Online Linear Programming with Batching
Haoran Xu, Peter W. Glynn, Yinyu Ye

TL;DR
This paper investigates online linear programming with batching, establishing regret bounds and proposing algorithms that optimize decision delays under continuous reward-resource distributions.
Contribution
It provides the first analysis of regret bounds in continuous distribution settings and proposes algorithms with optimal regret scaling for various batching scenarios.
Findings
Proposes an $O(\log K)$ regret algorithm for single-resource case.
Establishes a $\Omega(\log K)$ regret lower bound, matching the upper bound.
Develops algorithms with $O(\log K)$ regret for multiple resources and Poisson arrivals.
Abstract
We study Online Linear Programming (OLP) with batching. The planning horizon is cut into batches, and the decisions on customers arriving within a batch can be delayed to the end of their associated batch. Compared with OLP without batching, the ability to delay decisions brings better operational performance, as measured by regret. Two research questions of interest are: (1) What is a lower bound of the regret as a function of ? (2) What algorithms can achieve the regret lower bound? These questions have been analyzed in the literature when the distribution of the reward and the resource consumption of the customers have finite support. By contrast, this paper analyzes these questions when the conditional distribution of the reward given the resource consumption is continuous, and we show the answers are different under this setting. When there is only a single type of resource…
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Taxonomy
TopicsOptimization and Search Problems · Smart Parking Systems Research · Scheduling and Optimization Algorithms
