Solving Runtime error in Bayesian optimization: element 0 of tensors does not require grad and does not have a grad_fn

[MJeong19]

Currently, I am coding the acquisition function for multi-objective Bayesian optimization.

The “element 0 of tensors does not require grad and does not have a grad_fn” occured, so I am trying to fix this error. This error did not occur when I used other acquisition function, so I am trying to modify the code of acquisition function. To fix this, I removed .item() from hv = bd.compute_hypervolume().item(). However, since the result of bd.compute_hypervolume().item() was 0-dimension tensor, I added the code hv.unsqueeze(0).

However, an error occured:

After anomaly detection, the error was from the acquisition function.
I added .clone() in mean and variance of the posterior model in forward function, but the error still occured.
I would like to know how can I solve this error.
Here is the code of the acquisition function.

class UCBHypervolumeImprovement(MultiObjectiveAnalyticAcquisitionFunction):
    def __init__(
        self,
        model,
        train_Y: Tensor,
        ref_point: Tensor,
        partitioning: NondominatedPartitioning,
        posterior_transform: PosteriorTransform | None = None,
        beta: float = 0.1,
    ) -> None:
        """
        UCB-Hypervolume Improvement acquisition function for multi-objective BO.

        Args:
            model: A fitted multi-output GP model.
            train_Y: A `n x m` tensor of previously observed outcomes.
            ref_point: A `1 x m` reference point tensor (for HV calculation).
            partitioning: BoxDecomposition of non-dominated space.
            posterior_transform: Optional posterior transform.
            beta: UCB parameter controlling exploration (higher = more exploration).
        """
        super().__init__(model=model, posterior_transform=posterior_transform)
        self.train_Y = train_Y
        self.ref_point = ref_point
        self.partitioning = partitioning
        self.beta = beta

    def forward(self, X: Tensor) -> Tensor:
        """
        Evaluate the UCB-HVI acquisition function at the candidate points X.

        Args:
            X: A `batch_shape x q x d` tensor of candidate points.

        Returns:
            A `batch_shape` tensor of acquisition values.
        """
        posterior = self.model.posterior(X, posterior_transform=self.posterior_transform)
        mean = posterior.mean.clone()  # shape: batch_shape x q x m
        variance=posterior.variance.clamp_min(1e-9).clone
        std = variance.sqrt() # avoid sqrt(0)

        # UCB formulation for minimization: lower mean - beta * std
        ucb = mean - self.beta * std  # shape: batch_shape x q x m

        # Assume q=1 for analytic HVI (single candidate point per forward call)
        if ucb.shape[-2] != 1:
            raise NotImplementedError("Only q=1 (single candidate point) is supported.")

        # Remove q-dimension: shape becomes batch_shape x m
        ucb_point = ucb.squeeze(-2)
        Ref_point=torch.tensor(self.ref_point, dtype=torch.float64)
        Ref_pointm=Ref_point*-1
        # Compute hypervolume improvement
        # Expand train_Y and append the new point (in each batch)
    
        for i in range(ucb_point.shape[0]):
            # Combine the existing Pareto front with new candidate
            expanded_Y = torch.cat([self.train_Y, ucb_point[i].unsqueeze(0)], dim=0)
            # Filter non-dominated points
            train_Ym=self.train_Y*-1
            expanded_Ym=expanded_Y*-1
            bd = DominatedPartitioning(ref_point=Ref_pointm, Y=train_Ym)
            hv = bd.compute_hypervolume()
            Hv=hv.unsqueeze(0)
            bd2 = DominatedPartitioning(ref_point=Ref_pointm, Y=expanded_Ym)
            hv2 = bd2.compute_hypervolume()
            Hv2=hv2.unsqueeze(0)
            hvi=Hv2-Hv
            if i==0:
                batch_hvi=hvi
            else:
                batch_hvi=torch.cat((batch_hvi,hvi))
        #assert batch_hvi.requires_grad, "Output does not track gradients!"
        return batch_hvi

[esantorella]

Hi @MJeong19 ,

Currently, I am coding the acquisition function for multi-objective Bayesian optimization.

The “element 0 of tensors does not require grad and does not have a grad_fn” occured, so I am trying to fix this error. This error did not occur when I used other acquisition function, so I am trying to modify the code of acquisition function.

Sorry, I'm not sure I understand your question. Are you saying that you are trying to use an existing BoTorch acquisition function and you got an error, so you tried modifying the code? Or have you been working with an acquisition function that you wrote yourself all along?

[saitcakmak]

Hi @MJeong19. I see that you're using DominatedPartitioning to compute the hypervolume. However, the HV computed this way is not differentiable w.r.t. the inputs. As a result, your acquisition function will not be differentiable. The existing acquisition functions like NEHVI use the inclusion / exclusion principle to compute the hypervolume, to ensure it can be differentiated.

[MJeong19]

Thank you for the answer. Then, is there a way to compute HV differentiable w.r.t. the inputs?

[saitcakmak]

Yes. I am not too familiar with the details but you can check out the implementation of qExpectedHypervolumeImprovement. The referenced paper also discussed the approach used there, I believe: https://github.com/pytorch/botorch/blob/main/botorch/acquisition/multi_objective/monte_carlo.py