KL-based Control of the Learning Schedule for Surrogate Black-Box Optimization

Ilya Loshchilov (1) , Marc Schoenauer (2, 3) , Michèle Sebag (3)

1 Laboratory of Intelligent Systems (LIS)
2 TAO - Machine Learning and Optimisation
3 LRI - Laboratoire de Recherche en Informatique

This paper investigates the control of an ML component within the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) devoted to black-box optimization. The known CMA-ES weakness is its sample complexity, the number of evaluations of the objective function needed to approximate the global optimum. This weakness is commonly addressed through surrogate optimization, learning an estimate of the objective function a.k.a. surrogate model, and replacing most evaluations of the true objective function with the (inexpensive) evaluation of the surrogate model. This paper presents a principled control of the learning schedule (when to relearn the surrogate model), based on the Kullback-Leibler divergence of the current search distribution and the training distribution of the former surrogate model. The experimental validation of the proposed approach shows significant performance gains on a comprehensive set of ill-conditioned benchmark problems, compared to the best state of the art including the quasi-Newton high-precision BFGS method.

Domaines: Intelligence artificielle [cs.AI]

Ilya Loshchilov, Marc Schoenauer, Michèle Sebag. KL-based Control of the Learning Schedule for Surrogate Black-Box Optimization. Conférence sur l'Apprentissage Automatique, Jul 2013, Lille, France. ⟨hal-00851189v2⟩