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

21 Pages Posted: 25 Nov 2019

See all articles by Daniel Freund

Daniel Freund

MIT Sloan School of Management

Siddhartha Banerjee

Cornell University - School of Operations Research and Information Engineering

Date Written: November 1, 2019

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

Suggested Citation

Freund, Daniel and Banerjee, Siddhartha, Uniform Loss Algorithms for Online Stochastic Decision-Making With Applications to Bin Packing (November 1, 2019). Available at SSRN: https://ssrn.com/abstract=3479189 or http://dx.doi.org/10.2139/ssrn.3479189

Daniel Freund (Contact Author)

MIT Sloan School of Management ( email )

100 Main Street
E62-584
Cambridge, MA 02142
United States

Siddhartha Banerjee

Cornell University - School of Operations Research and Information Engineering ( email )

237 Rhodes Hall
Ithaca, NY 14853
United States

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