Modelling the dynamics of multi-agent learning has long been an important research topic, but all of the previous works focus on 2-agent settings and mostly use evolutionary game theoretic approaches. In this paper, we study an n-agent setting with n tends to infinity, such that agents learn their policies concurrently over repeated symmetric bimatrix games with some other agents. Using mean field theory, we approximate the effects of other agents on a single agent by an averaged effect. A Fokker-Planck equation that describes the evolution of the probability distribution of Q-values in the agent population is derived. To the best of our knowledge, this is the first time to show the Q-learning dynamics under an n-agent setting can be described by a system of only three equations.

We show for the first time that it is possible to reconcile in online learning in zero-sum games two seemingly contradictory objectives: vanishing time-average regret and non-vanishing step sizes. This phenomenon, that we coin ``fast and furious learning in games, sets a new benchmark about what is possible both in max-min optimization as well as in multi-agent systems. Our analysis does not depend on introducing a carefully tailored dynamic. Instead we focus on the most well studied online dynamic, gradient descent. Similarly, we focus on the simplest textbook class of games, two-agent two-strategy zero-sum games, such as Matching Pennies. Even for this simplest of benchmarks the best known bound for total regret, prior to our work, was the trivial one of $O(T)$, which is immediately applicable even to a non-learning agent. Based on a tight understanding of the geometry of the non-equilibrating trajectories in the dual space we prove a regret bound of $\Theta(\sqrt{T})$ matching the well known optimal bound for adaptive step sizes in the online setting. This guarantee holds for all fixed step-sizes without having to know the time horizon in advance and adapt the fixed step-size accordingly.As a corollary, we establish that even with fixed learning rates the time-average of mixed strategies, utilities converge to their exact Nash equilibrium values. We also provide experimental evidence suggesting the stronger regret bound holds for all zero-sum games.

Covering option discovery has been developed to improve the exploration of RL in single-agent scenarios with sparse reward signals, through connecting the most distant states in the embedding space provided by the Fiedler vector of the state transition graph. Given that joint state space grows exponentially with the number of agents in multi-agent systems, existing researches still relying on single-agent option discovery either become prohibitive or fail to directly discover joint options that improve the connectivity of the joint state space. In this paper, we show how to directly compute multi-agent options with collaborative exploratory behaviors while still enjoying the ease of decomposition. Our key idea is to approximate the joint state space as a Kronecker graph, based on which we can directly estimate its Fiedler vector using the Laplacian spectrum of individual agents' transition graphs. Further, considering that directly computing the Laplacian spectrum is intractable for tasks with infinite-scale state spaces, we further propose a deep learning extension of our method by estimating eigenfunctions through NN-based representation learning techniques. The evaluation on multi-agent tasks built with simulators like Mujoco, shows that the proposed algorithm can successfully identify multi-agent options, and significantly outperforms the state-of-the-art. Codes are available at: https://github.itap.purdue.edu/Clan-labs/Scalable

In many real-world cooperative multiagent reinforcement learning (MARL) tasks, teams of agents can rehearse together before deployment, but then communication constraints may force individual agents to execute independently when deployed. Centralized training and decentralized execution (CTDE) is increasingly popular in recent years, focusing mainly on this setting. In the value-based MARL branch, credit assignment mechanism is typically used to factorize the team reward into each individual's reward -- individual-global-max (IGM) is a condition on the factorization ensuring that agents' action choices coincide with team's optimal joint action. However, current architectures fail to consider local coordination within sub-teams that should be exploited for more effective factorization, leading to faster learning. We propose a novel value factorization framework, called multiagent Q-learning with sub-team coordination (QSCAN), to flexibly represent sub-team coordination while honoring the IGM condition. QSCAN encompasses the full spectrum of sub-team coordination according to sub-team size, ranging from the monotonic value function class to the entire IGM function class, with familiar methods such as QMIX and QPLEX located at the respective extremes of the spectrum. Experimental results show that QSCAN's performance dominates state-of-the-art methods in matrix games, predator-prey tasks, the Switch challenge in MA-Gym. Additionally, QSCAN achieves comparable performances to those methods in a selection of StarCraft II micro-management tasks.

Due to the broad range of applications of multi-agent reinforcement learning (MARL), understanding the effects of adversarial attacks against MARL model is essential for the safe applications of this model. Motivated by this, we investigate the impact of adversarial attacks on MARL. In the considered setup, there is an exogenous attacker who is able to modify the rewards before the agents receive them or manipulate the actions before the environment receives them. The attacker aims to guide each agent into a target policy or maximize the cumulative rewards under some specific reward function chosen by the attacker, while minimizing the amount of the manipulation on feedback and action. We first show the limitations of the action poisoning only attacks and the reward poisoning only attacks. We then introduce a mixed attack strategy with both the action poisoning and reward poisoning. We show that the mixed attack strategy can efficiently attack MARL agents even if the attacker has no prior information about the underlying environment and the agents' algorithms.

Learning the distribution of future trajectories conditioned on the past is a crucial problem for understanding multi-agent systems. This is challenging because humans make decisions based on complex social relations and personal intents, resulting in highly complex uncertainties over trajectories. To address this problem, we propose a conditional deep generative model that combines advances in graph neural networks. The prior and recognition model encodes two types of latent codes for each agent: an inter-agent latent code to represent social relations and an intra-agent latent code to represent agent intentions. The decoder is carefully devised to leverage the codes in a disentangled way to predict multi-modal future trajectory distribution. Specifically, a graph attention network built upon inter-agent latent code is used to learn continuous pair-wise relations, and an agent's motion is controlled by its latent intents and its observations of all other agents. Through experiments on both synthetic and real-world datasets, we show that our model outperforms previous work in multiple performance metrics. We also show that our model generates realistic multi-modal trajectories.

As deep networks begin to be deployed as autonomous agents, the issue of how they can communicate with each other becomes important. Here, we train two deep nets from scratch to perform realistic referent identification through unsupervised emergent communication. We show that the largely interpretable emergent protocol allows the nets to successfully communicate even about object types they did not see at training time. The visual representations induced as a by-product of our training regime, moreover, show comparable quality, when re-used as generic visual features, to a recent self-supervised learning model. Our results provide concrete evidence of the viability of (interpretable) emergent deep net communication in a more realistic scenario than previously considered, as well as establishing an intriguing link between this field and self-supervised visual learning.

Due to its high sample complexity, simulation is, as of today, critical for the successful application of reinforcement learning.

When one agent interacts with a multi-agent environment, it is challenging to deal with various opponents unseen before. Modeling the behaviors, goals, or beliefs of opponents could help the agent adjust its policy to adapt to different opponents. In addition, it is also important to consider opponents who are learning simultaneously or capable of reasoning. However, existing work usually tackles only one of the aforementioned types of opponents. In this paper, we propose model-based opponent modeling (MBOM), which employs the environment model to adapt to all kinds of opponents. MBOM simulates the recursive reasoning process in the environment model and imagines a set of improving opponent policies. To effectively and accurately represent the opponent policy, MBOM further mixes the imagined opponent policies according to the similarity with the real behaviors of opponents. Empirically, we show that MBOM achieves more effective adaptation than existing methods in a variety of tasks, respectively with different types of opponents, i.e., fixed policy, naive learner, and reasoning learner.

We present Coordinated Proximal Policy Optimization (CoPPO), an algorithm that extends the original Proximal Policy Optimization (PPO) to the multi-agent setting. The key idea lies in the coordinated adaptation of step size during the policy update process among multiple agents. We prove the monotonicity of policy improvement when optimizing a theoretically-grounded joint objective, and derive a simplified optimization objective based on a set of approximations. We then interpret that such an objective in CoPPO can achieve dynamic credit assignment among agents, thereby alleviating the high variance issue during the concurrent update of agent policies. Finally, we demonstrate that CoPPO outperforms several strong baselines and is competitive with the latest multi-agent PPO method (i.e.