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

Predictor-corrector algorithms for stochastic optimization under gradual distribution shift