Stochastic Optimization for Performative Prediction

TL;DR

This paper studies stochastic optimization in performative prediction, where model deployment influences future data distribution, providing convergence rates and analyzing deployment strategies through theoretical and experimental insights.

Contribution

It introduces stochastic optimization methods tailored for performative prediction, analyzing deployment strategies and deriving convergence rates under various performativity strengths.

Findings

Convergence rates depend on performativity strength.

Deploying models after each update can outperform lazy deployment.

Experimental results validate theoretical trade-offs.

Abstract

In performative prediction, the choice of a model influences the distribution of future data, typically through actions taken based on the model's predictions. We initiate the study of stochastic optimization for performative prediction. What sets this setting apart from traditional stochastic optimization is the difference between merely updating model parameters and deploying the new model. The latter triggers a shift in the distribution that affects future data, while the former keeps the distribution as is. Assuming smoothness and strong convexity, we prove rates of convergence for both greedily deploying models after each stochastic update (greedy deploy) as well as for taking several updates before redeploying (lazy deploy). In both cases, our bounds smoothly recover the optimal $O(1/k)$ rate as the strength of performativity decreases. Furthermore, they illustrate how depending on the strength of performative effects, there exists a regime where either approach outperforms the other. We experimentally explore the trade-off on both synthetic data and a strategic classification simulator.