Fully Dynamic Online Selection through Online Contention Resolution Schemes

TL;DR

This paper introduces a general method for constructing Online Contention Resolution Schemes (OCRS) tailored for fully dynamic online selection problems, enabling effective online decision-making under adversarial and stochastic conditions.

Contribution

It presents a novel framework for creating OCRS in fully dynamic settings and demonstrates their application to develop no-regret algorithms with semi-bandit feedback.

Findings

Developed a general construction method for OCRS in dynamic settings.

Applied OCRS to design no-regret algorithms under adversarial inputs.

Extended online selection models to include limited active periods for elements.

Abstract

We study fully dynamic online selection problems in an adversarial/stochastic setting that includes Bayesian online selection, prophet inequalities, posted price mechanisms, and stochastic probing problems subject to combinatorial constraints. In the classical ``incremental'' version of the problem, selected elements remain active until the end of the input sequence. On the other hand, in the fully dynamic version of the problem, elements stay active for a limited time interval, and then leave. This models, for example, the online matching of tasks to workers with task/worker-dependent working times, and sequential posted pricing of perishable goods. A successful approach to online selection problems in the adversarial setting is given by the notion of Online Contention Resolution Scheme (OCRS), that uses a priori information to formulate a linear relaxation of the underlying optimization problem, whose optimal fractional solution is rounded online for any adversarial order of the input sequence. Our main contribution is providing a general method for constructing an OCRS for fully dynamic online selection problems. Then, we show how to employ such OCRS to construct no-regret algorithms in a partial information model with semi-bandit feedback and adversarial inputs.