is calculated by the loss function and the loss is backpropagated to update the model.
        Arguments:
            - data (:obj:`Tuple[torch.Tensor]`): The data sampled from replay buffer, which is a tuple of tensors.
                The first tensor is the current_batch, the second tensor is the target_batch.
        Returns:
            - info_dict (:obj:`Dict[str, Union[float, int]]`): The information dict to be logged, which contains \
                current learning loss and learning statistics.
        """
        self._learn_model.train()
        self._target_model.train()

        current_batch, target_batch = data
        # ==============================================================
        # sampled related core code
        # ==============================================================
        obs_batch_ori, action_batch, child_sampled_actions_batch, mask_batch, indices, weights, make_time = current_batch
        target_value_prefix, target_value, target_policy = target_batch

        obs_batch, obs_target_batch = prepare_obs(obs_batch_ori, self._cfg)

        # do augmentations
        if self._cfg.use_augmentation:
            obs_batch = self.image_transforms.transform(obs_batch)
            if self._cfg.model.self_supervised_learning_loss:
                obs_target_batch = self.image_transforms.transform(obs_target_batch)

        # shape: (batch_size, num_unroll_steps, action_dim)
        # NOTE: .float() in continuous action space.
        action_batch = torch.from_numpy(action_batch).to(self._cfg.device)
        data_list = [
            mask_batch,
            target_value_prefix,
            target_value, target_policy, weights
        ]
        [mask_batch, target_value_prefix, target_value, target_policy,
         weights] = to_torch_float_tensor(data_list, self._cfg.device)
        # ==============================================================
        # sampled related core code
        # ==============================================================
        # shape: (batch_size, num_unroll_steps+1, num_of_sampled_actions, action_dim), e.g. (4, 6, 5, 1)
        child_sampled_actions_batch = torch.from_numpy(child_sampled_actions_batch).to(self._cfg.device)

        target_value_prefix = target_value_prefix.view(self._cfg.batch_size, -1)
        target_value = target_value.view(self._cfg.batch_size, -1)

        assert obs_batch.size(0) == self._cfg.batch_size == target_value_prefix.size(0)

        # ``scalar_transform`` to transform the original value to the scaled value,
        # i.e. h(.) function in paper https://arxiv.org/pdf/1805.11593.pdf.
        transformed_target_value_prefix = scalar_transform(target_value_prefix)
        transformed_target_value = scalar_transform(target_value)
        # transform a scalar to its categorical_distribution. After this transformation, each scalar is
        # represented as the linear combination of its two adjacent supports.
        target_value_prefix_categorical = phi_transform(self.reward_support, transformed_target_value_prefix)
        target_value_categorical = phi_transform(self.value_support, transformed_target_value)

        # ==============================================================
        # the core initial_inference in SampledEfficientZero policy.
        # ==============================================================
        network_output = self._learn_model.initial_inference(obs_batch)
        # value_prefix shape: (batch_size, 10), the ``value_prefix`` at the first step is zero padding.
        latent_state, value_prefix, reward_hidden_state, value, policy_logits = ez_network_output_unpack(network_output)

        # transform the scaled value or its categorical representation to its original value,
        # i.e. h^(-1)(.) function in paper https://arxiv.org/pdf/1805.11593.pdf.
        original_value = self.inverse_scalar_transform_handle(value)

        # Note: The following lines are just for logging.
        predicted_value_prefixs = []
        if self._cfg.monitor_extra_statistics:
            predicted_values, predicted_policies = original_value.detach().cpu(), torch.softmax(
                policy_logits, dim=1
            ).detach().cpu()

        # calculate the new priorities for each transition.
        value_priority = L1Loss(reduction='none')(original_value.squeeze(-1), target_value[:, 0])
        value_priority = value_priority.data.cpu().numpy() + 1e-6

        # ==============================================================
        # calculate policy and value loss for the first step.
        # ==============================================================
        value_loss = cross_entropy_loss(value, target_value_categorical[:, 0])

        policy_loss = torch.zeros(self._cfg.batch_size, device=self._cfg.device)
        # ==============================================================
        # sampled related core code: calculate policy loss, typically cross_entropy_loss
        # ==============================================================
        if self._cfg.model.continuous_action_space:
            """continuous action space"""
            policy_loss, policy_entropy, policy_entropy_loss, target_policy_entropy, target_sampled_actions, mu, sigma = self._calculate_policy_loss_cont(
                policy_loss, policy_logits, target_policy, mask_batch, child_sampled_actions_batch, unroll_step=0
            )
        else:
            """discrete action space"""
            policy_loss, policy_entropy, policy_entropy_loss, target_policy_entropy, target_sampled_actions = self._calculate_policy_loss_disc(
                policy_loss, policy_logits, target_policy, mask_batch, child_sampled_actions_batch, unroll_step=0
            )

        value_prefix_loss = torch.zeros(self._cfg.batch_size, device=self._cfg.device)
        consistency_loss = torch.zeros(self._cfg.batch_size, device=self._cfg.device)

        # ==============================================================
        # the core recurrent_inference in SampledEfficientZero policy.
        # ==============================================================
        for step_k in range(self._cfg.num_unroll_steps):
            # unroll with the dynamics function: predict the next ``latent_state``, ``reward_hidden_state``,
            # `` value_prefix`` given current ``latent_state`` ``reward_hidden_state`` and ``action``.
            # And then predict policy_logits and value  with the prediction function.
            network_output = self._learn_model.recurrent_inference(
                latent_state, reward_hidden_state, action_batch[:, step_k]
            )
            latent_state, value_prefix, reward_hidden_state, value, policy_logits = ez_network_output_unpack(
                network_output
            )

            if self._cfg.model.self_supervised_learning_loss:
                # ==============================================================
                # calculate consistency loss for the next ``num_unroll_steps`` unroll steps.
                # ==============================================================
                if self._cfg.ssl_loss_weight > 0:
                    # obtain the oracle latent states from representation function.
                    beg_index, end_index = self._get_target_obs_index_in_step_k(step_k)
                    network_output = self._learn_model.initial_inference(obs_target_batch[:, beg_index:end_index])

                    latent_state = to_tensor(latent_state)
                    representation_state = to_tensor(network_output.latent_state)

                    # NOTE: no grad for the representation_state branch.
                    dynamic_proj = self._learn_model.project(latent_state, with_grad=True)
                    observation_proj = self._learn_model.project(representation_state, with_grad=False)
                    temp_loss = negative_cosine_similarity(dynamic_proj, observation_proj) * mask_batch[:, step_k]

                    consistency_loss += temp_loss

            # NOTE: the target policy, target_value_categorical, target_value_prefix_categorical is calculated in
            # game buffer now.
            # ==============================================================
            # sampled related core code:
            # calculate policy loss for the next ``num_unroll_steps`` unroll steps.
            # NOTE: the += in policy loss.
            # ==============================================================
            if self._cfg.model.continuous_action_space:
                """continuous action space"""
                policy_loss, policy_entropy, policy_entropy_loss, target_policy_entropy, target_sampled_actions, mu, sigma = self._calculate_policy_loss_cont(
                    policy_loss,
                    policy_logits,
                    target_policy,
                    mask_batch,
                    child_sampled_actions_batch,
                    unroll_step=step_k + 1
                )
            else:
                """discrete action space"""
                policy_loss, policy_entropy, policy_entropy_loss, target_policy_entropy, target_sampled_actions = self._calculate_policy_loss_disc(
                    policy_loss,
                    policy_logits,
                    target_policy,
                    mask_batch,
                    child_sampled_actions_batch,
                    unroll_step=step_k + 1
                )

            value_loss += cross_entropy_loss(value, target_value_categorical[:, step_k + 1])
            value_prefix_loss += cross_entropy_loss(value_prefix, target_value_prefix_categorical[:, step_k])

            # reset hidden states every ``lstm_horizon_len`` unroll steps.
            if (step_k + 1) % self._cfg.lstm_horizon_len == 0:
                reward_hidden_state = (
                    torch.zeros(1, self._cfg.batch_size, self._cfg.model.lstm_hidden_size).to(self._cfg.device),
                    torch.zeros(1, self._cfg.batch_size, self._cfg.model.lstm_hidden_size).to(self._cfg.device)
                )

            if self._cfg.monitor_extra_statistics:
                original_value_prefixs = self.inverse_scalar_transform_handle(value_prefix)
                original_value_prefixs_cpu = original_value_prefixs.detach().cpu()

                predicted_values = torch.cat(
                    (predicted_values, self.inverse_scalar_transform_handle(value).detach().cpu())
                )
                predicted_value_prefixs.append(original_value_prefixs_cpu)
                predicted_policies = torch.cat((predicted_policies, torch.softmax(policy_logits, dim=1).detach().cpu()))

        # ==============================================================
        # the core learn model update step.
        # ==============================================================
        # weighted loss with masks (some invalid states which are out of trajectory.)
        loss = (
                self._cfg.ssl_loss_weight * consistency_loss + self._cfg.policy_loss_weight * policy_loss +
                self._cfg.value_loss_weight * value_loss + self._cfg.reward_loss_weight * value_prefix_loss +
                self._cfg.policy_entropy_loss_weight * policy_entropy_loss
        )
        weighted_total_loss = (weights * loss).mean()

        gradient_scale = 1 / self._cfg.num_unroll_steps
        weighted_total_loss.register_hook(lambda grad: grad * gradient_scale)
        self._optimizer.zero_grad()
        weighted_total_loss.backward()
        if self._cfg.multi_gpu:
            self.sync_gradients(self._learn_model)
        total_grad_norm_before_clip = torch.nn.utils.clip_grad_norm_(
            self._learn_model.parameters(), self._cfg.grad_clip_value
        )
        self._optimizer.step()
        if self._cfg.cos_lr_scheduler or self._cfg.lr_piecewise_constant_decay:
            self.lr_scheduler.step()

        # ==============================================================
        # the core target model update step.
        # ==============================================================
        self._target_model.update(self._learn_model.state_dict())

        if self._cfg.monitor_extra_statistics:
            predicted_value_prefixs = torch.stack(predicted_value_prefixs).transpose(1, 0).squeeze(-1)
            predicted_value_prefixs = predicted_value_prefixs.reshape(-1).unsqueeze(-1)

        return_data = {
            'cur_lr': self._optimizer.param_groups[0]['lr'],
            'collect_mcts_temperature': self._collect_mcts_temperature,
            'weighted_total_loss': weighted_total_loss.item(),
            'total_loss': loss.mean().item(),
            'policy_loss': policy_loss.mean().item(),
            'policy_entropy': policy_entropy.item() / (self._cfg.num_unroll_steps + 1),
            'target_policy_entropy': target_policy_entropy / (self._cfg.num_unroll_steps + 1),
            'value_prefix_loss': value_prefix_loss.mean().item(),
            'value_loss': value_loss.mean().item(),
            'consistency_loss': consistency_loss.mean().item() / self._cfg.num_unroll_steps,

            # ==============================================================
            # priority related
            # ==============================================================
            'value_priority': value_priority.flatten().mean().item(),
            'value_priority_orig': value_priority,
            'target_value_prefix': target_value_prefix.detach().cpu().numpy().mean().item(),
            'target_value': target_value.detach().cpu().numpy().mean().item(),
            'transformed_target_value_prefix': transformed_target_value_prefix.detach().cpu().numpy().mean().item(),
            'transformed_target_value': transformed_target_value.detach().cpu().numpy().mean().item(),
            'predicted_value_prefixs': predicted_value_prefixs.detach().cpu().numpy().mean().item(),
            'predicted_values': predicted_values.detach().cpu().numpy().mean().item()
        }

        if self._cfg.model.continuous_action_space:
            return_data.update({
                # ==============================================================
                # sampled related core code
                # ==============================================================
                'policy_mu_max': mu[:, 0].max().item(),
                'policy_mu_min': mu[:, 0].min().item(),
                'policy_mu_mean': mu[:, 0].mean().item(),
                'policy_sigma_max': sigma.max().item(),
                'policy_sigma_min': sigma.min().item(),
                'policy_sigma_mean': sigma.mean().item(),
                # take the fist dim in action space
                'target_sampled_actions_max': target_sampled_actions[:, :, 0].max().item(),
                'target_sampled_actions_min': target_sampled_actions[:, :, 0].min().item(),
                'target_sampled_actions_mean': target_sampled_actions[:, :, 0].mean().item(),
                'total_grad_norm_before_clip': total_grad_norm_before_clip.item()
            })
        else:
            return_data.update({
                # ==============================================================
                # sampled related core code
                # ==============================================================
                # take the fist dim in action space
                'target_sampled_actions_max': target_sampled_actions[:, :].float().max().item(),
                'target_sampled_actions_min': target_sampled_actions[:, :].float().min().item(),
                'target_sampled_actions_mean': target_sampled_actions[:, :].float().mean().item(),
                'total_grad_norm_before_clip': total_grad_norm_before_clip.item()
            })

        return return_data

    def _calculate_policy_loss_cont(
            self, policy_loss: torch.Tensor, policy_logits: torch.Tensor, target_policy: torch.Tensor,
            mask_batch: torch.Tensor, child_sampled_actions_batch: torch.Tensor, unroll_step: int
    ) -> Tuple[torch.Tensor]:
        """
        Overview:
            Calculate the policy loss for continuous action space.
        Arguments:
            - policy_loss (:obj:`torch.Tensor`): The policy loss tensor.
            - policy_logits (:obj:`torch.Tensor`): The policy logits tensor.
            - target_policy (:obj:`torch.Tensor`): The target policy tensor.
            - mask_batch (:obj:`torch.Tensor`): The mask tensor.
            - child_sampled_actions_batch (:obj:`torch.Tensor`): The child sampled actions tensor.
            - unroll_step (:obj:`int`): The unroll step.
        Returns:
            - policy_loss (:obj:`torch.Tensor`): The policy loss tensor.
            - policy_entropy (:obj:`torch.Tensor`): The policy entropy tensor.
            - policy_entropy_loss (:obj:`torch.Tensor`): The policy entropy loss tensor.
            - target_policy_entropy (:obj:`torch.Tensor`): The target policy entropy tensor.
            - target_sampled_actions (:obj:`torch.Tensor`): The target sampled actions tensor.
            - mu (:obj:`torch.Tensor`): The mu tensor.
            - sigma (:obj:`torch.Tensor`): The sigma tensor.
        """
        (mu, sigma
         ) = policy_logits[:, :self._cfg.model.action_space_size], policy_logits[:, -self._cfg.model.action_space_size:]

        dist = Independent(Normal(mu, sigma), 1)

        # take the init hypothetical step k=unroll_step
        target_normalized_visit_count = target_policy[:, unroll_step]

        # ******* NOTE: target_policy_entropy is only for debug.  ******
        non_masked_indices = torch.nonzero(mask_batch[:, unroll_step]).squeeze(-1)
        # Check if there are any unmasked rows
        if len(non_masked_indices) > 0:
            target_normalized_visit_count_masked = torch.index_select(
                target_normalized_visit_count, 0, non_masked_indices
            )
            target_dist = Categorical(target_normalized_visit_count_masked)
            target_policy_entropy = target_dist.entropy().mean()
        else:
            # Set target_policy_entropy to 0 if all rows are masked
            target_policy_entropy = 0

        # shape: (batch_size, num_unroll_steps, num_of_sampled_actions, action_dim) -> (batch_size,
        # num_of_sampled_actions, action_dim) e.g. (4, 6, 20, 2) ->  (4, 20, 2)
        target_sampled_actions = child_sampled_actions_batch[:, unroll_step]

        policy_entropy = dist.entropy().mean()
        policy_entropy_loss = -dist.entropy()

        # Project the sampled-based improved policy back onto the space of representable policies. calculate KL
        # loss (batch_size, num_of_sampled_actions) -> (4,20) target_normalized_visit_count is
        # categorical distribution, the range of target_log_prob_sampled_actions is (-inf, 0), add 1e-6 for
        # numerical stability.
        target_log_prob_sampled_actions = torch.log(target_normalized_visit_count + 1e-6)
        log_prob_sampled_actions = []
        for k in range(self._cfg.model.num_of_sampled_actions):
            # target_sampled_actions[:,i,:].shape: batch_size, action_dim -> 4,2
            # dist.log_prob(target_sampled_actions[:,i,:]).shape: batch_size -> 4
            # dist is normal distribution, the range of log_prob_sampled_actions is (-inf, inf)

            # way 1:
            # log_prob = dist.log_prob(target_sampled_actions[:, k, :])

            # way 2: SAC-like
            y = 1 - target_sampled_actions[:, k, :].pow(2)

            # NOTE: for numerical stability.
            min_val = torch.tensor(-1 + 1e-6).to(target_sampled_actions.device)
            max_val = torch.tensor(1 - 1e-6).to(target_sampled_actions.device)
            target_sampled_actions_clamped = torch.clamp(target_sampled_actions[:, k, :], min_val, max_val)
            target_sampled_actions_before_tanh = torch.arctanh(target_sampled_actions_clamped)

            # keep dimension for loss computation (usually for action space is 1 env. e.g. pendulum)
            log_prob = dist.log_prob(target_sampled_actions_before_tanh).unsqueeze(-1)
            log_prob = log_prob - torch.log(y + 1e-6).sum(-1, keepdim=True)
            log_prob = log_prob.squeeze(-1)

            log_prob_sampled_actions.append(log_prob)

        # shape: (batch_size, num_of_sampled_actions) e.g. (4,20)
        log_prob_sampled_actions = torch.stack(log_prob_sampled_actions, dim=-1)

        if self._cfg.normalize_prob_of_sampled_actions:
            # normalize the prob of sampled actions
            prob_sampled_actions_norm = torch.exp(log_prob_sampled_actions) / torch.exp(log_prob_sampled_actions).sum(
                -1
            ).unsqueeze(-1).repeat(1, log_prob_sampled_actions.shape[-1]).detach()
            # the above line is equal to the following line.
            # prob_sampled_actions_norm = F.normalize(torch.exp(log_prob_sampled_actions), p=1., dim=-1, eps=1e-6)
            log_prob_sampled_actions = torch.log(prob_sampled_actions_norm + 1e-6)

        # NOTE: the +=.
        if self._cfg.policy_loss_type == 'KL':
            # KL divergence loss: sum( p* log(p/q) ) = sum( p*log(p) - p*log(q) )= sum( p*log(p)) - sum( p*log(q) )
            policy_loss += (
                                   torch.exp(target_log_prob_sampled_actions.detach()) *
                                   (target_log_prob_sampled_actions.detach() - log_prob_sampled_actions)
                           ).sum(-1) * mask_batch[:, unroll_step]
        elif self._cfg.policy_loss_type == 'cross_entropy':
            # cross_entropy loss: - sum(p * log (q) )
            policy_loss += -torch.sum(
                torch.exp(target_log_prob_sampled_actions.detach()) * log_prob_sampled_actions, 1
            ) * mask_batch[:, unroll_step]

        return policy_loss, policy_entropy, policy_entropy_loss, target_policy_entropy, target_sampled_actions, mu, sigma

    def _calculate_policy_loss_disc(
            self, policy_loss: torch.Tensor, policy_logits: torch.Tensor, target_policy: torch.Tensor,
            mask_batch: torch.Tensor, child_sampled_actions_batch: torch.Tensor, unroll_step: int
    ) -> Tuple[torch.Tensor]:
        """
        Overview:
            Calculate the policy loss for discrete action space.
        Arguments:
            - policy_loss (:obj:`torch.Tensor`): The policy loss tensor.
            - policy_logits (:obj:`torch.Tensor`): The policy logits tensor.
            - target_policy (:obj:`torch.Tensor`): The target policy tensor.
            - mask_batch (:obj:`torch.Tensor`): The mask tensor.
            - child_sampled_actions_batch (:obj:`torch.Tensor`): The child sampled actions tensor.
            - unroll_step (:obj:`int`): The unroll step.
        Returns:
            - policy_loss (:obj:`torch.Tensor`): The policy loss tensor.
            - policy_entropy (:obj:`torch.Tensor`): The policy entropy tensor.
            - policy_entropy_loss (:obj:`torch.Tensor`): The policy entropy loss tensor.
            - target_policy_entropy (:obj:`torch.Tensor`): The target policy entropy tensor.
            - target_sampled_actions (:obj:`torch.Tensor`): The target sampled actions tensor.
        """
        prob = torch.softmax(policy_logits, dim=-1)

        # take the init hypothetical step k=unroll_step
        target_normalized_visit_count = target_policy[:, unroll_step]

        # Note: The target_policy_entropy is just for debugging.
        target_normalized_visit_count_masked = torch.index_select(
            target_normalized_visit_count, 0,
            torch.nonzero(mask_batch[:, unroll_step]).squeeze(-1)
        )

        target_policy_entropy = -((target_normalized_visit_count_masked + 1e-6) * (
                    target_normalized_visit_count_masked + 1e-6).log()).sum(-1).mean()

        # shape: (batch_size, num_unroll_steps, num_of_sampled_actions, action_dim) -> (batch_size,
        # num_of_sampled_actions, action_dim) e.g. (4, 6, 20, 2) ->  (4, 20, 2)
        target_sampled_actions = child_sampled_actions_batch[:, unroll_step]

        entropy = -(prob * prob.log()).sum(-1)
        policy_entropy = entropy.mean()
        policy_entropy_loss = -entropy

        # Project the sampled-based improved policy back onto the space of representable policies. calculate KL
        # loss (batch_size, num_of_sampled_actions) -> (4,20) target_normalized_visit_count is
        # categorical distribution, the range of target_log_prob_sampled_actions is (-inf, 0), add 1e-6 for
        # numerical stability.
        target_log_prob_sampled_actions = torch.log(target_normalized_visit_count + 1e-6)

        log_prob_sampled_actions = []
        for k in range(self._cfg.model.num_of_sampled_actions):
            # target_sampled_actions[:,i,:] shape: (batch_size, action_dim) e.g. (4,2)
            # dist.log_prob(target_sampled_actions[:,i,:]) shape: batch_size e.g. 4
            # dist is normal distribution, the range of log_prob_sampled_actions is (-inf, inf)

            if len(target_sampled_actions.shape) == 2:
                target_sampled_actions = target_sampled_actions.unsqueeze(-1)

            log_prob = torch.log(prob.gather(-1, target_sampled_actions[:, k].long()).squeeze(-1) + 1e-6)
            log_prob_sampled_actions.append(log_prob)

        # (batch_size, num_of_sampled_actions) e.g. (4,20)
        log_prob_sampled_actions = torch.stack(log_prob_sampled_actions, dim=-1)

        if self._cfg.normalize_prob_of_sampled_actions:
            # normalize the prob of sampled actions
            prob_sampled_actions_norm = torch.exp(log_prob_sampled_actions) / torch.exp(log_prob_sampled_actions).sum(
                -1
            ).unsqueeze(-1).repeat(1, log_prob_sampled_actions.shape[-1]).detach()
            # the above line is equal to the following line.
            # prob_sampled_actions_norm = F.normalize(torch.exp(log_prob_sampled_actions), p=1., dim=-1, eps=1e-6)
            log_prob_sampled_actions = torch.log(prob_sampled_actions_norm + 1e-6)

        # NOTE: the +=.
        if self._cfg.policy_loss_type == 'KL':
            # KL divergence loss: sum( p* log(p/q) ) = sum( p*log(p) - p*log(q) )= sum( p*log(p)) - sum( p*log(q) )
            policy_loss += (
                                   torch.exp(target_log_prob_sampled_actions.detach()) *
                                   (target_log_prob_sampled_actions.detach() - log_prob_sampled_actions)
                           ).sum(-1) * mask_batch[:, unroll_step]
        elif self._cfg.policy_loss_type == 'cross_entropy':
            # cross_entropy loss: - sum(p * log (q) )
            policy_loss += -torch.sum(
                torch.exp(target_log_prob_sampled_actions.detach()) * log_prob_sampled_actions, 1
            ) * mask_batch[:, unroll_step]

        return policy_loss, policy_entropy, policy_entropy_loss, target_policy_entropy, target_sampled_actions

    def _init_collect(self) -> None:
        """
          Overview:
              Collect mode init method. Called by ``self.__init__``. Initialize the collect model and MCTS utils.
          """
        self._collect_model = self._model
        if self._cfg.mcts_ctree:
            self._mcts_collect = MCTSCtree(self._cfg)
        else:
            self._mcts_collect = MCTSPtree(self._cfg)
        self._collect_mcts_temperature = 1

    def _forward_collect(
            self, data: torch.Tensor, action_mask: list = None, temperature: np.ndarray = 1, to_play=-1,
            epsilon: float = 0.25, ready_env_id: np.array = None,
    ):
        """
        Overview:
            The forward function for collecting data in collect mode. Use model to execute MCTS search.
            Choosing the action through sampling during the collect mode.
        Arguments:
            - data (:obj:`torch.Tensor`): The input data, i.e. the observation.
            - action_mask (:obj:`list`): The action mask, i.e. the action that cannot be selected.
            - temperature (:obj:`float`): The temperature of the policy.
            - to_play (:obj:`int`): The player to play.
            - ready_env_id (:obj:`list`): The id of the env that is ready to collect.
        Shape:
            - data (:obj:`torch.Tensor`):
                - For Atari, :math:`(N, C*S, H, W)`, where N is the number of collect_env, C is the number of channels, \
                    S is the number of stacked frames, H is the height of the image, W is the width of the image.
                - For lunarlander, :math:`(N, O)`, where N is the number of collect_env, O is the observation space size.
            - action_mask: :math:`(N, action_space_size)`, where N is the number of collect_env.
            - temperature: :math:`(1, )`.
            - to_play: :math:`(N, 1)`, where N is the number of collect_env.
            - ready_env_id: None
        Returns:
            - output (:obj:`Dict[int, Any]`): Dict type data, the keys including ``action``, ``distributions``, \
                ``visit_count_distribution_entropy``, ``value``, ``pred_value``, ``policy_logits``.
        """
        self._collect_model.eval()
        self._collect_mcts_temperature = temperature
        active_collect_env_num = data.shape[0]
        if ready_env_id is None:
            ready_env_id = np.arange(active_collect_env_num)
        output = {i: None for i in ready_env_id}
        with torch.no_grad():
            # data shape [B, S x C, W, H], e.g. {Tensor:(B, 12, 96, 96)}
            network_output = self._collect_model.initial_inference(data)
            latent_state_roots, value_prefix_roots, reward_hidden_state_roots, pred_values, policy_logits = ez_network_output_unpack(
                network_output
            )

            pred_values = self.inverse_scalar_transform_handle(pred_values).detach().cpu().numpy()
            latent_state_roots = latent_state_roots.detach().cpu().numpy()
            reward_hidden_state_roots = (
                reward_hidden_state_roots[0].detach().cpu().numpy(),
                reward_hidden_state_roots[1].detach().cpu().numpy()
            )
            policy_logits = policy_logits.detach().cpu().numpy().tolist()

            if self._cfg.model.continuous_action_space is True:
                # when the action space of the environment is continuous, action_mask[:] is None.
                # NOTE: in continuous action space env: we set all legal_actions as -1
                legal_actions = [
                    [-1 for _ in range(self._cfg.model.num_of_sampled_actions)] for _ in range(active_collect_env_num)
                ]
            else:
                legal_actions = [
                    [i for i, x in enumerate(action_mask[j]) if x == 1] for j in range(active_collect_env_num)
                ]

            if self._cfg.mcts_ctree:
                # cpp mcts_tree
                roots = MCTSCtree.roots(
                    active_collect_env_num, legal_actions, self._cfg.model.action_space_size,
                    self._cfg.model.num_of_sampled_actions, self._cfg.model.continuous_action_space
                )
            else:
                # python mcts_tree
                roots = MCTSPtree.roots(
                    active_collect_env_num, legal_actions, self._cfg.model.action_space_size,
                    self._cfg.model.num_of_sampled_actions, self._cfg.model.continuous_action_space
                )

            # the only difference between collect and eval is the dirichlet noise
            noises = [
                np.random.dirichlet([self._cfg.root_dirichlet_alpha] * int(self._cfg.model.num_of_sampled_actions)
                                    ).astype(np.float32).tolist() for j in range(active_collect_env_num)
            ]

            roots.prepare(self._cfg.root_noise_weight, noises, value_prefix_roots, policy_logits, to_play)
            self._mcts_collect.search(
                roots, self._collect_model, latent_state_roots, reward_hidden_state_roots, to_play
            )

            # list of list, shape: ``{list: batch_size} -> {list: action_space_size}``
            roots_visit_count_distributions = roots.get_distributions()
            roots_values = roots.get_values()  # shape: {list: batch_size}
            roots_sampled_actions = roots.get_sampled_actions()  # {list: 1}->{list:6}

            for i, env_id in enumerate(ready_env_id):
                distributions, value = roots_visit_count_distributions[i], roots_values[i]
                if self._cfg.mcts_ctree:
                    # In ctree, the method roots.get_sampled_actions() returns a list object.
                    root_sampled_actions = np.array([action for action in roots_sampled_actions[i]])
                else:
                    # In ptree, the same method roots.get_sampled_actions() returns an Action object.
                    root_sampled_actions = np.array([action.value for action in roots_sampled_actions[i]])

                # NOTE: Only legal actions possess visit counts, so the ``action_index_in_legal_action_set`` represents
                # the index within the legal action set, rather than the index in the entire action set.
                action, visit_count_distribution_entropy = select_action(
                    distributions, temperature=self._collect_mcts_temperature, deterministic=False
                )

                if self._cfg.mcts_ctree:
                    # In ctree, the method roots.get_sampled_actions() returns a list object.
                    action = np.array(roots_sampled_actions[i][action])
                else:
                    # In ptree, the same method roots.get_sampled_actions() returns an Action object.
                    action = roots_sampled_actions[i][action].value

                if not self._cfg.model.continuous_action_space:
                    if len(action.shape) == 0:
                        action = int(action)
                    elif len(action.shape) == 1:
                        action = int(action[0])

                output[env_id] = {
                    'action': action,
                    'visit_count_distributions': distributions,
                    'root_sampled_actions': root_sampled_actions,
                    'visit_count_distribution_entropy': visit_count_distribution_entropy,
                    'searched_value': value,
                    'predicted_value': pred_values[i],
                    'predicted_policy_logits': policy_logits[i],
                }

        return output

    def _init_eval(self) -> None:
        """
         Overview:
             Evaluate mode init method. Called by ``self.__init__``. Initialize the eval model and MCTS utils.
         """
        self._eval_model = self._model
        if self._cfg.mcts_ctree:
            self._mcts_eval = MCTSCtree(self._cfg)
        else:
            self._mcts_eval = MCTSPtree(self._cfg)

    def _forward_eval(self, data: torch.Tensor, action_mask: list, to_play: -1, ready_env_id: np.array = None,):
        """
         Overview:
             The forward function for evaluating the current policy in eval mode. Use model to execute MCTS search.
             Choosing the action with the highest value (argmax) rather than sampling during the eval mode.
         Arguments:
             - data (:obj:`torch.Tensor`): The input data, i.e. the observation.
             - action_mask (:obj:`list`): The action mask, i.e. the action that cannot be selected.
             - to_play (:obj:`int`): The player to play.
             - ready_env_id (:obj:`list`): The id of the env that is ready to collect.
         Shape:
             - data (:obj:`torch.Tensor`):
                 - For Atari, :math:`(N, C*S, H, W)`, where N is the number of collect_env, C is the number of channels, \
                     S is the number of stacked frames, H is the height of the image, W is the width of the image.
                 - For lunarlander, :math:`(N, O)`, where N is the number of collect_env, O is the observation space size.
             - action_mask: :math:`(N, action_space_size)`, where N is the number of collect_env.
             - to_play: :math:`(N, 1)`, where N is the number of collect_env.
             - ready_env_id: None
         Returns:
             - output (:obj:`Dict[int, Any]`): Dict type data, the keys including ``action``, ``distributions``, \
                 ``visit_count_distribution_entropy``, ``value``, ``pred_value``, ``policy_logits``.
         """
        self._eval_model.eval()
        active_eval_env_num = data.shape[0]
        if ready_env_id is None:
            ready_env_id = np.arange(active_eval_env_num)
        output = {i: None for i in ready_env_id}
        with torch.no_grad():
            # data shape [B, S x C, W, H], e.g. {Tensor:(B, 12, 96, 96)}
            network_output = self._eval_model.initial_inference(data)
            latent_state_roots, value_prefix_roots, reward_hidden_state_roots, pred_values, policy_logits = ez_network_output_unpack(
                network_output
            )

            if not self._eval_model.training:
                # if not in training, obtain the scalars of the value/reward
                pred_values = self.inverse_scalar_transform_handle(pred_values).detach().cpu().numpy()  # shape（B, 1）
                latent_state_roots = latent_state_roots.detach().cpu().numpy()
                reward_hidden_state_roots = (
                    reward_hidden_state_roots[0].detach().cpu().numpy(),
                    reward_hidden_state_roots[1].detach().cpu().numpy()
                )
                policy_logits = policy_logits.detach().cpu().numpy().tolist()  # list shape（B, A）

            if self._cfg.model.continuous_action_space is True:
                # when the action space of the environment is continuous, action_mask[:] is None.
                # NOTE: in continuous action space env: we set all legal_actions as -1
                legal_actions = [
                    [-1 for _ in range(self._cfg.model.num_of_sampled_actions)] for _ in range(active_eval_env_num)
                ]
            else:
                legal_actions = [
                    [i for i, x in enumerate(action_mask[j]) if x == 1] for j in range(active_eval_env_num)
                ]

            # cpp mcts_tree
            if self._cfg.mcts_ctree:
                roots = MCTSCtree.roots(
                    active_eval_env_num, legal_actions, self._cfg.model.action_space_size,
                    self._cfg.model.num_of_sampled_actions, self._cfg.model.continuous_action_space
                )
            else:
                # python mcts_tree
                roots = MCTSPtree.roots(
                    active_eval_env_num, legal_actions, self._cfg.model.action_space_size,
                    self._cfg.model.num_of_sampled_actions, self._cfg.model.continuous_action_space
                )

            roots.prepare_no_noise(value_prefix_roots, policy_logits, to_play)
            self._mcts_eval.search(roots, self._eval_model, latent_state_roots, reward_hidden_state_roots, to_play)

            # list of list, shape: ``{list: batch_size} -> {list: action_space_size}``
            roots_visit_count_distributions = roots.get_distributions()
            roots_values = roots.get_values()  # shape: {list: batch_size}
            # ==============================================================
            # sampled related core code
            # ==============================================================
            roots_sampled_actions = roots.get_sampled_actions(
            )  # shape: ``{list: batch_size} ->{list: action_space_size}``

            for i, env_id in enumerate(ready_env_id):
                distributions, value = roots_visit_count_distributions[i], roots_values[i]
                try:
                    root_sampled_actions = np.array([action.value for action in roots_sampled_actions[i]])
                except Exception:
                    # logging.warning('ctree_sampled_efficientzero roots.get_sampled_actions() return list')
                    root_sampled_actions = np.array([action for action in roots_sampled_actions[i]])
                # NOTE: Only legal actions possess visit counts, so the ``action_index_in_legal_action_set`` represents
                # the index within the legal action set, rather than the index in the entire action set.
                # Setting deterministic=True implies choosing the action with the highest value (argmax) rather than sampling during the evaluation phase.
                action, visit_count_distribution_entropy = select_action(
                    distributions, temperature=1, deterministic=True
                )
                # ==============================================================
                # sampled related core code
                # ==============================================================

                try:
                    action = roots_sampled_actions[i][action].value
                    # logging.warning('ptree_sampled_efficientzero roots.get_sampled_actions() return array')
                except Exception:
                    # logging.warning('ctree_sampled_efficientzero roots.get_sampled_actions() return list')
                    action = np.array(roots_sampled_actions[i][action])

                if not self._cfg.model.continuous_action_space:
                    if len(action.shape) == 0:
                        action = int(action)
                    elif len(action.shape) == 1:
                        action = int(action[0])

                output[env_id] = {
                    'action': action,
                    'visit_count_distributions': distributions,
                    'root_sampled_actions': root_sampled_actions,
                    'visit_count_distribution_entropy': visit_count_distribution_entropy,
                    'searched_value': value,
                    'predicted_value': pred_values[i],
                    'predicted_policy_logits': policy_logits[i],
                }

        return output

    def _monitor_vars_learn(self) -> List[str]:
        """
        Overview:
             Register the variables to be monitored in learn mode. The registered variables will be logged in
             tensorboard according to the return value ``_forward_learn``.
        """
        if self._cfg.model.continuous_action_space:
            return [
                'collect_mcts_temperature',
                'cur_lr',
                'total_loss',
                'weighted_total_loss',
                'policy_loss',
                'value_prefix_loss',
                'value_loss',
                'consistency_loss',
                'value_priority',
                'target_value_prefix',
                'target_value',
                'predicted_value_prefixs',
                'predicted_values',
                'transformed_target_value_prefix',
                'transformed_target_value',

                # ==============================================================
                # sampled related core code
                # ==============================================================
                'policy_entropy',
                'target_policy_entropy',
                'policy_mu_max',
                'policy_mu_min',
                'policy_mu_mean',
                'policy_sigma_max',
                'policy_sigma_min',
                'policy_sigma_mean',
                # take the fist dim in action space
                'target_sampled_actions_max',
                'target_sampled_actions_min',
                'target_sampled_actions_mean',
                'total_grad_norm_before_clip',
            ]
        else:
            return [
                'collect_mcts_temperature',
                'cur_lr',
                'total_loss',
                'weighted_total_loss',
                'loss_mean',
                'policy_loss',
                'value_prefix_loss',
                'value_loss',
                'consistency_loss',
                'value_priority',
                'target_value_prefix',
                'target_value',
                'predicted_value_prefixs',
                'predicted_values',
                'transformed_target_value_prefix',
                'transformed_target_value',

                # ==============================================================
                # sampled related core code
                # ==============================================================
                'policy_entropy',
                'target_policy_entropy',

                # take the fist dim in action space
                'target_sampled_actions_max',
                'target_sampled_actions_min',
                'target_sampled_actions_mean',
                'total_grad_norm_before_clip',
            ]

    def _state_dict_learn(self) -> Dict[str, Any]:
        """
        Overview:
            Return the state_dict of learn mode, usually including model and optimizer.
        Returns:
            - state_dict (:obj:`Dict[str, Any]`): the dict of current policy learn state, for saving and restoring.
        """
        return {
            'model': self._learn_model.state_dict(),
            'target_model': self._target_model.state_dict(),
            'optimizer': self._optimizer.state_dict(),
        }

    def _load_state_dict_learn(self, state_dict: Dict[str, Any]) -> None:
        """
        Overview:
            Load the state_dict variable into policy learn mode.
        Arguments:
            - state_dict (:obj:`Dict[str, Any]`): the dict of policy learn state saved before.
        """
        self._learn_model.load_state_dict(state_dict['model'])
        self._target_model.load_state_dict(state_dict['target_model'])
        self._optimizer.load_state_dict(state_dict['optimizer'])

    def _process_transition(self, obs, policy_output, timestep):
        # be compatible with DI-engine Policy class
        pass

    def _get_train_sample(self, data):
        # be compatible with DI-engine Policy class
        pass