arXiv:2509.02619cs.GTcs.LG2025-09

提出新方法实现任意数据分布下的稳定决策均衡,无需依赖未知的平滑性假设。

Towards Performatively Stable Equilibria in Decision-Dependent Games for Arbitrary Data Distribution Maps

  • 设计梯度敏感度度量,直接评估决策对数据分布的影响。
  • 在强单调性假设下证明收敛性,适用于任意数据分布映射。
  • 新算法在多个博弈场景中收敛更快、损失更低,适合实际应用。

在决策依赖型博弈中,多个参与者在随联合决策动态变化的数据分布下优化自身策略,这在市场定价等应用中引发复杂动态。其核心是“表演稳定均衡”——每个玩家的策略均为诱导分布下的最优响应。以往工作依赖β-平滑性假设(即损失函数梯度对数据分布的Lipschitz连续性),但数据分布映射通常未知,导致β不可获取。为此,本文提出一种基于梯度的敏感度度量,直接量化决策引起的分布变化影响。基于该度量,在可实践的强单调性假设下,推导出表演稳定均衡的收敛保证。进一步设计了一种敏感度感知的重复重训练算法,根据敏感度调整玩家损失函数,确保对任意数据分布映射都能收敛至表演稳定均衡。在预测误差最小化博弈、古诺竞争和收入最大化博弈上的实验表明,该方法优于现有基线,实现更低损失与更快收敛。

原文摘要 · Abstract (English)

In decision-dependent games, multiple players optimize their decisions under a data distribution that shifts with their joint actions, creating complex dynamics in applications like market pricing. A practical consequence of these dynamics is the \textit{performatively stable equilibrium}, where each player's strategy is a best response under the induced distribution. Prior work relies on $β$-smoothness, assuming Lipschitz continuity of loss function gradients with respect to the data distribution, which is impractical as the data distribution maps, i.e., the relationship between joint decision and the resulting distribution shifts, are typically unknown, rendering $β$ unobtainable. To overcome this limitation, we propose a gradient-based sensitivity measure that directly quantifies the impact of decision-induced distribution shifts. Leveraging this measure, we derive convergence guarantees for performatively stable equilibria under a practically feasible assumption of strong monotonicity. Accordingly, we develop a sensitivity-informed repeated retraining algorithm that adjusts players' loss functions based on the sensitivity measure, guaranteeing convergence to performatively stable equilibria for arbitrary data distribution maps. Experiments on prediction error minimization game, Cournot competition, and revenue maximization game show that our approach outperforms state-of-the-art baselines, achieving lower losses and faster convergence.

博弈论决策优化稳定均衡

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