Minimax Optimal Variance-Aware Regret Bounds for Multinomial Logistic MDPs
The article discusses a new algorithm for reinforcement learning in multinomial logistic Markov Decision Processes (MDPs). This algorithm achieves improved regret bounds compared to existing methods, particularly for structured MDPs. The authors establish both upper and lower bounds, demonstrating the minimax optimality of their approach.
- ▪The proposed algorithm achieves a regret of O(dH^2barσT√T).
- ▪For KL-constrained robust MDPs, the algorithm reduces the horizon dependence by a factor of H.
- ▪This work fully characterizes the regret complexity of multinomial logistic mixture MDPs for the first time.
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| Original publisher | arXiv cs.AI |
| Canonical URL | https://arxiv.org/abs/2605.19768 |
| Publication time | Wed, 20 May 2026 00:00:00 -0400 |
| Retrieval time | 2026-05-20T04:04:59.484Z |
| Last seen | 2026-05-20T04:04:59.484Z |
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| Summary source text | contentText |
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| Commercial reuse | May the content be reused commercially? | Not permitted |
Basis: Derived from the published RSS/Atom feed. Contact: [email protected]. Reviewed: 2026-07-24.
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Computer Science > Artificial Intelligence arXiv:2605.19768 (cs) [Submitted on 19 May 2026] Title:Minimax Optimal Variance-Aware Regret Bounds for Multinomial Logistic MDPs Authors:Pierre Boudart (SIERRA), Pierre Gaillard (Thoth), Alessandro Rudi (PSL, DI-ENS, Inria) View a PDF of the paper titled Minimax Optimal Variance-Aware Regret Bounds for Multinomial Logistic MDPs, by Pierre Boudart (SIERRA) and 4 other authors View PDF Abstract: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.
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