The article discusses stochastic approximation algorithms for decision-dependent distributions, focusing on performative prediction. It analyzes the convergence properties of the Stochastic Forward-Backward (SFB) method and establishes its asymptotic optimality. The key results include the existence and uniqueness of equilibrium points, convergence to these points almost surely, and the asymptotic normality of average iterates. Assumptions on Lipschitz continuity, strong monotonicity, variance bounds, interiority, and Lindeberg’s condition are crucial for proving these results. Theorems 1.1 and 1.2 provide theoretical foundations for practical applications of SFB in optimization problems.
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by Josh... às arxiv.org 03-15-2024
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