# V-Learning -- A Simple, Efficient, Decentralized Algorithm for Multiagent RL

arXiv: https://arxiv.org/abs/2110.14555 · HTML: https://mlsanity.com/paper/2110.14555/

## Key facts

- Cited by 114 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 65 references that are in the map.
- First posted on arXiv 27 Oct 2021.

## Builds on (most cited first, 30 of 34)

- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [QMIX: Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1803.11485/) (2018)
- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [Minimax Regret Bounds for Reinforcement Learning](https://mlsanity.com/paper/1703.05449/) (2017)
- [Value-Decomposition Networks For Cooperative Multi-Agent Learning](https://mlsanity.com/paper/1706.05296/) (2017)
- [Is Q-learning Provably Efficient?](https://mlsanity.com/paper/1807.03765/) (2018)
- [QTRAN: Learning to Factorize with Transformation for Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1905.05408/) (2019)
- [Emergent Tool Use From Multi-Agent Autocurricula](https://mlsanity.com/paper/1909.07528/) (2019)
- [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)
- [Actor-Attention-Critic for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1810.02912/) (2018)
- [Bellman Eluder Dimension: New Rich Classes of RL Problems, and Sample-Efficient Algorithms](https://mlsanity.com/paper/2102.00815/) (2021)
- [Fully Decentralized Multi-Agent Reinforcement Learning with Networked Agents](https://mlsanity.com/paper/1802.08757/) (2018)
- [Learning Near Optimal Policies with Low Inherent Bellman Error](https://mlsanity.com/paper/2003.00153/) (2020)
- [Unifying PAC and Regret: Uniform PAC Bounds for Episodic Reinforcement Learning](https://mlsanity.com/paper/1703.07710/) (2017)
- [Explore no more: Improved high-probability regret bounds for non-stochastic bandits](https://mlsanity.com/paper/1506.03271/) (2015)
- [Provable Self-Play Algorithms for Competitive Reinforcement Learning](https://mlsanity.com/paper/2002.04017/) (2020)
- [Generalization and Exploration via Randomized Value Functions](https://mlsanity.com/paper/1402.0635/) (2014)
- [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)
- [Independent Policy Gradient Methods for Competitive Reinforcement Learning](https://mlsanity.com/paper/2101.04233/) (2021)
- [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)
- [Last-iterate Convergence of Decentralized Optimistic Gradient Descent/Ascent in Infinite-horizon Competitive Markov Games](https://mlsanity.com/paper/2102.04540/) (2021)
- [Online Reinforcement Learning in Stochastic Games](https://mlsanity.com/paper/1712.00579/) (2017)
- [When Can We Learn General-Sum Markov Games with a Large Number of Players Sample-Efficiently?](https://mlsanity.com/paper/2110.04184/) (2021)
- [Decentralized Q-Learning in Zero-sum Markov Games](https://mlsanity.com/paper/2106.02748/) (2021)
- [The Power of Exploiter: Provable Multi-Agent RL in Large State Spaces](https://mlsanity.com/paper/2106.03352/) (2021)
- [Solving Discounted Stochastic Two-Player Games with Near-Optimal Time and Sample Complexity](https://mlsanity.com/paper/1908.11071/) (2019)
- [Provably Efficient Reinforcement Learning in Decentralized General-Sum Markov Games](https://mlsanity.com/paper/2110.05682/) (2021)

## Built on by (most cited first, 30 of 114)

- [Independent Policy Gradient for Large-Scale Markov Potential Games: Sharper Rates, Function Approximation, and Game-Agnostic Convergence](https://mlsanity.com/paper/2202.04129/) (2022)
- [The Complexity of Markov Equilibrium in Stochastic Games](https://mlsanity.com/paper/2204.03991/) (2022)
- [Iterative Nash Policy Optimization: Aligning LLMs with General Preferences via No-Regret Learning](https://mlsanity.com/paper/2407.00617/) (2024)
- [Provably Efficient Offline Multi-agent Reinforcement Learning via Strategy-wise Bonus](https://mlsanity.com/paper/2206.00159/) (2022)
- [Breaking the Curse of Multiagency: Provably Efficient Decentralized Multi-Agent RL with Function Approximation](https://mlsanity.com/paper/2302.06606/) (2023)
- [Uncoupled and Convergent Learning in Two-Player Zero-Sum Markov Games with Bandit Feedback](https://mlsanity.com/paper/2303.02738/) (2023)
- [When is Offline Two-Player Zero-Sum Markov Game Solvable?](https://mlsanity.com/paper/2201.03522/) (2022)
- [Sample-Efficient Reinforcement Learning of Partially Observable Markov Games](https://mlsanity.com/paper/2206.01315/) (2022)
- [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)
- [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)
- [Sample-Efficient Robust Multi-Agent Reinforcement Learning in the Face of Environmental Uncertainty](https://mlsanity.com/paper/2404.18909/) (2024)
- [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)
- [Improving LLM General Preference Alignment via Optimistic Online Mirror Descent](https://mlsanity.com/paper/2502.16852/) (2025)
- [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)
- [What is the Solution for State-Adversarial Multi-Agent Reinforcement Learning?](https://mlsanity.com/paper/2212.02705/) (2022)
- [Offline Learning in Markov Games with General Function Approximation](https://mlsanity.com/paper/2302.02571/) (2023)
- [Policy Optimization for Markov Games: Unified Framework and Faster Convergence](https://mlsanity.com/paper/2206.02640/) (2022)
- [On the convergence of policy gradient methods to Nash equilibria in general stochastic games](https://mlsanity.com/paper/2210.08857/) (2022)
- [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)
- [A Finite-Sample Analysis of Payoff-Based Independent Learning in Zero-Sum Stochastic Games](https://mlsanity.com/paper/2303.03100/) (2023)
- [Decentralized Cooperative Reinforcement Learning with Hierarchical Information Structure](https://mlsanity.com/paper/2111.00781/) (2021)
- [A Survey on Large-Population Systems and Scalable Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2209.03859/) (2022)
- [On the Statistical Efficiency of Mean-Field Reinforcement Learning with General Function Approximation](https://mlsanity.com/paper/2305.11283/) (2023)
- [Provably Efficient Generalized Lagrangian Policy Optimization for Safe Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2306.00212/) (2023)
- [Performative Reinforcement Learning in Gradually Shifting Environments](https://mlsanity.com/paper/2402.09838/) (2024)

## Abstract (arXiv)

A major challenge of multiagent reinforcement learning (MARL) is the curse of multiagents, where the size of the joint action space scales exponentially with the number of agents. This remains to be a bottleneck for designing efficient MARL algorithms even in a basic scenario with finitely many states and actions. This paper resolves this challenge for the model of episodic Markov games. We design a new class of fully decentralized algorithms -- V-learning, which provably learns Nash equilibria (in the two-player zero-sum setting), correlated equilibria and coarse correlated equilibria (in the multiplayer general-sum setting) in a number of samples that only scales with maxi∈[m] Ai, where Ai is the number of actions for the irm th player. This is in sharp contrast to the size of the joint action space which is prodi=1m Ai. V-learning (in its basic form) is a new class of single-agent RL algorithms that convert any adversarial bandit algorithm with suitable regret guarantees into a RL algorithm. Similar to the classical Q-learning algorithm, it performs incremental updates to the value functions. Different from Q-learning, it only maintains the estimates of V-values instead of Q-values. This key difference allows V-learning to achieve the claimed guarantees in the MARL setting by simply letting all agents run V-learning independently.