# Independent Policy Gradient Methods for Competitive Reinforcement Learning

arXiv: https://arxiv.org/abs/2101.04233 · HTML: https://mlsanity.com/paper/2101.04233/

## Key facts

- Cited by 101 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 83 references that are in the map.
- First posted on arXiv 11 Jan 2021.

## Builds on (most cited first, 30 of 49)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [End-to-End Training of Deep Visuomotor Policies](https://mlsanity.com/paper/1504.00702/) (2015)
- [Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms](https://mlsanity.com/paper/1911.10635/) (2019)
- [Minimax Regret Bounds for Reinforcement Learning](https://mlsanity.com/paper/1703.05449/) (2017)
- [Is Q-learning Provably Efficient?](https://mlsanity.com/paper/1807.03765/) (2018)
- [Information-Theoretic Considerations in Batch Reinforcement Learning](https://mlsanity.com/paper/1905.00360/) (2019)
- [On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/1906.00331/) (2019)
- [Training GANs with Optimism](https://mlsanity.com/paper/1711.00141/) (2017)
- [A Theoretical Analysis of Deep Q-Learning](https://mlsanity.com/paper/1901.00137/) (2019)
- [On the Theory of Policy Gradient Methods: Optimality, Approximation, and Distribution Shift](https://mlsanity.com/paper/1908.00261/) (2019)
- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Stochastic model-based minimization of weakly convex functions](https://mlsanity.com/paper/1803.06523/) (2018)
- [Solving a Class of Non-Convex Min-Max Games Using Iterative First Order Methods](https://mlsanity.com/paper/1902.08297/) (2019)
- [A Variational Inequality Perspective on Generative Adversarial Networks](https://mlsanity.com/paper/1802.10551/) (2018)
- [A Unified Analysis of Extra-gradient and Optimistic Gradient Methods for Saddle Point Problems: Proximal Point Approach](https://mlsanity.com/paper/1901.08511/) (2019)
- [Optimistic mirror descent in saddle-point problems: Going the extra (gradient) mile](https://mlsanity.com/paper/1807.02629/) (2018)
- [Cycles in adversarial regularized learning](https://mlsanity.com/paper/1709.02738/) (2017)
- [Stabilising Experience Replay for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1702.08887/) (2017)
- [Provable Self-Play Algorithms for Competitive Reinforcement Learning](https://mlsanity.com/paper/2002.04017/) (2020)
- [Near-Optimal Reinforcement Learning with Self-Play](https://mlsanity.com/paper/2006.12007/) (2020)
- [Sample Complexity of Episodic Fixed-Horizon Reinforcement Learning](https://mlsanity.com/paper/1510.08906/) (2015)
- [The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimization](https://mlsanity.com/paper/1807.03907/) (2018)
- [Learning Zero-Sum Simultaneous-Move Markov Games Using Function Approximation and Correlated Equilibrium](https://mlsanity.com/paper/2002.07066/) (2020)
- [Last-Iterate Convergence: Zero-Sum Games and Constrained Min-Max Optimization](https://mlsanity.com/paper/1807.04252/) (2018)
- [A Survey of Learning in Multiagent Environments: Dealing with Non-Stationarity](https://mlsanity.com/paper/1707.09183/) (2017)
- [Model-Based Multi-Agent RL in Zero-Sum Markov Games with Near-Optimal Sample Complexity](https://mlsanity.com/paper/2007.07461/) (2020)
- [Optimistic Policy Optimization with Bandit Feedback](https://mlsanity.com/paper/2002.08243/) (2020)
- [Efficient Algorithms for Smooth Minimax Optimization](https://mlsanity.com/paper/1907.01543/) (2019)

## Built on by (most cited first, 30 of 101)

- [A Minimaximalist Approach to Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2401.04056/) (2024)
- [V-Learning -- A Simple, Efficient, Decentralized Algorithm for Multiagent RL](https://mlsanity.com/paper/2110.14555/) (2021)
- [Global Convergence of Multi-Agent Policy Gradient in Markov Potential Games](https://mlsanity.com/paper/2106.01969/) (2021)
- [Last-iterate Convergence of Decentralized Optimistic Gradient Descent/Ascent in Infinite-horizon Competitive Markov Games](https://mlsanity.com/paper/2102.04540/) (2021)
- [Fast Policy Extragradient Methods for Competitive Games with Entropy Regularization](https://mlsanity.com/paper/2105.15186/) (2021)
- [Decentralized Q-Learning in Zero-sum Markov Games](https://mlsanity.com/paper/2106.02748/) (2021)
- [Independent Policy Gradient for Large-Scale Markov Potential Games: Sharper Rates, Function Approximation, and Game-Agnostic Convergence](https://mlsanity.com/paper/2202.04129/) (2022)
- [MARFT: Multi-Agent Reinforcement Fine-Tuning](https://mlsanity.com/paper/2504.16129/) (2025)
- [The Complexity of Markov Equilibrium in Stochastic Games](https://mlsanity.com/paper/2204.03991/) (2022)
- [Provably Efficient Reinforcement Learning in Decentralized General-Sum Markov Games](https://mlsanity.com/paper/2110.05682/) (2021)
- [Principled Penalty-based Methods for Bilevel Reinforcement Learning and RLHF](https://mlsanity.com/paper/2402.06886/) (2024)
- [Policy Gradient in Robust MDPs with Global Convergence Guarantee](https://mlsanity.com/paper/2212.10439/) (2022)
- [Independent Natural Policy Gradient Always Converges in Markov Potential Games](https://mlsanity.com/paper/2110.10614/) (2021)
- [Complexity Lower Bounds for Nonconvex-Strongly-Concave Min-Max Optimization](https://mlsanity.com/paper/2104.08708/) (2021)
- [On Improving Model-Free Algorithms for Decentralized Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2110.05707/) (2021)
- [Gradient play in stochastic games: stationary points, convergence, and sample complexity](https://mlsanity.com/paper/2106.00198/) (2021)
- [Multi-Agent Reinforcement Learning for Autonomous Driving: A Survey](https://mlsanity.com/paper/2408.09675/) (2024)
- [Uncoupled and Convergent Learning in Two-Player Zero-Sum Markov Games with Bandit Feedback](https://mlsanity.com/paper/2303.02738/) (2023)
- [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)
- [Sample and Communication-Efficient Decentralized Actor-Critic Algorithms with Finite-Time Analysis](https://mlsanity.com/paper/2109.03699/) (2021)
- [Near-Optimal Learning of Extensive-Form Games with Imperfect Information](https://mlsanity.com/paper/2202.01752/) (2022)
- [Faster Last-iterate Convergence of Policy Optimization in Zero-Sum Markov Games](https://mlsanity.com/paper/2210.01050/) (2022)
- [Policy Mirror Ascent for Efficient and Independent Learning in Mean Field Games](https://mlsanity.com/paper/2212.14449/) (2022)
- [Can Reinforcement Learning Find Stackelberg-Nash Equilibria in General-Sum Markov Games with Myopic Followers?](https://mlsanity.com/paper/2112.13521/) (2021)
- [ESCHER: Eschewing Importance Sampling in Games by Computing a History Value Function to Estimate Regret](https://mlsanity.com/paper/2206.04122/) (2022)
- [Regret Minimization and Convergence to Equilibria in General-sum Markov Games](https://mlsanity.com/paper/2207.14211/) (2022)
- [Independent Learning in Stochastic Games](https://mlsanity.com/paper/2111.11743/) (2021)
- [Independent and Decentralized Learning in Markov Potential Games](https://mlsanity.com/paper/2205.14590/) (2022)
- [Exploration-Exploitation in Multi-Agent Competition: Convergence with Bounded Rationality](https://mlsanity.com/paper/2106.12928/) (2021)
- [Escaping limit cycles: Global convergence for constrained nonconvex-nonconcave minimax problems](https://mlsanity.com/paper/2302.09831/) (2023)

## Abstract (arXiv)

We obtain global, non-asymptotic convergence guarantees for independent learning algorithms in competitive reinforcement learning settings with two agents (i.e., zero-sum stochastic games). We consider an episodic setting where in each episode, each player independently selects a policy and observes only their own actions and rewards, along with the state. We show that if both players run policy gradient methods in tandem, their policies will converge to a min-max equilibrium of the game, as long as their learning rates follow a two-timescale rule (which is necessary). To the best of our knowledge, this constitutes the first finite-sample convergence result for independent policy gradient methods in competitive RL; prior work has largely focused on centralized, coordinated procedures for equilibrium computation.