2019/12/20 by Deming Yuan, Yuan, Deming, Alexandre Proutière +4 · 5 citations
Computer Science · Decision Sciences · Mathematics · #Advanced Bandit Algorithms Research #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Optimization and Search Problems #Stochastic Gradient Optimization Techniques #cs.LG #math.OC #stat.ML
paper · pdf · doi:10.48550/arxiv.1912.09705
arxiv created 2019/12/20 · openalex publication_date 2019/12/20 · arxiv updated 2019/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider distributed online convex optimization problems, where the distributed system consists of various computing units connected through a time-varying communication graph. In each time step, each computing unit selects a constrained vector, experiences a loss equal to an arbitrary convex function evaluated at this vector, and may communicate to its neighbors in the graph. The objective is to minimize the system-wide loss accumulated over time. We propose a decentralized algorithm with regret and cumulative constraint violation in O(T^max\c,1-c\ ) and O(T1-c/2), respectively, for any c∈ (0,1), where T is the time horizon. When the loss functions are strongly convex, we establish improved regret and constraint violation upper bounds in O(log(T)) and O(√(Tlog(T))). These regret scalings match those obtained by state-of-the-art algorithms and fundamental limits in the corresponding centralized online optimization problem (for both convex and strongly convex loss functions). In the case of bandit feedback, the proposed algorithms achieve a regret and constraint violation in O(T^max\c,1-c/3 \ ) and O(T1-c/2) for any c∈ (0,1). We numerically illustrate the performance of our algorithms for the particular case of distributed online regularized linear regression problems.