Optimal Guarantees for Online Selection Over Time
Sebastian Perez-Salazar, Victor Verdugo

TL;DR
This paper establishes optimal approximation ratios for online selection over time, analyzing single-threshold and dynamic policies in IID and adversarial settings, with implications for online decision-making and prophet inequalities.
Contribution
It provides the best possible worst-case approximation ratios for the prophet inequality over time problem, including for single-threshold, multi-threshold, and dynamic policies, in both IID and adversarial scenarios.
Findings
Single-threshold algorithm achieves an approximation ratio of ~0.567.
Three-threshold algorithms can surpass a 0.602 ratio.
Asymptotic analysis yields a ratio of ~0.618 for the optimal dynamic policy.
Abstract
Prophet inequalities are a cornerstone in optimal stopping and online decision-making. Traditionally, they involve the sequential observation of non-negative independent random variables and face irrevocable accept-or-reject choices. The goal is to provide policies that provide a good approximation ratio against the optimal offline solution that can access all the values upfront -- the so-called prophet value. In the prophet inequality over time problem (POT), the decision-maker can commit to an accepted value for units of time, during which no new values can be accepted. This creates a trade-off between the duration of commitment and the opportunity to capture potentially higher future values. In this work, we provide best possible worst-case approximation ratios in the IID setting of POT for single-threshold algorithms and the optimal dynamic programming policy. We show a…
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Taxonomy
TopicsAdvanced Bandit Algorithms Research · Mobile Crowdsensing and Crowdsourcing · Optimization and Search Problems
