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

作者：Guangzheng Zhong, Yang Liu, Jiming Liu · 发表于：Machine Learning · 年份：2026 · DOI：10.1007/s10994-026-07115-w · 研究领域：Reinforcement Learning in Robotics、Stochastic Gradient Optimization Techniques、Advanced Bandit Algorithms Research

Abstract In decision-dependent games, multiple players optimize their decisions under data distributions that shift with their joint actions, creating complex dynamics in applications like market pricing. A practical consequence of these dynamics is the performatively stable equilibrium , where each player’s strategy is a best response under the induced distribution. Prior work relies on $$\beta $$ -smoothness, assuming Lipschitz continuity of loss function gradients with respect to data distributions, which is impractical as the data distribution maps, i.e., the relationship between joint decision and the resulting distribution shifts, are typically unknown, rendering $$\beta $$ unobtainable. To overcome this limitation, we propose a gradient-based $$\hat{\varepsilon }_i$$ -sensitivity measure. It directly quantifies the impact of decision-induced distribution shifts on decision-making and is calculable for arbitrary data distribution maps. Leveraging this measure, we derive convergence guarantees for performatively stable equilibria under a practically feasible assumption of $$\alpha $$ -strong monotonicity. Notably, we establish a linear convergence rate in finite sample scenarios when $$\alpha > 2 \sqrt{\sum _{i = 1}^n \hat{\varepsilon }_i^2}$$ , with a probability depending on sample complexity. Accordingly, we develop a sensitivity-informed repeated retraining algorithm that adjusts players’ loss functions based on the sensitivity measure to achieve the strong monoto...