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Non-Stationary Stochastic Optimization

Omar Besbes¹; Yonatan Gur²; Assaf Zeevi¹

¹ Columbia University, New York, New York 10027; · ² Stanford University, Stanford, California 94305;

We consider a non-stationary variant of a sequential stochastic optimization problem, in which the underlying cost functions may change along the horizon. We propose a measure, termed variation budget, that controls the extent of said change, and study how restrictions on this budget impact achievable performance. We identify sharp conditions under which it is possible to achieve long-run average optimality and more refined performance measures such as rate optimality that fully characterize the complexity of such problems. In doing so, we also establish a strong connection between two rather disparate strands of literature: (1) adversarial online convex optimization and (2) the more traditional stochastic approximation paradigm (couched in a non-stationary setting). This connection is the key to deriving well-performing policies in the latter, by leveraging structure of optimal policies in the former. Finally, tight bounds on the minimax regret allow us to quantify the “price of non-stationarity,” which mathematically captures the added complexity embedded in a temporally changing environment versus a stationary one.

DOI

10.1287/opre.2015.1408

Volume

63 (5)

Pages

1227-1244

Language

en

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