Minimax Optimal Variance-Aware Regret Bounds for Multinomial Logistic MDPs

• URL: http://arxiv.org/abs/2605.19768v1
• Date: Tue, 19 May 2026 12:39:32 GMT
• Title: Minimax Optimal Variance-Aware Regret Bounds for Multinomial Logistic MDPs
• Abstract summary: Existing algorithms for episodic Markov Decision Processes yield a regret of $smashtildeO(dH2sqrtT)$.<n>We propose an algorithm achieving a regret of $smashtildeO(dH2bar_TsqrtT)$, which recovers the existing bound in the worst case and improves upon it for structured MDPs.
• Score: 56.28491566735463
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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. 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 $\smash{\tilde{O}(dH^2\barσ\_T\sqrt{T})}$, which recovers the existing bound in the worst case and improves upon it for structured MDPs. For instance, for KL-constrained robust MDPs, $\barσ\_T = O(H^{-1})$, reducing the horizon dependence by a factor $H$. We further establish a matching $\smash{Ω(dH^2\barσ\_T\sqrt{T})}$ lower bound, proving minimax optimality (up to logarithmic factors) and fully characterising the regret complexity of MNL mixture MDPs for the first time.

Related papers

• Reinforcement Learning from Adversarial Preferences in Tabular MDPs [62.73758165845971]
  We introduce a new framework of episodic Markov decision processes (MDPs) with adversarial preferences.<n>Unlike standard episodic MDPs with adversarial losses, in PbMDPs the learner instead observes preferences between two candidate arms.<n>We develop algorithms that achieve a regret bound of order $T2/3$ under known transitions.
  arXiv  Detail & Related papers  (2025-07-15T20:19:32Z)
• Infinite-Horizon Reinforcement Learning with Multinomial Logistic Function Approximation [3.2703356989962518]
  We study model-based reinforcement learning with non-linear function approximation. We develop a provably efficient discounted value iteration-based algorithm that works for both infinite-horizon average-reward and discounted-reward settings.
  arXiv  Detail & Related papers  (2024-06-19T15:29:14Z)
• Randomized Exploration for Reinforcement Learning with Multinomial Logistic Function Approximation [8.274693573069442]
  We study reinforcement learning with multinomial logistic (MNL) function approximation. We propose provably efficient algorithms with randomized exploration having frequentist regret guarantees. Numerical experiments demonstrate the superior performance of the proposed algorithms.
  arXiv  Detail & Related papers  (2024-05-30T15:39:19Z)
• Projection by Convolution: Optimal Sample Complexity for Reinforcement Learning in Continuous-Space MDPs [56.237917407785545]
  We consider the problem of learning an $varepsilon$-optimal policy in a general class of continuous-space Markov decision processes (MDPs) having smooth Bellman operators. Key to our solution is a novel projection technique based on ideas from harmonic analysis. Our result bridges the gap between two popular but conflicting perspectives on continuous-space MDPs.
  arXiv  Detail & Related papers  (2024-05-10T09:58:47Z)
• Horizon-Free and Variance-Dependent Reinforcement Learning for Latent Markov Decision Processes [62.90204655228324]
  We study regret minimization for reinforcement learning (RL) in Latent Markov Decision Processes (LMDPs) with context in hindsight. We design a novel model-based algorithmic framework which can be instantiated with both a model-optimistic and a value-optimistic solver.
  arXiv  Detail & Related papers  (2022-10-20T21:32:01Z)
• Reward-Mixing MDPs with a Few Latent Contexts are Learnable [75.17357040707347]
  We consider episodic reinforcement learning in reward-mixing Markov decision processes (RMMDPs) Our goal is to learn a near-optimal policy that nearly maximizes the $H$ time-step cumulative rewards in such a model.
  arXiv  Detail & Related papers  (2022-10-05T22:52:00Z)
• Provably Breaking the Quadratic Error Compounding Barrier in Imitation Learning, Optimally [58.463668865380946]
  We study the statistical limits of Imitation Learning in episodic Markov Decision Processes (MDPs) with a state space $mathcalS$. We establish an upper bound $O(|mathcalS|H3/2/N)$ for the suboptimality using the Mimic-MD algorithm in Rajaraman et al ( 2020) We show the minimax suboptimality grows as $Omega( H3/2/N)$ when $mathcalS|geq 3$ while the unknown-transition setting suffers from a larger sharp rate
  arXiv  Detail & Related papers  (2021-02-25T15:50:19Z)
• Nearly Minimax Optimal Reinforcement Learning for Linear Mixture Markov Decision Processes [91.38793800392108]
  We study reinforcement learning with linear function approximation where the underlying transition probability kernel of the Markov decision process (MDP) is a linear mixture model. We propose a new, computationally efficient algorithm with linear function approximation named $textUCRL-VTR+$ for the aforementioned linear mixture MDPs. To the best of our knowledge, these are the first computationally efficient, nearly minimax optimal algorithms for RL with linear function approximation.
  arXiv  Detail & Related papers  (2020-12-15T18:56:46Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.