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COLA: Consistent Learning with Opponent-Learning Awareness
Timon Willi · Alistair Letcher · Johannes Treutlein · Jakob Foerster

Thu Jul 21 03:00 PM -- 05:00 PM (PDT) @ Hall E #811

Learning in general-sum games is unstable and frequently leads to socially undesirable (Pareto-dominated) outcomes. To mitigate this, Learning with Opponent-Learning Awareness (LOLA) introduced opponent shaping to this setting, by accounting for each agent's influence on their opponents' anticipated learning steps. However, the original LOLA formulation (and follow-up work) is inconsistent because LOLA models other agents as naive learners rather than LOLA agents.In previous work, this inconsistency was suggested as a cause of LOLA's failure to preserve stable fixed points (SFPs). First, we formalize consistency and show that higher-order LOLA (HOLA) solves LOLA's inconsistency problem if it converges. Second, we correct a claim made in the literature by Schäfer and Anandkumar (2019), proving that Competitive Gradient Descent (CGD) does not recover HOLA as a series expansion (and fails to solve the consistency problem).Third, we propose a new method called Consistent LOLA (COLA), which learns update functions that are consistent under mutual opponent shaping. It requires no more than second-order derivatives and learns consistent update functions even when HOLA fails to converge. However, we also prove that even consistent update functions do not preserve SFPs, contradicting the hypothesis that this shortcoming is caused by LOLA's inconsistency.Finally, in an empirical evaluation on a set of general-sum games, we find that COLA finds prosocial solutions and that it converges under a wider range of learning rates than HOLA and LOLA. We support the latter finding with a theoretical result for a simple game.

Author Information

Timon Willi (University of Oxford)
Alistair Letcher (None)
Johannes Treutlein (University of Toronto, Vector Institute)
Jakob Foerster (Oxford university)
Jakob Foerster

Jakob Foerster started as an Associate Professor at the department of engineering science at the University of Oxford in the fall of 2021. During his PhD at Oxford he helped bring deep multi-agent reinforcement learning to the forefront of AI research and interned at Google Brain, OpenAI, and DeepMind. After his PhD he worked as a research scientist at Facebook AI Research in California, where he continued doing foundational work. He was the lead organizer of the first Emergent Communication workshop at NeurIPS in 2017, which he has helped organize ever since and was awarded a prestigious CIFAR AI chair in 2019. His past work addresses how AI agents can learn to cooperate and communicate with other agents, most recently he has been developing and addressing the zero-shot coordination problem setting, a crucial step towards human-AI coordination.

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