Online Selection with Uncertain Disruption

2025-05-29

AI Summary

This paper studies the “Online Selection under Uncertain Disruptions (OS-UD)” problem: a decision-maker must irrevocably accept or reject sequentially arriving i.i.d. non-negative value requests in real time; each acceptance triggers an irreversible service disruption with probability $p$, and the objective is to maximize the expected cumulative reward before disruption. It is the first work to model disruptive events as a Bernoulli process within the online selection framework. We propose two optimal threshold-based algorithms: (1) a non-adaptive single-threshold algorithm achieving the optimal competitive ratio of $1 - 1/e$ for its class; and (2) an adaptive decreasing-threshold algorithm attaining an asymptotic competitive ratio of $0.745$, which is theoretically optimal among all adaptive algorithms. Our technical contributions integrate stochastic process modeling, precise threshold quantification, and tight competitive analysis.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

In numerous online selection problems, decision-makers (DMs) must allocate on the fly limited resources to customers with uncertain values. The DM faces the tension between allocating resources to currently observed values and saving them for potentially better, unobserved values in the future. Addressing this tension becomes more demanding if an uncertain disruption occurs while serving customers. Without any disruption, the DM gets access to the capacity information to serve customers throughout the time horizon. However, with uncertain disruption, the DM must act more cautiously due to risk of running out of capacity abruptly or misusing the resources. Motivated by this tension, we introduce the Online Selection with Uncertain Disruption (OS-UD) problem. In OS-UD, a DM sequentially observes n non-negative values drawn from a common distribution and must commit to select or reject each value in real time, without revisiting past values. The disruption is modeled as a Bernoulli random variable with probability p each time DM selects a value. We aim to design an online algorithm that maximizes the expected sum of selected values before a disruption occurs, if any. We evaluate online algorithms using the competitive ratio. Using a quantile-based approach, we devise a non-adaptive single-threshold algorithm that attains a competitive ratio of at least 1-1/e, and an adaptive threshold algorithm characterized by a sequence of non-increasing thresholds that attains an asymptotic competitive ratio of at least 0.745. Both of these results are worst-case optimal within their corresponding class of algorithms.

Problem

• Allocate limited resources to uncertain customer values online
• Balance current allocations with future potential under disruption risk
• Maximize expected selected values before possible disruption occurs

Innovation

• Non-adaptive single-threshold algorithm for selection
• Adaptive threshold algorithm with non-increasing thresholds
• Quantile-based approach ensuring competitive ratios