Problem using Gaussian Process when the objective function value is constant

[rzahra]

Hi,

I've tried to run your "branin" example and considering a constant objective value, like "y_value = 1" for each input parameter. I set up the "model" to "Gaussian Process". "models": { "model": "gaussian_process" },

But, it does not work and I've got the following error. Would you please let me know what is the problem?

Best Regards, Zahra

Traceback (most recent call last): File "branin.py", line 39, in main() File "branin.py", line 34, in main optimizer.optimize(parameters_file, branin_function) File "/home/zahra/anaconda3/lib/python3.7/site-packages/hypermapper/optimizer.py", line 125, in optimize config, black_box_function=black_box_function, profiling=profiling File "/home/zahra/anaconda3/lib/python3.7/site-packages/hypermapper/bo.py", line 391, in main objective_limits=objective_limits, File "/home/zahra/anaconda3/lib/python3.7/site-packages/hypermapper/models.py", line 457, in generate_mono_output_regression_models regressor[Ycol].optimize() File "/home/zahra/anaconda3/lib/python3.7/site-packages/GPy/core/gp.py", line 659, in optimize ret = super(GP, self).optimize(optimizer, start, messages, max_iters, ipython_notebook, clear_after_finish, kwargs) File "/home/zahra/anaconda3/lib/python3.7/site-packages/paramz/model.py", line 111, in optimize opt.run(start, f_fp=self._objective_grads, f=self._objective, fp=self._grads) File "/home/zahra/anaconda3/lib/python3.7/site-packages/paramz/optimization/optimization.py", line 51, in run self.opt(x_init, kwargs) File "/home/zahra/anaconda3/lib/python3.7/site-packages/paramz/optimization/optimization.py", line 124, in opt opt_result = optimize.fmin_l_bfgs_b(f_fp, x_init, maxfun=self.max_iters, maxiter=self.max_iters, opt_dict) File "/home/zahra/anaconda3/lib/python3.7/site-packages/scipy/optimize/lbfgsb.py", line 199, in fmin_l_bfgs_b opts) File "/home/zahra/anaconda3/lib/python3.7/site-packages/scipy/optimize/lbfgsb.py", line 345, in _minimize_lbfgsb f, g = func_and_grad(x) File "/home/zahra/anaconda3/lib/python3.7/site-packages/scipy/optimize/lbfgsb.py", line 295, in func_and_grad f = fun(x, args) File "/home/zahra/anaconda3/lib/python3.7/site-packages/scipy/optimize/optimize.py", line 327, in function_wrapper return function((wrapper_args + args)) File "/home/zahra/anaconda3/lib/python3.7/site-packages/scipy/optimize/optimize.py", line 65, in call fg = self.fun(x, args) File "/home/zahra/anaconda3/lib/python3.7/site-packages/paramz/model.py", line 273, in _objective_grads self.optimizer_array = x File "/home/zahra/anaconda3/lib/python3.7/site-packages/paramz/parameterized.py", line 339, in setattr return object.setattr(self, name, val) File "/home/zahra/anaconda3/lib/python3.7/site-packages/paramz/core/parameter_core.py", line 124, in optimizer_array self.trigger_update() File "/home/zahra/anaconda3/lib/python3.7/site-packages/paramz/core/updateable.py", line 79, in trigger_update self._trigger_params_changed(trigger_parent) File "/home/zahra/anaconda3/lib/python3.7/site-packages/paramz/core/parameter_core.py", line 134, in _trigger_params_changed self.notify_observers(None, None if trigger_parent else -np.inf) File "/home/zahra/anaconda3/lib/python3.7/site-packages/paramz/core/observable.py", line 91, in notifyobservers [callble(self, which=which) for , , callble in self.observers] File "/home/zahra/anaconda3/lib/python3.7/site-packages/paramz/core/observable.py", line 91, in [callble(self, which=which) for , _, callble in self.observers] File "/home/zahra/anaconda3/lib/python3.7/site-packages/paramz/core/parameter_core.py", line 508, in _parameters_changed_notification self.parameters_changed() File "/home/zahra/anaconda3/lib/python3.7/site-packages/GPy/core/gp.py", line 267, in parameters_changed self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference(self.kern, self.X, self.likelihood, self.Y_normalized, self.mean_function, self.Y_metadata) File "/home/zahra/anaconda3/lib/python3.7/site-packages/GPy/inference/latent_function_inference/exact_gaussian_inference.py", line 58, in inference Wi, LW, LWi, W_logdet = pdinv(Ky) File "/home/zahra/anaconda3/lib/python3.7/site-packages/GPy/util/linalg.py", line 207, in pdinv L = jitchol(A, args) File "/home/zahra/anaconda3/lib/python3.7/site-packages/GPy/util/linalg.py", line 75, in jitchol raise linalg.LinAlgError("not positive definite, even with jitter.") numpy.linalg.LinAlgError: not positive definite, even with jitter."

[ksehic]

@rzahra Can you copy-paste the py and json file of the Branin function that you are using here? As I was running myself with y_value=1 and GP, I did not get the error. In general, using a GP for a constant function is not smart but it should work...

[rzahra]

!/usr/bin/python

import math

import os import sys import warnings from collections import OrderedDict

from hypermapper import optimizer # noqa

def branin_function(X): """ Compute the branin function. :param X: dictionary containing the input points. :return: the value of the branin function """ x1 = X["x1"] x2 = X["x2"] a = 1.0 b = 5.1 / (4.0 math.pi math.pi) c = 5.0 / math.pi r = 6.0 s = 10.0 t = 1.0 / (8.0 * math.pi)

#y_value = a * (x2 - b * x1 * x1 + c * x1 - r) ** 2 + s * (1 - t) * math.cos(x1) + s
y_value = 1
return y_value

def main(): parameters_file = "/home/zahra/Desktop/hypermapper-simple-test/example_scenarios/quick_start/branin_scenario.json" optimizer.optimize(parameters_file, branin_function) print("End of Branin.")

if name == "main": main()

[rzahra]

{ "application_name": "branin", "optimization_objectives": ["Value"], "optimization_iterations": 20, "optimization_method": "bayesian_optimization", "acquisition_function_optimizer": "local_search", "design_of_experiment": { "doe_type": "random sampling", "number_of_samples": 3

 },

 "models": {
    "model": "gaussian_process"
},

"input_parameters" : {
    "x1": {
        "parameter_type" : "real",
        "values" : [-5, 10],
        "parameter_default" : 0
    },
    "x2": {
        "parameter_type" : "real",
        "values" : [0, 15],
        "parameter_default" : 0
    }
}

}

[ksehic]

@rzahra Strange. I didn't get the error. I was using the latest version of Hypermapper from this repo. Pip version is not yet updated as I can see... Can you maybe check that you are using the latest version of Hypermapper or check is there any mismatch between anaconda3 and Hypermapper

My result...

x1	x2	Value	Timestamp
0	0	1	1
5.60301701755873	6.04807923864642	1	1
-3.24438823881358	12.702020869894	1	1
2.19105319236382	2.32721787344419	1	368
1.18058256785225	0.280883034597277	1	816
3.77255434050274	1.29103718689401	1	1267
7.45611027312549	0.329748493671475	1	1706
10	0.396969533465726	1	2113
1.51087515746304	1.89817942409036	1	2500
8.33121229115913	1.29476803461852	1	2949
5.098804488615	1.87438181073141	1	3388
3.51543678199592	1.7371702889608	1	3824
3.12219508823726	1.00400351211924	1	4260
3.88174205850473	1.53863041723447	1	4736
8.54319783549642	0.8461187299401	1	5171
7.85486273117496	1.34970757932602	1	5637
8.57199759865176	0.755149316832652	1	6061
-1.64473966669573	0.213732575999534	1	6544
8.3284077498699	3.34379278975797	1	6618
8.26472155895912	0.574587731483283	1	7075
6.74071982162813	2.10840547806442	1	7528
6.5380851578267	0.668962647053504	1	8053
-2.16236399703512	0.712652098237651	1	8510