Online Sequential Decision-Making with Unknown Delays
Keywords: Sequential decision-making, Online convex optimization, Unknown delays, Approximate solution
TL;DR: We present three types of algorithms designed to address delayed sequential decision-making process by leveraging approximate solutions.
Abstract: In the field of online sequential decision-making, we address the problem with delays utilizing the framework of online convex optimization (OCO), where the feedback of a decision can arrive with an unknown delay. Unlike previous research that is limited to Euclidean norm and gradient information, we propose three families of delayed algorithms based on approximate solutions to handle different types of received feedback. Our proposed algorithms are versatile and applicable to universal norms. Specifically, we introduce a family of Follow the Delayed Regularized Leader algorithms for feedback with full information on the loss function, a family of Delayed Mirror Descent algorithms for feedback with gradient information on the loss function and a family of Simplified Delayed Mirror Descent algorithms for feedback with the value information of the loss function's gradients at corresponding decision points.
For each type of algorithm, we provide corresponding regret bounds under cases of general convexity and relative strong convexity, respectively. We also demonstrate the efficiency of each algorithm under different norms through concrete examples. Furthermore, our theoretical results are consistent with the current best bounds when degenerated to standard settings.
Track: Web Mining and Content Analysis
Submission Guidelines Scope: Yes
Submission Guidelines Blind: Yes
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Student Author: Yes
Submission Number: 430
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