Kernel-Based Reinforcement Learning in Average-Cost Problems: An Application to Optimal Portfolio Choice

Many approaches to reinforcement learning combine neural networks orother parametric function approximators with a form of temporal-difference learning to estimate the value function of a Markov Decision Process. A significant disadvantage of those procedures isthat the resulting learning algorithms are frequently unstable. In this work, we present a new, kernel-based approach to reinforcement learning which overcomes this difficulty and provably converges to a unique solution. By contrast to existing algorithms, our method can also be shown to be consistent in the sense that its costs converge to the optimal costs asymptotically. Our focus is on learning in an average-cost framework and on a practical application tothe optimal portfolio choice problem. 1 Introduction Temporal-difference (TD) learning has been applied successfully to many real-world applications that can be formulated as discrete state Markov Decision Processes (MDPs) with unknown transition probabilities.