Improving Reinforcement Learning Sample-Efficiency using Local Approximation

• URL: http://arxiv.org/abs/2507.12383v1
• Date: Wed, 16 Jul 2025 16:31:17 GMT
• Title: Improving Reinforcement Learning Sample-Efficiency using Local Approximation
• Authors: Mohit Prashant, Arvind Easwaran,
• Abstract summary: We derive PAC bounds on the sample-complexity for RL within the infinite-horizon Markov Decision Process setting.<n>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.
• Score: 2.5582913676558205
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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