Stable Opponent Shaping in Differentiable Games
This addresses the challenge of ensuring stable and cooperative learning in multi-objective optimization settings, which is crucial for applications like generative models and multi-agent systems, though it builds incrementally on existing opponent shaping techniques.
The paper tackles the problem of unstable learning dynamics in differentiable games, such as GANs and multi-agent RL, by introducing Stable Opponent Shaping (SOS), which combines opponent shaping with theoretical stability guarantees, leading to improved convergence and performance compared to prior methods like LOLA.
A growing number of learning methods are actually differentiable games whose players optimise multiple, interdependent objectives in parallel -- from GANs and intrinsic curiosity to multi-agent RL. Opponent shaping is a powerful approach to improve learning dynamics in these games, accounting for player influence on others' updates. Learning with Opponent-Learning Awareness (LOLA) is a recent algorithm that exploits this response and leads to cooperation in settings like the Iterated Prisoner's Dilemma. Although experimentally successful, we show that LOLA agents can exhibit 'arrogant' behaviour directly at odds with convergence. In fact, remarkably few algorithms have theoretical guarantees applying across all (n-player, non-convex) games. In this paper we present Stable Opponent Shaping (SOS), a new method that interpolates between LOLA and a stable variant named LookAhead. We prove that LookAhead converges locally to equilibria and avoids strict saddles in all differentiable games. SOS inherits these essential guarantees, while also shaping the learning of opponents and consistently either matching or outperforming LOLA experimentally.