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# Model-Free Opponent Shaping

*Proceedings of the 39th International Conference on Machine Learning*, PMLR 162:14398-14411, 2022.

#### Abstract

In general-sum games the interaction of self-interested learning agents commonly leads to collectively worst-case outcomes, such as defect-defect in the iterated prisoner’s dilemma (IPD). To overcome this, some methods, such as Learning with Opponent-Learning Awareness (LOLA), directly shape the learning process of their opponents. However, these methods are myopic since only a small number of steps can be anticipated, are asymmetric since they treat other agents as naive learners, and require the use of higher-order derivatives, which are calculated through white-box access to an opponent’s differentiable learning algorithm. To address these issues, we propose Model-Free Opponent Shaping (M-FOS). M-FOS learns in a meta-game in which each meta-step is an episode of the underlying game. The meta-state consists of the policies in the underlying game and the meta-policy produces a new policy to be used in the next episode. M-FOS then uses generic model-free optimisation methods to learn meta-policies that accomplish long-horizon opponent shaping. Empirically, M-FOS near-optimally exploits naive learners and other, more sophisticated algorithms from the literature. For example, to the best of our knowledge, it is the first method to learn the well-known ZD extortion strategy in the IPD. In the same settings, M-FOS leads to socially optimal outcomes under meta-self-play. Finally, we show that M-FOS can be scaled to high-dimensional settings.