Improving Reinforcement Learning Sample-Efficiency using Local Approximation

TL;DR

This paper introduces a novel approach to improve reinforcement learning sample-efficiency by leveraging local approximations of the MDP, resulting in sharper PAC bounds and a logarithmic reduction in sample complexity.

Contribution

The study derives sharper PAC bounds for RL, introduces a local approximation method to reduce sample complexity, and extends the approach to model-free settings with experimental validation.

Findings

Sample complexity reduced to O(SA log A)

Sharper PAC bounds than existing literature

Significant empirical improvements demonstrated

Abstract

In this study, we derive Probably Approximately Correct (PAC) bounds on the asymptotic sample-complexity for RL within the infinite-horizon Markov Decision Process (MDP) setting that are sharper than those in existing literature. The premise of our study is twofold: firstly, the further two states are from each other, transition-wise, the less relevant the value of the first state is when learning the $\epsilon$-optimal value of the second; secondly, the amount of 'effort', sample-complexity-wise, expended in learning the $\epsilon$-optimal value of a state is independent of the number of samples required to learn the $\epsilon$-optimal value of a second state that is a sufficient number of transitions away from the first. Inversely, states within each other's vicinity have values that are dependent on each other and will require a similar number of samples to learn. By approximating the original MDP using smaller MDPs constructed using subsets of the original's state-space, we are able to reduce the sample-complexity by a logarithmic factor to $O(SA \log A)$ timesteps, where $S$ and $A$ are the state and action space sizes. We are able to extend these results to an infinite-horizon, model-free setting by constructing a PAC-MDP algorithm with the aforementioned sample-complexity. We conclude with showing how significant the improvement is by comparing our algorithm against prior work in an experimental setting.