Minimax Optimal Variance-Aware Regret Bounds for Multinomial Logistic MDPs
We study reinforcement learning for episodic Markov Decision Processes (MDPs) whose transitions are modelled by a multinomial logistic (MNL) model. Existing algorithms for MNL mixture MDPs yield a regret of $\smash{\tilde{O}(dH^2\sqrt{T})}$ (Li et al., 2024), where $d$ is the feature dimension, $H$ the episode length, and $T$ the number of episodes. Inspired by the logistic bandit literature (Abeille et al., 2021; Faury et al., 2022; Boudart et al., 2026), we introduce a problem-dependent constant $\barσ\_T \leq 1/2$, measuring the normalised average variance of the optimal downstream value function along the learner's trajectory. We propose an algorithm achieving a regret of $\smash{\til...
| Authors | Pierre Boudart, Pierre Gaillard, Alessandro Rudi |
|---|---|
| Primary category | cs.AI |
| Published | 19 May 2026 |
| Last updated at source | 19 May 2026 |
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