Reinforcement Learning (RL) has shown great empirical success in various application domains. The theoretical aspects of the problem have been extensively studied over past decades, particularly under tabular and linear Markov Decision Process structures. Recently, non-linear function approximation using kernel-based prediction has gained traction. This approach is particularly interesting as it naturally extends the linear structure, and helps explain the behavior of neural-network-based models at their infinite width limit. The analytical results however do not adequately address the performance guarantees for this case. We will highlight this open problem, overview existing partial results, and discuss related challenges.

Many approaches to reinforcement learning combine neural net(cid:173) works or other 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 pro(cid:173) cedures is that the resulting learning algorithms are frequently un(cid:173) stable. 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 ap(cid:173) plication to the optimal portfolio choice problem.

Markov decision processes (MDPs) are an established framework for solving sequential decision-making problems under uncertainty. In this work, we propose a new method for batch-mode reinforcement learning (RL) with continuous state variables. The method is an approximation to kernel-based RL on a set of k representative states. Similarly to kernel-based RL, our solution is a fixed point of a kernelized Bellman operator and can approximate the optimal solution to an arbitrary level of granularity. Unlike kernel-based RL, our method is fast. In particular, our policies can be computed in O ( n ) time, where n is the number of training examples. The time complexity of kernel-based RL is Ω( n 2 ). We introduce our method, analyze its convergence, and compare it to existing work. The method is evaluated on two existing control problems with 2 to 4 continuous variables and a new problem with 64 variables. In all cases, we outperform state-of-the-art results and offer simpler solutions.

Many approaches to reinforcement learning combine neural networks or other 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 is that 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 to the optimal portfolio choice problem.

Many approaches to reinforcement learning combine neural networks or other 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 is that 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 to the optimal portfolio choice problem.

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.