Predictor-corrector algorithms for stochastic optimization under gradual distribution shift

TL;DR

This paper introduces predictor-corrector algorithms tailored for stochastic optimization problems with gradual distribution shifts, leveraging the continuous nature of the underlying process to improve convergence and accuracy.

Contribution

The paper develops novel predictor-corrector algorithms for time-varying stochastic optimization, providing theoretical error bounds and demonstrating superior performance over existing methods.

Findings

Error bounds established for the algorithms.

Method outperforms non-predictor corrector approaches.

Validated through theoretical analysis and empirical examples.

Abstract

Time-varying stochastic optimization problems frequently arise in machine learning practice (e.g. gradual domain shift, object tracking, strategic classification). Although most problems are solved in discrete time, the underlying process is often continuous in nature. We exploit this underlying continuity by developing predictor-corrector algorithms for time-varying stochastic optimizations. We provide error bounds for the iterates, both in presence of pure and noisy access to the queries from the relevant derivatives of the loss function. Furthermore, we show (theoretically and empirically in several examples) that our method outperforms non-predictor corrector methods that do not exploit the underlying continuous process.