No Arabic abstract
When solving two-player zero-sum games, multi-agent reinforcement learning (MARL) algorithms often create populations of agents where, at each iteration, a new agent is discovered as the best response to a mixture over the opponent population. Within such a process, the update rules of who to compete with (i.e., the opponent mixture) and how to beat them (i.e., finding best responses) are underpinned by manually developed game theoretical principles such as fictitious play and Double Oracle. In this paper we introduce a framework, LMAC, based on meta-gradient descent that automates the discovery of the update rule without explicit human design. Specifically, we parameterise the opponent selection module by neural networks and the best-response module by optimisation subroutines, and update their parameters solely via interaction with the game engine, where both players aim to minimise their exploitability. Surprisingly, even without human design, the discovered MARL algorithms achieve competitive or even better performance with the state-of-the-art population-based game solvers (e.g., PSRO) on Games of Skill, differentiable Lotto, non-transitive Mixture Games, Iterated Matching Pennies, and Kuhn Poker. Additionally, we show that LMAC is able to generalise from small games to large games, for example training on Kuhn Poker and outperforming PSRO on Leduc Poker. Our work inspires a promising future direction to discover general MARL algorithms solely from data.
We consider a scenario in which two reinforcement learning agents repeatedly play a matrix game against each other and update their parameters after each round. The agents decision-making is transparent to each other, which allows each agent to predict how their opponent will play against them. To prevent an infinite regress of both agents recursively predicting each other indefinitely, each agent is required to give an opponent-independent response with some probability at least epsilon. Transparency also allows each agent to anticipate and shape the other agents gradient step, i.e. to move to regions of parameter space in which the opponents gradient points in a direction favourable to them. We study the resulting dynamics experimentally, using two algorithms from previous literature (LOLA and SOS) for opponent-aware learning. We find that the combination of mutually transparent decision-making and opponent-aware learning robustly leads to mutual cooperation in a single-shot prisoners dilemma. In a game of chicken, in which both agents try to manoeuvre their opponent towards their preferred equilibrium, converging to a mutually beneficial outcome turns out to be much harder, and opponent-aware learning can even lead to worst-case outcomes for both agents. This highlights the need to develop opponent-aware learning algorithms that achieve acceptable outcomes in social dilemmas involving an equilibrium selection problem.
Zero-sum games have long guided artificial intelligence research, since they possess both a rich strategy space of best-responses and a clear evaluation metric. Whats more, competition is a vital mechanism in many real-world multi-agent systems capable of generating intelligent innovations: Darwinian evolution, the market economy and the AlphaZero algorithm, to name a few. In two-player zero-sum games, the challenge is usually viewed as finding Nash equilibrium strategies, safeguarding against exploitation regardless of the opponent. While this captures the intricacies of chess or Go, it avoids the notion of cooperation with co-players, a hallmark of the major transitions leading from unicellular organisms to human civilization. Beyond two players, alliance formation often confers an advantage; however this requires trust, namely the promise of mutual cooperation in the face of incentives to defect. Successful play therefore requires adaptation to co-players rather than the pursuit of non-exploitability. Here we argue that a systematic study of many-player zero-sum games is a crucial element of artificial intelligence research. Using symmetric zero-sum matrix games, we demonstrate formally that alliance formation may be seen as a social dilemma, and empirically that naive multi-agent reinforcement learning therefore fails to form alliances. We introduce a toy model of economic competition, and show how reinforcement learning may be augmented with a peer-to-peer contract mechanism to discover and enforce alliances. Finally, we generalize our agent model to incorporate temporally-extended contracts, presenting opportunities for further work.
We study the problem of learning a Nash equilibrium (NE) in an imperfect information game (IIG) through self-play. Precisely, we focus on two-player, zero-sum, episodic, tabular IIG under the perfect-recall assumption where the only feedback is realizations of the game (bandit feedback). In particular, the dynamic of the IIG is not known -- we can only access it by sampling or interacting with a game simulator. For this learning setting, we provide the Implicit Exploration Online Mirror Descent (IXOMD) algorithm. It is a model-free algorithm with a high-probability bound on the convergence rate to the NE of order $1/sqrt{T}$ where $T$ is the number of played games. Moreover, IXOMD is computationally efficient as it needs to perform the updates only along the sampled trajectory.
The MAPF problem is the fundamental problem of planning paths for multiple agents, where the key constraint is that the agents will be able to follow these paths concurrently without colliding with each other. Applications of MAPF include automated warehouses and autonomous vehicles. Research on MAPF has been flourishing in the past couple of years. Different MAPF research papers make different assumptions, e.g., whether agents can traverse the same road at the same time, and have different objective functions, e.g., minimize makespan or sum of agents actions costs. These assumptions and objectives are sometimes implicitly assumed or described informally. This makes it difficult to establish appropriate baselines for comparison in research papers, as well as making it difficult for practitioners to find the papers relevant to their concrete application. This paper aims to fill this gap and support researchers and practitioners by providing a unifying terminology for describing common MAPF assumptions and objectives. In addition, we also provide pointers to two MAPF benchmarks. In particular, we introduce a new grid-based benchmark for MAPF, and demonstrate experimentally that it poses a challenge to contemporary MAPF algorithms.
We present a scalable tree search planning algorithm for large multi-agent sequential decision problems that require dynamic collaboration. Teams of agents need to coordinate decisions in many domains, but naive approaches fail due to the exponential growth of the joint action space with the number of agents. We circumvent this complexity through an anytime approach that allows us to trade computation for approximation quality and also dynamically coordinate actions. Our algorithm comprises three elements: online planning with Monte Carlo Tree Search (MCTS), factored representations of local agent interactions with coordination graphs, and the iterative Max-Plus method for joint action selection. We evaluate our approach on the benchmark SysAdmin domain with static coordination graphs and achieve comparable performance with much lower computation cost than our MCTS baselines. We also introduce a multi-drone delivery domain with dynamic, i.e., state-dependent coordination graphs, and demonstrate how our approach scales to large problems on this domain that are intractable for other MCTS methods. We provide an open-source implementation of our algorithm at https://github.com/JuliaPOMDP/FactoredValueMCTS.jl.