A Black-Box Approach for Exogenous Replenishment in Online Resource Allocation

TL;DR

This paper presents a black-box method to adapt existing online resource allocation algorithms to handle exogenous replenishment, maintaining competitive ratios across adversarial and stochastic replenishment processes.

Contribution

It introduces a generic black-box approach that extends any existing algorithm to incorporate unknown exogenous replenishment in online resource allocation.

Findings

Preserves original algorithm's competitive ratio with large initial inventory.

Applicable to both adversarial and stochastic replenishment models.

Enables seamless integration of replenishment into existing algorithms.

Abstract

In a typical online resource allocation problem, we start with a fixed inventory of resources and make online allocation decisions in response to resource requests that arrive sequentially over a finite horizon. We consider settings where the inventory is replenished over time according to an unknown exogenous process. We introduce black-box methods that extend any existing algorithm, originally designed without considering replenishment, into one that works with an arbitrary (adversarial or stochastic) replenishment process. Our approach preserves the original algorithm's competitive ratio in regimes with large initial inventory, thereby enabling the seamless integration of exogenous replenishment into a large body of existing algorithmic results for both adversarial and stochastic arrival models.