# RL in Markov Games with Independent Function Approximation: Improved Sample Complexity Bound under the Local Access Model

arXiv: https://arxiv.org/abs/2403.11544 · HTML: https://mlsanity.com/paper/2403.11544/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 45 references that are in the map.
- First posted on arXiv 18 Mar 2024.

## Builds on (most cited first, 30 of 31)

- [Safe, Multi-Agent, Reinforcement Learning for Autonomous Driving](https://mlsanity.com/paper/1610.03295/) (2016)
- [Contextual Decision Processes with Low Bellman Rank are PAC-Learnable](https://mlsanity.com/paper/1610.09512/) (2016)
- [Bellman Eluder Dimension: New Rich Classes of RL Problems, and Sample-Efficient Algorithms](https://mlsanity.com/paper/2102.00815/) (2021)
- [The Statistical Complexity of Interactive Decision Making](https://mlsanity.com/paper/2112.13487/) (2021)
- [Go-Explore: a New Approach for Hard-Exploration Problems](https://mlsanity.com/paper/1901.10995/) (2019)
- [Reinforcement Learning in Feature Space: Matrix Bandit, Kernels, and Regret Bound](https://mlsanity.com/paper/1905.10389/) (2019)
- [Learning Near Optimal Policies with Low Inherent Bellman Error](https://mlsanity.com/paper/2003.00153/) (2020)
- [Bilinear Classes: A Structural Framework for Provable Generalization in RL](https://mlsanity.com/paper/2103.10897/) (2021)
- [On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning](https://mlsanity.com/paper/1704.00805/) (2017)
- [V-Learning -- A Simple, Efficient, Decentralized Algorithm for Multiagent RL](https://mlsanity.com/paper/2110.14555/) (2021)
- [Breaking the Sample Size Barrier in Model-Based Reinforcement Learning with a Generative Model](https://mlsanity.com/paper/2005.12900/) (2020)
- [Near-Optimal Reinforcement Learning with Self-Play](https://mlsanity.com/paper/2006.12007/) (2020)
- [A Sharp Analysis of Model-based Reinforcement Learning with Self-Play](https://mlsanity.com/paper/2010.01604/) (2020)
- [Learning Zero-Sum Simultaneous-Move Markov Games Using Function Approximation and Correlated Equilibrium](https://mlsanity.com/paper/2002.07066/) (2020)
- [Model-Based Multi-Agent RL in Zero-Sum Markov Games with Near-Optimal Sample Complexity](https://mlsanity.com/paper/2007.07461/) (2020)
- [The Complexity of Markov Equilibrium in Stochastic Games](https://mlsanity.com/paper/2204.03991/) (2022)
- [The Power of Exploiter: Provable Multi-Agent RL in Large State Spaces](https://mlsanity.com/paper/2106.03352/) (2021)
- [Towards General Function Approximation in Zero-Sum Markov Games](https://mlsanity.com/paper/2107.14702/) (2021)
- [An Exponential Lower Bound for Linearly-Realizable MDPs with Constant Suboptimality Gap](https://mlsanity.com/paper/2103.12690/) (2021)
- [On Improving Model-Free Algorithms for Decentralized Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2110.05707/) (2021)
- [Breaking the Curse of Multiagency: Provably Efficient Decentralized Multi-Agent RL with Function Approximation](https://mlsanity.com/paper/2302.06606/) (2023)
- [Sample-Efficient Reinforcement Learning Is Feasible for Linearly Realizable MDPs with Limited Revisiting](https://mlsanity.com/paper/2105.08024/) (2021)
- [Breaking the Curse of Multiagents in a Large State Space: RL in Markov Games with Independent Linear Function Approximation](https://mlsanity.com/paper/2302.03673/) (2023)
- [Efficient Reinforcement Learning in Deterministic Systems with Value Function Generalization](https://mlsanity.com/paper/1307.4847/) (2013)
- [On Query-efficient Planning in MDPs under Linear Realizability of the Optimal State-value Function](https://mlsanity.com/paper/2102.02049/) (2021)
- [Minimax-Optimal Multi-Agent RL in Markov Games With a Generative Model](https://mlsanity.com/paper/2208.10458/) (2022)
- [Representation Learning for General-sum Low-rank Markov Games](https://mlsanity.com/paper/2210.16976/) (2022)
- [Sample Efficient Deep Reinforcement Learning via Local Planning](https://mlsanity.com/paper/2301.12579/) (2023)
- [Can Agents Run Relay Race with Strangers? Generalization of RL to Out-of-Distribution Trajectories](https://mlsanity.com/paper/2304.13424/) (2023)
- [Confident Approximate Policy Iteration for Efficient Local Planning in qπ-realizable MDPs](https://mlsanity.com/paper/2210.15755/) (2022)

## Abstract (arXiv)

Efficiently learning equilibria with large state and action spaces in general-sum Markov games while overcoming the curse of multi-agency is a challenging problem. Recent works have attempted to solve this problem by employing independent linear function classes to approximate the marginal Q-value for each agent. However, existing sample complexity bounds under such a framework have a suboptimal dependency on the desired accuracy varepsilon or the action space. In this work, we introduce a new algorithm, Lin-Confident-FTRL, for learning coarse correlated equilibria (CCE) with local access to the simulator, i.e., one can interact with the underlying environment on the visited states. Up to a logarithmic dependence on the size of the state space, Lin-Confident-FTRL learns ε-CCE with a provable optimal accuracy bound O(ε-2) and gets rids of the linear dependency on the action space, while scaling polynomially with relevant problem parameters (such as the number of agents and time horizon). Moreover, our analysis of Linear-Confident-FTRL generalizes the virtual policy iteration technique in the single-agent local planning literature, which yields a new computationally efficient algorithm with a tighter sample complexity bound when assuming random access to the simulator.