Two-timescale Derivative Free Optimization for Performative Prediction with Markovian Data

Haitong LIU, Qiang LI, Hoi To Wai

Keywords: Performative Prediction, Derivative Free Optimization, Markovian data

TL;DR: We propose a novel derivative free optimization algorithm to solve state-dependent performative prediction problem.

Abstract: This paper studies the performative prediction problem where the learner aims to minimize the expected loss with a decision-dependent data distribution. Such setting is motivated when outcomes can be affected by the prediction model. We consider a state-dependent setting where the data distribution evolves according to an underlying controlled Markov chain. We focus on derivative free optimization (DFO) where the learner is given access to a loss function evaluation oracle with the above Markov chain data. We propose a two-timescale DFO($\lambda$) algorithm that features (i) a novel forgetting factor $\lambda$ to utilize every observed sample as opposed to the common sample burn-in approach, and (ii) a two-timescale diminishing step size to balance the rates of DFO updates and bias reduction. Under a general non-convex optimization setting, we show that DFO($\lambda$) requires at most ${\cal O}(d^2/\epsilon^3)$ samples (up to a log factor) to attain a near-stationary solution with expected squared gradient norm less than $\epsilon$. Numerical experiments verify our analysis.

Submission Number: 12483