Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2105.08024

Sample-Efficient Reinforcement Learning Is Feasible for Linearly Realizable MDPs with Limited Revisiting

Gen Li·Yuxin Chen·Yuejie Chi·Yuantao Gu·Yuting Wei
View original source ↗Read source document ↗Export metadata ↓

Abstract

Low-complexity models such as linear function representation play a pivotal role in enabling sample-efficient reinforcement learning (RL). The current paper pertains to a scenario with value-based linear representation, which postulates the linear realizability of the optimal Q-function (also called the "linear $Q^{\star}$ problem"). While linear realizability alone does not allow for sample-efficient solutions in general, the presence of a large sub-optimality gap is a potential game changer, depending on the sampling mechanism in use. Informally, sample efficiency is achievable with a large sub-optimality gap when a generative model is available but is unfortunately infeasible when we turn to standard online RL settings. In this paper, we make progress towards understanding this linear $Q^{\star}$ problem by investigating a new sampling protocol, which draws samples in an online/exploratory fashion but allows one to backtrack and revisit previous states in a controlled and infrequent manner. This protocol is more flexible than the standard online RL setting, while being practically relevant and far more restrictive than the generative model. We develop an algorithm tailored to this setting, achieving a sample complexity that scales polynomially with the feature dimension, the horizon, and the inverse sub-optimality gap, but not the size of the state/action space. Our findings underscore the fundamental interplay between sampling protocols and low-complexity structural representation in RL.

Explore related subjects

cs.LGcs.ITmath.ITmath.OCmath.STstat.MLstat.TH

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Gen Li, Yuxin Chen, Yuejie Chi, Yuantao Gu, Yuting Wei. 2021-10-18. Sample-Efficient Reinforcement Learning Is Feasible for Linearly Realizable MDPs with Limited Revisiting. https://arxiv.org/abs/2105.08024

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Incentivizing Honesty among Competitors in Collaborative Learning and Optimization

Collaborative learning techniques have the potential to enable training machine learning models that are superior to models trained on a single entity's data. However, in many cases, potential participants in such collaborative schemes are competitors on a downstream task, such as firms that each aim to attract customers by providing the best recommendations. This can incentivize dishonest updates that damage other participants' models, potentially undermining the benefits of collaboration. In this work, we formulate a game that models such interactions and study two learning tasks within this framework: single-round mean estimation and multi-round SGD on strongly-convex objectives. For a natural class of player actions, we show that rational clients are incentivized to strongly manipulate their updates, preventing learning. We then propose mechanisms that incentivize honest communication and ensure learning quality comparable to full cooperation. Lastly, we empirically demonstrate the effectiveness of our incentive scheme on a standard non-convex federated learning benchmark. Our work shows that explicitly modeling the incentives and actions of dishonest clients, rather than assuming them malicious, can enable strong robustness guarantees for collaborative learning.

cs.LG↗
arXiv2026

Hierarchical Deep Counterfactual Regret Minimization

Imperfect Information Games (IIGs) are used to model games under uncertainty or lack complete information. Counterfactual Regret Minimization (CFR) is one of the most successful families of algorithms for IIGs. The integration of skill-based strategy learning with CFR could potentially mirror more human-like decision-making and improve learning on complex IIGs. It enables the learning of a hierarchical strategy, wherein low-level components represent skills for solving subgames and the high-level component manages the transition between skills. In this paper, we introduce the first hierarchical version of Deep CFR (HDCFR), an innovative method that boosts learning efficiency in tasks involving extensively large state spaces and deep game trees. Notably, HDCFR enables learning with predefined (human) expertise and extracting skills transferable to similar tasks. We first present the algorithm and establish its theory in a tabular setting, including hierarchical CFR update rules and a variance-reduced Monte Carlo sampling extension for the model-free setting, where backtracking is infeasible. We then extend HDCFR to large-scale tasks via deep learning objectives that match the tabular targets under exact function fitting. Code: https://anonymous.4open.science/r/HDCFR_RUN-677B.

cs.LG↗
arXiv2026

Achieving Linear Speedup with ProxSkip in Distributed Stochastic Optimization

The ProxSkip algorithm for distributed optimization is gaining increasing attention due to its effectiveness in reducing communication. However, existing analyses of ProxSkip are limited to the strongly convex setting and fail to achieve linear speedup with respect to the number of nodes. Key questions regarding its behavior in the non-convex setting and the achievability of linear speedup remain open. In this paper, we revisit decentralized ProxSkip and answer these questions affirmatively. We provide a unified convergence analysis for stochastic non-convex, convex, and strongly convex problems, revealing how gradient noise, local updates, network connectivity, and data heterogeneity jointly determine the convergence behavior. To the best of our knowledge, this is the first analysis showing that decentralized ProxSkip achieves linear speedup in the number of nodes under stochastic gradients. Moreover, our results demonstrate that local updates can effectively reduce communication frequency and improve communication efficiency.

cs.LG↗