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arXiv · 2404.00686

Utilizing Maximum Mean Discrepancy Barycenter for Propagating the Uncertainty of Value Functions in Reinforcement Learning

Srinjoy Roy·Swagatam Das
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Abstract

Accounting for the uncertainty of value functions boosts exploration in Reinforcement Learning (RL). Our work introduces Maximum Mean Discrepancy Q-Learning (MMD-QL) to improve Wasserstein Q-Learning (WQL) for uncertainty propagation during Temporal Difference (TD) updates. MMD-QL uses the MMD barycenter for this purpose, as MMD provides a tighter estimate of closeness between probability measures than the Wasserstein distance. Firstly, we establish that MMD-QL is Probably Approximately Correct in MDP (PAC-MDP) under the average loss metric. Concerning the accumulated rewards, experiments on tabular environments show that MMD-QL outperforms WQL and other algorithms. Secondly, we incorporate deep networks into MMD-QL to create MMD Q-Network (MMD-QN). Making reasonable assumptions, we analyze the convergence rates of MMD-QN using function approximation. Empirical results on challenging Atari games demonstrate that MMD-QN performs well compared to benchmark deep RL algorithms, highlighting its effectiveness in handling large state-action spaces.

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Srinjoy Roy, Swagatam Das. 2024-03-31. Utilizing Maximum Mean Discrepancy Barycenter for Propagating the Uncertainty of Value Functions in Reinforcement Learning. https://arxiv.org/abs/2404.00686

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