Non-parametric contextual stochastic search

Abstract

Stochastic search algorithms are black-box optimizer of an objective function. They have recently gained a lot of attention in operations research, machine learning and policy search of robot motor skills due to their ease of use and their generality. Yet, many stochastic search algorithms require relearning if the task or objective function changes slightly to adapt the solution to the new situation or the new context. In this paper, we consider the contextual stochastic search setup. Here, we want to find multiple good parameter vectors for multiple related tasks, where each task is described by a continuous context vector. Hence, the objective function might change slightly for each parameter vector evaluation of a task or context. Contextual algorithms have been investigated in the field of policy search, however, the search distribution typically uses a parametric model that is linear in the some hand-defined context features. Finding good context features is a challenging task, and hence, non-parametric methods are often preferred over their parametric counter-parts. In this paper, we propose a non-parametric contextual stochastic search algorithm that can learn a non-parametric search distribution for multiple tasks simultaneously. In difference to existing methods, our method can also learn a context dependent covariance matrix that guides the exploration of the search process. We illustrate its performance on several non-linear contextual tasks.