Fully Dynamic Online Selection through Online Contention Resolution Schemes
This addresses online resource allocation challenges, such as matching tasks to workers with varying durations or pricing perishable goods, but is incremental as it extends existing OCRS frameworks to dynamic scenarios.
The paper tackles fully dynamic online selection problems, where elements have limited active intervals, by developing a general method to construct Online Contention Resolution Schemes (OCRS) for adversarial settings, and applies it to create no-regret algorithms with semi-bandit feedback.
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.