Uniform Loss Algorithms for Online Stochastic Decision-Making With Applications to Bin Packing

Abstract

We consider a general class of finite-horizon online decision-making problems, where in each period, a controller is presented a stochastic arrival and needs to choose one of a set of permissible actions, and the objective measured at the end of the horizon depends only on the aggregate type-action counts. Such a framework encapsulates many online stochastic variants of common optimization problems including bin packing, generalized assignment, and network revenue management. In such settings, we study a natural model-predictive control algorithm that acts greedily based on an updated certainty-equivalent optimization problem in each period. We introduce a simple, yet general, condition under which this algorithm obtains uniform additive loss (independent of the horizon) compared to an optimal solution with full knowledge of arrivals. Our condition is fulfilled by the above-mentioned problems, as well as more general settings involving piece-wise linear objectives and offline index policies.

Keywords: online stochastic decision-making, approximate dynamic programing, prophet inequalities, bin packing