Eluder-based Regret for Stochastic Contextual MDPs

• URL: http://arxiv.org/abs/2211.14932v3
• Date: Wed, 29 May 2024 08:57:58 GMT
• Title: Eluder-based Regret for Stochastic Contextual MDPs
• Authors: Orin Levy, Asaf Cassel, Alon Cohen, Yishay Mansour,
• Abstract summary: We present the E-UC$3$RL algorithm for regret minimization in Contextual Markov Decision Processes (CMDPs) Our algorithm is efficient (assuming efficient offline regression oracles) and enjoys a regret guarantee of $ widetildeO(H3 sqrtT |S| |A|d_mathrmE(mathcalP)$.
• Score: 43.19667415823089
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present the E-UC$^3$RL algorithm for regret minimization in Stochastic Contextual Markov Decision Processes (CMDPs). The algorithm operates under the minimal assumptions of realizable function class and access to \emph{offline} least squares and log loss regression oracles. Our algorithm is efficient (assuming efficient offline regression oracles) and enjoys a regret guarantee of $ \widetilde{O}(H^3 \sqrt{T |S| |A|d_{\mathrm{E}}(\mathcal{P}) \log (|\mathcal{F}| |\mathcal{P}|/ \delta) )}) , $ with $T$ being the number of episodes, $S$ the state space, $A$ the action space, $H$ the horizon, $\mathcal{P}$ and $\mathcal{F}$ are finite function classes used to approximate the context-dependent dynamics and rewards, respectively, and $d_{\mathrm{E}}(\mathcal{P})$ is the Eluder dimension of $\mathcal{P}$ w.r.t the Hellinger distance. To the best of our knowledge, our algorithm is the first efficient and rate-optimal regret minimization algorithm for CMDPs that operates under the general offline function approximation setting. In addition, we extend the Eluder dimension to general bounded metrics which may be of separate interest.

Related papers

• 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)
• Achieving Tractable Minimax Optimal Regret in Average Reward MDPs [19.663336027878408]
  We present the first tractable algorithm with minimax optimal regret of $widetildemathrmO(sqrtmathrmsp(h*) S A T)$. Remarkably, our algorithm does not require prior information on $mathrmsp(h*)$.
  arXiv  Detail & Related papers  (2024-06-03T11:53:44Z)
• A Doubly Robust Approach to Sparse Reinforcement Learning [19.68978899041642]
  We propose a new regret algorithm for episodic sparse linear Markov decision process (SMDP) The proposed algorithm is $tildeO(sigma-1_min s_star H sqrtN)$, where $sigma_min$ denotes the restrictive minimum eigenvalue of the average Gram matrix of feature vectors.
  arXiv  Detail & Related papers  (2023-10-23T18:52:17Z)
• Efficient Rate Optimal Regret for Adversarial Contextual MDPs Using Online Function Approximation [47.18926328995424]
  We present the OMG-CMDP! algorithm for regret minimization in adversarial Contextual MDPs. Our algorithm is efficient (assuming efficient online regression oracles) and simple and robust to approximation errors.
  arXiv  Detail & Related papers  (2023-03-02T18:27:00Z)
• 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)
• Private Isotonic Regression [54.32252900997422]
  We consider the problem of isotonic regression over a partially ordered set (poset) $mathcalX$ and for any Lipschitz loss function. We obtain a pure-DP algorithm that has an expected excess empirical risk of roughly $mathrmwidth(mathcalX) cdot log|mathcalX| / n$, where $mathrmwidth(mathcalX)$ is the width of the poset. We show that the bounds above are essentially the best that can be
  arXiv  Detail & Related papers  (2022-10-27T05:08:07Z)
• Optimism in Face of a Context: Regret Guarantees for Stochastic Contextual MDP [46.86114958340962]
  We present regret algorithms for contextual MDPs under minimum reachability assumption. Our approach is the first optimistic approach applied to contextual MDPs with general function approximation.
  arXiv  Detail & Related papers  (2022-07-22T15:00:15Z)
• Optimal Regret Algorithm for Pseudo-1d Bandit Convex Optimization [51.23789922123412]
  We study online learning with bandit feedback (i.e. learner has access to only zeroth-order oracle) where cost/reward functions admit a "pseudo-1d" structure. We show a lower bound of $min(sqrtdT, T3/4)$ for the regret of any algorithm, where $T$ is the number of rounds. We propose a new algorithm sbcalg that combines randomized online gradient descent with a kernelized exponential weights method to exploit the pseudo-1d structure effectively.
  arXiv  Detail & Related papers  (2021-02-15T08:16:51Z)

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.