Differentiable Belief-based Opponent Shaping
Quick Take
Differentiable Belief-based Opponent Shaping (D-BOS) introduces a novel method for shaping beliefs in multi-agent reinforcement learning, outperforming PPO and BBM in hidden-role games, particularly in mixed-motive scenarios. By treating belief states as the target for shaping, D-BOS allows optimal strategies to emerge from the environment's reward structure without explicit rewards for deceptive or cooperative behavior.
Key Points
- D-BOS utilizes $k$-step softmax-Bayes belief dynamics for shaping opponent beliefs.
- The method aggregates gradients over individual inferred belief trajectories for multiple observers.
- Empirical results show significant performance gains in mixed-motive settings.
- D-BOS does not require hard-coded objectives for deception or cooperation.
Article Content
From source RSS / original summaryarXiv:2605. 29042v1 Announce Type: new Abstract: Human coordination often relies on the ability to influence the beliefs of others through strategic action. In multi-agent reinforcement learning, opponent shaping attempts to replicate this influence, though existing methods typically operate within an opponent's parameter, policy, or value space. Meanwhile, belief-manipulation techniques in hidden-role games often rely on hard-coded objectives, such as deception or belief saturation.
We propose Differentiable Belief-based Opponent Shaping (D-BOS), a first-order method that treats each observer's belief as the shaped opponent state and differentiates through $k$-step softmax-Bayes belief dynamics. Rather than explicitly rewarding deceptive or cooperative behavior, our method treats the belief state as the target for shaping. This allows the optimal strategy to emerge naturally from the environment's reward structure.
This belief-space formulation provides an opponent-shaping signal by differentiating through opponent belief updates, and naturally extends to multiple observers by aggregating gradients over their individual inferred belief trajectories. Empirically, D-BOS outperforms PPO and BBM in hidden-role games, with the largest gains in mixed-motive settings.
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