Policy Evaluation in Continuous MDPs with Efficient Kernelized Gradient Temporal Difference

TL;DR

This paper introduces a memory-efficient, non-parametric stochastic method for policy evaluation in continuous MDPs, leveraging kernelized gradient TD learning to achieve faster convergence with less memory.

Contribution

It extends gradient temporal difference learning to a non-parametric, kernel-based setting with guaranteed convergence and improved efficiency in continuous state spaces.

Findings

Faster convergence to lower Bellman error in Mountain Car domain

Achieves convergence with finite memory and complexity

Outperforms existing methods in efficiency and accuracy

Abstract

We consider policy evaluation in infinite-horizon discounted Markov decision problems (MDPs) with infinite spaces. We reformulate this task a compositional stochastic program with a function-valued decision variable that belongs to a reproducing kernel Hilbert space (RKHS). We approach this problem via a new functional generalization of stochastic quasi-gradient methods operating in tandem with stochastic sparse subspace projections. The result is an extension of gradient temporal difference learning that yields nonlinearly parameterized value function estimates of the solution to the Bellman evaluation equation. Our main contribution is a memory-efficient non-parametric stochastic method guaranteed to converge exactly to the Bellman fixed point with probability $1$ with attenuating step-sizes. Further, with constant step-sizes, we obtain mean convergence to a neighborhood and that the value function estimates have finite complexity. In the Mountain Car domain, we observe faster convergence to lower Bellman error solutions than existing approaches with a fraction of the required memory.