Cooperative multi-agent reinforcement learning (MARL) requires agents to explore to learn to cooperate. Existing value-based MARL algorithms commonly rely on random exploration, such as $\epsilon$-greedy, which is inefficient in discovering multi-agent cooperation. Additionally, the environment in MARL appears non-stationary to any individual agent due to the simultaneous training of other agents, leading to highly variant and thus unstable optimisation signals. In this work, we propose ensemble value functions for multi-agent exploration (EMAX), a general framework to extend any value-based MARL algorithm. EMAX trains ensembles of value functions for each agent to address the key challenges of exploration and non-stationarity: (1) The uncertainty of value estimates across the ensemble is used in a UCB policy to guide the exploration of agents to parts of the environment which require cooperation. (2) Average value estimates across the ensemble serve as target values. These targets exhibit lower variance compared to commonly applied target networks and we show that they lead to more stable gradients during the optimisation. We instantiate three value-based MARL algorithms with EMAX, independent DQN, VDN and QMIX, and evaluate them in 21 tasks across four environments. Using ensembles of five value functions, EMAX improves sample efficiency and final evaluation returns of these algorithms by 54%, 55%, and 844%, respectively, averaged all 21 tasks.

翻译：协同多智能体强化学习要求智能体通过探索来学习合作。现有基于价值的MARL算法通常依赖随机探索（如$\epsilon$-贪婪策略），这在发现多智能体协作方面效率低下。此外，由于其他智能体的同步训练，MARL环境对单个智能体而言呈现出非平稳性，导致高度变异且不稳定的优化信号。本文提出面向多智能体探索的集成价值函数（EMAX），这是一个可扩展任何基于价值MARL算法的通用框架。EMAX为每个智能体训练价值函数集成，以解决探索与非平稳性两大核心挑战：(1) 集成中价值估计的不确定性被用于上置信界策略，引导智能体探索环境中需要协作的区域；(2) 集成平均价值估计作为目标值。相较于常用的目标网络，这些目标值方差更低，我们证明其在优化过程中能产生更稳定的梯度。我们将EMAX实例化为三种基于价值的MARL算法：独立DQN、VDN和QMIX，并在四个环境的21个任务中进行评估。采用五个价值函数的集成后，EMAX使这些算法在所有21个任务中的样本效率和最终评估回报分别平均提升54%、55%和844%。