Stochastic Policy Gradient Ascent in Reproducing Kernel Hilbert Spaces

TL;DR

This paper introduces a novel stochastic policy gradient ascent algorithm for reinforcement learning in RKHS, featuring unbiased gradient estimates, variance reduction, and sparse representations, enabling efficient learning of low-complexity policies.

Contribution

The paper presents a new policy gradient method with unbiased estimates, variance reduction, and sparse RKHS representations, ensuring convergence and practical efficiency.

Findings

Successful learning of low-complexity policies

Convergence to stationary points demonstrated

Numerical examples confirm effectiveness

Abstract

Reinforcement learning consists of finding policies that maximize an expected cumulative long-term reward in a Markov decision process with unknown transition probabilities and instantaneous rewards. In this paper, we consider the problem of finding such optimal policies while assuming they are continuous functions belonging to a reproducing kernel Hilbert space (RKHS). To learn the optimal policy we introduce a stochastic policy gradient ascent algorithm with three unique novel features: (i) The stochastic estimates of policy gradients are unbiased. (ii) The variance of stochastic gradients is reduced by drawing on ideas from numerical differentiation. (iii) Policy complexity is controlled using sparse RKHS representations. Novel feature (i) is instrumental in proving convergence to a stationary point of the expected cumulative reward. Novel feature (ii) facilitates reasonable convergence times. Novel feature (iii) is a necessity in practical implementations which we show can be done in a way that does not eliminate convergence guarantees. Numerical examples in standard problems illustrate successful learning of policies with low complexity representations which are close to stationary points of the expected cumulative reward.