2020/01/09 by Pranay Sharma, Prashant Khanduri, Sharma, Pranay +7
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #Distributed #Distributed Control Multi-Agent Systems #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Parallel #Stochastic Gradient Optimization Techniques #Systems and Control (eess.SY) #and Cluster Computing (cs.DC) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2001.03166
openalex publication_date 2020/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this work, we consider a distributed online convex optimization problem, with time-varying (potentially adversarial) constraints. A set of nodes, jointly aim to minimize a global objective function, which is the sum of local convex functions. The objective and constraint functions are revealed locally to the nodes, at each time, after taking an action. Naturally, the constraints cannot be instantaneously satisfied. Therefore, we reformulate the problem to satisfy these constraints in the long term. To this end, we propose a distributed primal-dual mirror descent based approach, in which the primal and dual updates are carried out locally at all the nodes. This is followed by sharing and mixing of the primal variables by the local nodes via communication with the immediate neighbors. To quantify the performance of the proposed algorithm, we utilize the challenging, but more realistic metrics of dynamic regret and fit. Dynamic regret measures the cumulative loss incurred by the algorithm, compared to the best dynamic strategy. On the other hand, fit measures the long term cumulative constraint violations. Without assuming the restrictive Slater's conditions, we show that the proposed algorithm achieves sublinear regret and fit under mild, commonly used assumptions.