Local Policy Search in a Convex Space and Conservative Policy Iteration as Boosted Policy Search

Local Policy Search is a popular reinforcement learning approach for handling large state spaces. Formally, it searches locally in a parameterized policy space in order to maximize the associated value function averaged over some predefined distribution. The best one can hope in general from such an approach is to get a local optimum of this criterion. The first contribution of this article is the following surprising result: if the policy space is convex, any (approximate) local optimum enjoys a global performance guarantee. Unfortunately, the convexity assumption is strong: it is not satisfied by commonly used parameterizations and designing a parameterization that induces this property seems hard. A natural solution to alleviate this issue consists in deriving an algorithm that solves the local policy search problem using a boosting approach (constrained to the convex hull of the policy space). The resulting algorithm turns out to be a slight generalization of conservative policy iteration; thus, our second contribution is to highlight an original connection between local policy search and approximate dynamic programming.