Decision-Dependent Risk Minimization in Geometrically Decaying Dynamic Environments

Abstract

This paper studies the problem of expected loss minimization given a data distribution that is dependent on the decision-maker's action and evolves dynamically in time according to a geometric decay process. Novel algorithms for both the information setting in which the decision-maker has a first order gradient oracle and the setting in which they have simply a loss function oracle are introduced. The algorithms operate on the same underlying principle: the decision-maker deploys a fixed decision repeatedly over the length of an epoch, thereby allowing the dynamically changing environment to sufficiently mix before updating the decision. The iteration complexity in each of the settings is shown to match existing rates for first and zero order stochastic gradient methods up to logarithmic factors. The algorithms are evaluated on a ``semi-synthetic" example using real world data from the SFpark dynamic pricing pilot study; it is shown that the announced prices result in an improvement for the institution's objective (target occupancy), while achieving an overall reduction in parking rates.

Performative Federated Learning: A Solution to Model-Dependent and Heterogeneous Distribution Shifts

“…Performative prediction has been primarily studied in a centralized setting, with fruitful literature including the convergence analysis (Mendler-Dünner et al 2020;Drusvyatskiy and Xiao 2020;Brown, Hod, and Kalemaj 2020;Wood, Bianchin, and Dall'Anese 2022) and algorithm development (Izzo, Ying, and Zou 2021;Izzo, Zou, and Ying 2022;Miller, Perdomo, and Zrnic 2021;Ray et al 2022).…”