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Description
Hello,
I want to do a Bayesian optimization of a 2-dimensional multi-fidelity test problem. I therefore defined a linear multi-fidelity model and set up the acquisition function. I also set a context variable for the fidelity parameter. I set the fidelity parameter value for the optimization to the highest fidelity. But when trying to optimize the acquisition function an error returned immediately, originating form the scipy l-bfgs algorithm. I noticed that the shape of the gradient of the acquisition function was (1,2,2) instead of (2) or (1,2). I noticed the dimensionality error came from the expected improvement acquisition function definition specificially from this line:
dimprovement_dx = dstandard_deviation_dx * pdf - cdf * dmean_dx
the shape of dmean_dx was (1,2,1), this results in the dimprovement_dx.shape being (1,2,2).
quick fix for the evaluation was to add this line of code:
dimprovement_dx = np.diagonal(dimprovement_dx).T
which worked now for my 2-dimensional test problem. It will hopefully also still work for 1-dimensional test problems, but i think for higher dimensional problems it will not work, so its probably advisable to just fix the dimensionality of dmean_dx.
Code to replicat the error is here:
import numpy as np
import GPy
from emukit.core import ParameterSpace, ContinuousParameter, DiscreteParameter
from emukit.bayesian_optimization.acquisitions import ExpectedImprovement
from emukit.core.optimization import GradientAcquisitionOptimizer
import emukit.multi_fidelity
from emukit.model_wrappers.gpy_model_wrappers import GPyMultiOutputWrapper
from emukit.multi_fidelity.models import GPyLinearMultiFidelityModel
X_train = np.array([[ 0.13473929, -0.32606444, 0. ],
[-1.53102551, 1.4245339 , 0. ],
[-0.48998839, -1.29864283, 0. ],
[ 1.84718222, 0.45174302, 0. ],
[ 1.32512917, -1.85203682, 0. ],
[-0.96369396, 0.89760785, 0. ],
[-1.04751664, -0.76983995, 0. ],
[ 0.66267413, 1.9795312 , 0. ],
[ 0.80437702, -1.13627663, 0. ],
[-1.40778594, 0.11410064, 0. ],
[-0.5741273 , -0.24182373, 0. ],
[ 1.21662989, 1.00876794, 0. ],
[ 1.73703451, -0.66999665, 0. ],
[-0.0981639 , 1.57938117, 0. ],
[-1.88964734, -1.70531898, 0. ],
[ 0.27418341, 0.54433427, 0. ],
[ 0.47281786, -1.60549965, 0. ],
[-1.86141352, 0.64387054, 0. ],
[-0.14885246, -0.51576477, 0. ],
[ 1.51398075, 1.73388086, 0. ],
[-1.43824131, 0.65202268, 1. ],
[ 0.12916456, -1.85884469, 1. ],
[ 1.68246282, 1.32535729, 1. ],
[-0.99837652, -0.18159998, 1. ],
[-0.21917494, 1.69523472, 1. ],
[ 1.41106617, -0.80000571, 1. ],
[ 0.90085879, 0.26700687, 1. ],
[-1.71775573, -1.22432354, 1. ],
[-1.8063743 , 1.13146007, 1. ],
[ 0.62229842, -0.36158118, 1. ],
[ 1.06610087, 0.82823509, 1. ],
[-0.25701166, -1.66090378, 1. ],
[-0.52450227, 0.21373441, 1. ],
[ 1.84139629, -1.29492998, 1. ],
[ 0.34669023, 1.76207188, 1. ],
[-1.03858617, -0.74269003, 1. ],
[-1.24743496, 1.88256894, 1. ],
[ 0.43151265, -0.61242308, 1. ],
[ 1.88211933, 0.0793515 , 1. ],
[-0.69120659, -1.41173808, 1. ],
[ 1.75531639, 0.01006163, 2. ],
[-0.16598199, -1.41704852, 2. ],
[-1.39763355, 1.91486136, 2. ],
[ 0.55827226, -0.50934682, 2. ],
[ 0.28320662, 1.19174326, 2. ],
[-1.63918466, -0.34873588, 2. ],
[-0.92222783, 0.8503596 , 2. ],
[ 1.02817909, -1.6948546 , 2. ],
[ 1.41036964, 1.53844309, 2. ],
[-0.50848947, -0.88097757, 2. ],
[-1.80314409, 0.38062028, 2. ],
[ 0.15129807, -1.03565238, 2. ],
[ 0.87819937, 0.72781515, 2. ],
[-1.04663165, -1.82035536, 2. ],
[-0.2667013 , 1.32405309, 2. ],
[ 1.68516784, -0.22909473, 2. ],
[ 1.51735547, 1.44219314, 2. ],
[-0.43482649, -0.09917109, 2. ],
[-1.12851415, 0.59992489, 2. ],
[ 0.79601932, -1.94440427, 2. ]])
Y_train = np.array([[1.24180338e+00],
[9.84373290e+00],
[2.44074890e+01],
[8.03973669e+01],
[1.22073038e+02],
[4.11819471e-01],
[3.71351316e+01],
[2.31060430e+01],
[3.05597094e+01],
[3.80808397e+01],
[3.57512288e+00],
[2.20424659e+00],
[1.25195017e+02],
[2.49581510e+01],
[3.08139883e+02],
[2.26366363e+00],
[3.26536686e+01],
[8.85821224e+01],
[3.01479215e+00],
[3.07271610e+00],
[1.01034474e+02],
[1.81278479e+02],
[1.25356617e+02],
[7.10193407e+01],
[1.38096216e+02],
[4.00845553e+02],
[2.26572223e+01],
[8.73085407e+02],
[2.27545534e+02],
[3.47838964e+01],
[1.32073600e+01],
[1.53116297e+02],
[2.52078040e+00],
[1.11225838e+03],
[1.39240704e+02],
[1.67680976e+02],
[5.57808268e+00],
[3.78929038e+01],
[6.13716074e+02],
[1.81275800e+02],
[9.43720052e+02],
[2.10046008e+02],
[5.89701164e+00],
[6.76016433e+01],
[1.24065302e+02],
[9.28489813e+02],
[3.69496190e+00],
[7.57354963e+02],
[2.04814007e+01],
[1.32130481e+02],
[8.31954239e+02],
[1.12771727e+02],
[2.03356232e-01],
[8.54373681e+02],
[1.58586264e+02],
[9.42275205e+02],
[7.42576705e+01],
[1.03672545e+01],
[4.99068690e+01],
[6.64676317e+02]])
# Define kernels
kernels = [GPy.kern.Matern52(input_dim=2, ARD=True), GPy.kern.Matern52(input_dim=2, ARD=True), GPy.kern.Matern52(input_dim=2, ARD=True)]
lin_mf_kernel = emukit.multi_fidelity.kernels.LinearMultiFidelityKernel(kernels)
# Define Multi-fidelity model
gpy_lin_mf_model = GPyLinearMultiFidelityModel(X_train, Y_train, lin_mf_kernel, n_fidelities=3)
# Fix noise
gpy_lin_mf_model.mixed_noise.Gaussian_noise.fix(0)
gpy_lin_mf_model.mixed_noise.Gaussian_noise_1.fix(0)
gpy_lin_mf_model.mixed_noise.Gaussian_noise_2.fix(0)
# Wrap the model using the given 'GPyMultiOutputWrapper'
lin_mf_model = model = GPyMultiOutputWrapper(gpy_lin_mf_model, n_outputs=3, n_optimization_restarts=20)
## Fit the model
lin_mf_model.optimize()
# Define parameter space
parameter_space = ParameterSpace([ContinuousParameter('x1', 0, 1), ContinuousParameter('x2', 0, 1), DiscreteParameter('fid', [0, 1, 2])])
# Define acquisition function
ei_acquisition = ExpectedImprovement(model = lin_mf_model)
optimizer = GradientAcquisitionOptimizer(parameter_space, num_anchor=1)
new_x, _ = optimizer.optimize(ei_acquisition, context={'fid': 2})
Sorry for the messy training data. I thought it would be easiest to just copy my current training data.
I hope even my fix was kind of correct for 2-dimensional test problems. I am happy for any input on this matter.
Happy new year and best regards,
Stefan Tönnis
As quick edit:
This is the error message:
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
ValueError: too many axes: 2 (effrank=2), expected rank=1
The above exception was the direct cause of the following exception:
ValueError Traceback (most recent call last)
Cell In[21], [line 19](vscode-notebook-cell:?execution_count=21&line=19)
[15](vscode-notebook-cell:?execution_count=21&line=15) return np.min(self.model.Y[(Problem.n_fidelities-1)*10*Problem.dim:], axis=0)
[17](vscode-notebook-cell:?execution_count=21&line=17) log_cei_acquisition = LogAcquisition(CustomExpectedImprovement(model = lin_mf_model))
---> [19](vscode-notebook-cell:?execution_count=21&line=19) new_x, _ = optimizer.optimize(Log_ei_acquisition, context={'fid': 2})
[20](vscode-notebook-cell:?execution_count=21&line=20) new_xc, _ = optimizer.optimize(log_cei_acquisition, context={'fid': 2})
[22](vscode-notebook-cell:?execution_count=21&line=22) acq_val = log_cei_acquisition.evaluate(X_plot_h)
File c:\Users\StefanT\.conda\envs\ML\Lib\site-packages\emukit\core\optimization\acquisition_optimizer.py:53, in AcquisitionOptimizerBase.optimize(self, acquisition, context)
[50](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/acquisition_optimizer.py:50) context = dict()
[51](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/acquisition_optimizer.py:51) context_manager = ContextManager(self.space, context)
---> [53](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/acquisition_optimizer.py:53) max_x, max_value = self._optimize(acquisition, context_manager)
[55](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/acquisition_optimizer.py:55) # Optimization might not match any encoding exactly
[56](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/acquisition_optimizer.py:56) # Rounding operation here finds the closest encoding
[57](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/acquisition_optimizer.py:57) rounded_max_x = self.space.round(max_x)
File c:\Users\StefanT\.conda\envs\ML\Lib\site-packages\emukit\core\optimization\gradient_acquisition_optimizer.py:72, in GradientAcquisitionOptimizer._optimize(self, acquisition, context_manager)
[70](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/gradient_acquisition_optimizer.py:70) optimized_points = []
[71](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/gradient_acquisition_optimizer.py:71) for a in anchor_points:
---> [72](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/gradient_acquisition_optimizer.py:72) optimized_point = apply_optimizer(
[73](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/gradient_acquisition_optimizer.py:73) optimizer, a, space=self.space, f=f, df=None, f_df=f_df, context_manager=context_manager
[74](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/gradient_acquisition_optimizer.py:74) )
[75](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/gradient_acquisition_optimizer.py:75) optimized_points.append(optimized_point)
[77](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/gradient_acquisition_optimizer.py:77) x_min, fx_min = min(optimized_points, key=lambda t: t[1])
File c:\Users\StefanT\.conda\envs\ML\Lib\site-packages\emukit\core\optimization\optimizer.py:134, in apply_optimizer(optimizer, x0, space, f, df, f_df, context_manager)
[130](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/optimizer.py:130) else:
[131](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/optimizer.py:131) f_df_no_context = problem.f_df_no_context
--> [134](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/optimizer.py:134) optimized_x, _ = optimizer.optimize(problem.x0_no_context, f_no_context, df_no_context, f_df_no_context)
[136](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/optimizer.py:136) # Add context and round according to the type of variables of the design space
[137](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/optimizer.py:137) suggested_x_with_context = add_context(optimized_x)
File c:\Users\StefanT\.conda\envs\ML\Lib\site-packages\emukit\core\optimization\optimizer.py:73, in OptLbfgs.optimize(self, x0, f, df, f_df)
[69](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/optimizer.py:69) res = scipy.optimize.fmin_l_bfgs_b(
[70](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/optimizer.py:70) f, x0=x0, bounds=self.bounds, approx_grad=True, maxiter=self.max_iterations
[71](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/optimizer.py:71) )
[72](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/optimizer.py:72) else:
---> [73](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/optimizer.py:73) res = scipy.optimize.fmin_l_bfgs_b(_f_df, x0=x0, bounds=self.bounds, maxiter=self.max_iterations)
[75](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/optimizer.py:75) # We check here if the the optimizer moved. It it didn't we report x0 and f(x0) as scipy can return NaNs
[76](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/emukit/core/optimization/optimizer.py:76) if res[2]["task"] == b"ABNORMAL_TERMINATION_IN_LNSRCH":
File c:\Users\StefanT\.conda\envs\ML\Lib\site-packages\scipy\optimize\_lbfgsb_py.py:199, in fmin_l_bfgs_b(func, x0, fprime, args, approx_grad, bounds, m, factr, pgtol, epsilon, iprint, maxfun, maxiter, disp, callback, maxls)
[187](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:187) callback = _wrap_callback(callback)
[188](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:188) opts = {'disp': disp,
[189](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:189) 'iprint': iprint,
[190](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:190) 'maxcor': m,
(...)
[196](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:196) 'callback': callback,
[197](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:197) 'maxls': maxls}
--> [199](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:199) res = _minimize_lbfgsb(fun, x0, args=args, jac=jac, bounds=bounds,
[200](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:200) **opts)
[201](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:201) d = {'grad': res['jac'],
[202](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:202) 'task': res['message'],
[203](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:203) 'funcalls': res['nfev'],
[204](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:204) 'nit': res['nit'],
[205](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:205) 'warnflag': res['status']}
[206](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:206) f = res['fun']
File c:\Users\StefanT\.conda\envs\ML\Lib\site-packages\scipy\optimize\_lbfgsb_py.py:360, in _minimize_lbfgsb(fun, x0, args, jac, bounds, disp, maxcor, ftol, gtol, eps, maxfun, maxiter, iprint, callback, maxls, finite_diff_rel_step, **unknown_options)
[358](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:358) g = g.astype(np.float64)
[359](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:359) # x, f, g, wa, iwa, task, csave, lsave, isave, dsave = \
--> [360](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:360) _lbfgsb.setulb(m, x, low_bnd, upper_bnd, nbd, f, g, factr,
[361](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:361) pgtol, wa, iwa, task, iprint, csave, lsave,
[362](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:362) isave, dsave, maxls)
[363](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:363) task_str = task.tobytes()
[364](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:364) if task_str.startswith(b'FG'):
[365](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:365) # The minimization routine wants f and g at the current x.
[366](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:366) # Note that interruptions due to maxfun are postponed
[367](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:367) # until the completion of the current minimization iteration.
[368](file:///C:/Users/StefanT/.conda/envs/ML/Lib/site-packages/scipy/optimize/_lbfgsb_py.py:368) # Overwrite f and g:
ValueError: failed in converting 7th argument `g' of _lbfgsb.setulb to C/Fortran array
The function call is a bit different also i used the log expected improvement but the problem/error is the same.
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