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This paper considers online stochastic optimization problems where time constraints severely limit the number of offline optimizations which can be performed at decision time and/or in between decisions. It proposes a novel approach which combines the salient features of the earlier approaches: the evaluation of every decision on all samples (expectation) and the ability to avoid distributing the samples among decisions (consensus). The key idea underlying the novel algorithm is to approximate the regret of a decision d. The regret algorithm is evaluated on two fundamental different applications: online packet scheduling in networks and online multiple vehicle routing with time windows. On both applications, it produces significant benefits over prior approaches.
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