Provably Efficient Reinforcement Learning with Multinomial Logit Function Approximation

• URL: http://arxiv.org/abs/2405.17061v2
• Date: Tue, 05 Nov 2024 02:29:25 GMT
• Title: Provably Efficient Reinforcement Learning with Multinomial Logit Function Approximation
• Authors: Long-Fei Li, Yu-Jie Zhang, Peng Zhao, Zhi-Hua Zhou,
• Abstract summary: We study a new class of MDPs that employs multinomial logit (MNL) function approximation to ensure valid probability distributions over the state space. introducing the non-linear function raises significant challenges in both computational and statistical efficiency. We propose an algorithm that achieves the same regret with only $mathcalO(1)$ cost.
• Score: 67.8414514524356
• License:
• Abstract: We study a new class of MDPs that employs multinomial logit (MNL) function approximation to ensure valid probability distributions over the state space. Despite its benefits, introducing the non-linear function raises significant challenges in both computational and statistical efficiency. The best-known result of Hwang and Oh [2023] has achieved an $\widetilde{\mathcal{O}}(\kappa^{-1}dH^2\sqrt{K})$ regret, where $\kappa$ is a problem-dependent quantity, $d$ is the feature dimension, $H$ is the episode length, and $K$ is the number of episodes. While this result attains the same rate in $K$ as linear cases, the method requires storing all historical data and suffers from an $\mathcal{O}(K)$ computation cost per episode. Moreover, the quantity $\kappa$ can be exponentially small in the worst case, leading to a significant gap for the regret compared to linear function approximation. In this work, we first address the computational and storage issue by proposing an algorithm that achieves the same regret with only $\mathcal{O}(1)$ cost. Then, we design an enhanced algorithm that leverages local information to enhance statistical efficiency. It not only maintains an $\mathcal{O}(1)$ computation and storage cost per episode but also achieves an improved regret of $\widetilde{O}(dH^2\sqrt{K} + d^2H^2\kappa^{-1})$, nearly closing the gap with linear function approximation. Finally, we establish the first lower bound for MNL function approximation, justifying the optimality of our results in $d$ and $K$.

Related papers

• Improved Regret Bound for Safe Reinforcement Learning via Tighter Cost Pessimism and Reward Optimism [1.4999444543328293]
  We propose a model-based algorithm based on novel cost and reward function estimators. Our algorithm achieves a regret upper bound of $widetildemathcalO((bar C - bar C_b)-1H2.5 SsqrtAK)$ where $bar C$ is the cost budget for an episode.
  arXiv  Detail & Related papers  (2024-10-14T04:51:06Z)
• 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)
• Tackling Heavy-Tailed Rewards in Reinforcement Learning with Function Approximation: Minimax Optimal and Instance-Dependent Regret Bounds [26.277745106128197]
  In this work, we address the challenge of such rewards in reinforcement learning with linear function approximation. We first design an algorithm, textscHeavy-OFUL, for heavy-tailed linear bandits, achieving an emphinstance-dependent $T$-round regret of $tildeObig. Our result is achieved via a novel self-normalized concentration inequality that may be of independent interest in handling heavytailed noise in general online regression problems.
  arXiv  Detail & Related papers  (2023-06-12T02:56:09Z)
• Provably Efficient Reinforcement Learning via Surprise Bound [66.15308700413814]
  We propose a provably efficient reinforcement learning algorithm (both computationally and statistically) with general value function approximations. Our algorithm achieves reasonable regret bounds when applied to both the linear setting and the sparse high-dimensional linear setting.
  arXiv  Detail & Related papers  (2023-02-22T20:21:25Z)
• Refined Regret for Adversarial MDPs with Linear Function Approximation [50.00022394876222]
  We consider learning in an adversarial Decision Process (MDP) where the loss functions can change arbitrarily over $K$ episodes. This paper provides two algorithms that improve the regret to $tildemathcal O(K2/3)$ in the same setting.
  arXiv  Detail & Related papers  (2023-01-30T14:37:21Z)
• TURF: A Two-factor, Universal, Robust, Fast Distribution Learning Algorithm [64.13217062232874]
  One of its most powerful and successful modalities approximates every distribution to an $ell$ distance essentially at most a constant times larger than its closest $t$-piece degree-$d_$. We provide a method that estimates this number near-optimally, hence helps approach the best possible approximation.
  arXiv  Detail & Related papers  (2022-02-15T03:49:28Z)
• 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 Optimal Regret for Learning Adversarial MDPs with Linear Function Approximation [92.3161051419884]
  We study the reinforcement learning for finite-horizon episodic Markov decision processes with adversarial reward and full information feedback. We show that it can achieve $tildeO(dHsqrtT)$ regret, where $H$ is the length of the episode. We also prove a matching lower bound of $tildeOmega(dHsqrtT)$ up to logarithmic factors.
  arXiv  Detail & Related papers  (2021-02-17T18:54:08Z)

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.