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

2025-07-20

AI Summary

Online resource allocation under dynamic replenishment—where inventory is replenished over time by unknown external processes (adversarial or stochastic)—poses a fundamental challenge absent from classical models. Method: We propose the first black-box framework that seamlessly extends any classic online algorithm (designed for no-replenishment settings) to accommodate arbitrary external replenishment patterns, without altering its internal structure. The framework interfaces with the base algorithm via a lightweight adaptor and requires only a sufficiently large initial inventory. Contribution/Results: Theoretically, it preserves the original algorithm’s competitive ratio exactly under mild conditions, demonstrating both compatibility and robustness across replenishment models. We instantiate the framework with canonical algorithms—including greedy and water-filling—and prove performance guarantees for each. This yields a general-purpose enhancement paradigm for online decision-making under dynamic inventory constraints, unifying treatment of adversarial and stochastic replenishment while maintaining algorithmic modularity and theoretical rigor.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Extends algorithms to handle unknown exogenous replenishment processes
• Preserves competitive ratio with large initial inventory
• Integrates replenishment into existing adversarial and stochastic models

Innovation

• Black-box methods extend existing algorithms
• Handles arbitrary exogenous replenishment processes
• Preserves competitive ratio with large inventory