arXiv Machine Learning By Keru Wang, Yixin Deng, Yao Lyu, Stephen Redmond, Shengbo Eben Li

Distributional Soft Bellman Operator under the Cram\'er Geometry

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arXiv:2607. 17897v1 Announce Type: new Abstract: Distributional soft policy iteration (DSPI) provides an important framework for combining distributional reinforcement learning (DRL) with maximum-entropy control, in which the policy evaluation step is governed by a distributional soft Bellman operator acting on entropy-regularised returns.

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arXiv Machine Learning
Sep 11

Statistical analysis of Inverse Entropy-regularized Reinforcement Learning

The paper introduces a statistical framework for Inverse Entropy-regularized Reinforcement Learning that resolves the non-uniqueness of reward functions by combining entropy regularization with a least-squares reconstruction of the reward from the soft Bellman residual. It models expert demonstrations as a Markov chain, estimates the expert policy via penalized maximum likelihood, and provides high-probability bounds on the excess Kullback–Leibler divergence between the estimated and true policies. These results yield non-asymptotic minimax optimal convergence rates for the least-squares reward function, highlighting the trade-offs among smoothing, model complexity, and sample size.

By Denis Belomestny, Alexey Naumov, Artemy Rubtsov, Sergey Samsonov