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We consider the problem of minimizing a convex function that is evolvingaccording to unknown and possibly stochastic dynamics, which may depend jointlyon time and on the decision variable itself. Such problems abound in themachine learning and signal processing literature, under the names of conceptdrift, stochastic tracking, and performative prediction. We provide novelnon-asymptotic convergence guarantees for stochastic algorithms with iterateaveraging, focusing on bounds valid both in expectation and with highprobability. The efficiency estimates we obtain clearly decouple thecontributions of optimization error, gradient noise, and time drift. Notably,we identify a low drift-to-noise regime in which the tracking efficiency of theproximal stochastic gradient method benefits significantly from a step decayschedule. Numerical experiments illustrate our results.

Stochastic Optimization under Distributional Drift