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Mathematics > Optimization and Control
Title: Online Convex Optimization Using Coordinate Descent Algorithms
(Submitted on 25 Jan 2022 (v1), last revised 25 Apr 2024 (this version, v2))
Abstract: This paper considers the problem of online optimization where the objective function is time-varying. In particular, we extend coordinate descent type algorithms to the online case, where the objective function varies after a finite number of iterations of the algorithm. Instead of solving the problem exactly at each time step, we only apply a finite number of iterations at each time step. Commonly used notions of regret are used to measure the performance of the online algorithm. Moreover, coordinate descent algorithms with different updating rules are considered, including both deterministic and stochastic rules that are developed in the literature of classical offline optimization. A thorough regret analysis is given for each case. Finally, numerical simulations are provided to illustrate the theoretical results.
Submission history
From: Yankai Lin [view email][v1] Tue, 25 Jan 2022 00:22:14 GMT (2326kb)
[v2] Thu, 25 Apr 2024 07:08:20 GMT (1316kb)
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