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Tesseract: Tensorised Actors for Multi-Agent Reinforcement Learning
Anuj Mahajan · Mikayel Samvelyan · Lei Mao · Viktor Makoviychuk · Animesh Garg · Jean Kossaifi · Shimon Whiteson · Yuke Zhu · Anima Anandkumar

Tue Jul 20 07:20 AM -- 07:25 AM (PDT) @ None

Reinforcement Learning in large action spaces is a challenging problem. This is especially true for cooperative multi-agent reinforcement learning (MARL), which often requires tractable learning while respecting various constraints like communication budget and information about other agents. In this work, we focus on the fundamental hurdle affecting both value-based and policy-gradient approaches: an exponential blowup of the action space with the number of agents. For value-based methods, it poses challenges in accurately representing the optimal value function for value-based methods, thus inducing suboptimality. For policy gradient methods, it renders the critic ineffective and exacerbates the problem of the lagging critic. We show that from a learning theory perspective, both problems can be addressed by accurately representing the associated action-value function with a low-complexity hypothesis class. This requires accurately modelling the agent interactions in a sample efficient way. To this end, we propose a novel tensorised formulation of the Bellman equation. This gives rise to our method Tesseract, which utilises the view of Q-function seen as a tensor where the modes correspond to action spaces of different agents. Algorithms derived from Tesseract decompose the Q-tensor across the agents and utilise low-rank tensor approximations to model the agent interactions relevant to the task. We provide PAC analysis for Tesseract based algorithms and highlight their relevance to the class of rich observation MDPs. Empirical results in different domains confirm the gains in sample efficiency using Tesseract as supported by the theory.

Author Information

Anuj Mahajan (Dept. of Computer Science, University of Oxford)
Mikayel Samvelyan (University College London)
Lei Mao (NVIDIA)
Viktor Makoviychuk (NVIDIA)
Animesh Garg (University of Toronto, Vector Institute, Nvidia)
Jean Kossaifi (NVIDIA)
Shimon Whiteson (University of Oxford)
Yuke Zhu (University of Texas - Austin)
Anima Anandkumar (Caltech and NVIDIA)

Anima Anandkumar is a Bren Professor at Caltech and Director of ML Research at NVIDIA. She was previously a Principal Scientist at Amazon Web Services. She is passionate about designing principled AI algorithms and applying them to interdisciplinary domains. She has received several honors such as the IEEE fellowship, Alfred. P. Sloan Fellowship, NSF Career Award, Young investigator awards from DoD, Venturebeat’s “women in AI” award, NYTimes GoodTech award, and Faculty Fellowships from Microsoft, Google, Facebook, and Adobe. She is part of the World Economic Forum's Expert Network. She has appeared in the PBS Frontline documentary on the “Amazon empire” and has given keynotes in many forums such as the TEDx, KDD, ICLR, and ACM. Anima received her BTech from Indian Institute of Technology Madras, her PhD from Cornell University, and did her postdoctoral research at MIT and assistant professorship at University of California Irvine.

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