Cloud-Based Centralized/Decentralized Multi-Agent Optimization with Communication Delays

We present and analyze a computational hybrid architecture for performing multi-agent optimization. The optimization problems under consideration have convex objective and constraint functions with mild smoothness conditions imposed on them. For such problems, we provide a primal-dual algorithm implemented in the hybrid architecture, which consists of a decentralized network of agents into which centralized information is occasionally injected, and we establish its convergence properties. To accomplish this, a central cloud computer aggregates global information, carries out computations of the dual variables based on this information, and then distributes the updated dual variables to the agents. The agents update their (primal) state variables and also communicate among themselves with each agent sharing and receiving state information with some number of its neighbors. Throughout, communications with the cloud are not assumed to be synchronous or instantaneous, and communication delays are explicitly accounted for in the modeling and analysis of the system. Experimental results are presented to support the theoretical developments made.Comment: 8 pages, 4 figure

Variational Fair Clustering

We propose a general variational framework of fair clustering, which integrates an original Kullback-Leibler (KL) fairness term with a large class of clustering objectives, including prototype or graph based. Fundamentally different from the existing combinatorial and spectral solutions, our variational multi-term approach enables to control the trade-off levels between the fairness and clustering objectives. We derive a general tight upper bound based on a concave-convex decomposition of our fairness term, its Lipschitz-gradient property and the Pinsker's inequality. Our tight upper bound can be jointly optimized with various clustering objectives, while yielding a scalable solution, with convergence guarantee. Interestingly, at each iteration, it performs an independent update for each assignment variable. Therefore, it can be easily distributed for large-scale datasets. This scalability is important as it enables to explore different trade-off levels between the fairness and clustering objectives. Unlike spectral relaxation, our formulation does not require computing its eigenvalue decomposition. We report comprehensive evaluations and comparisons with state-of-the-art methods over various fair-clustering benchmarks, which show that our variational formulation can yield highly competitive solutions in terms of fairness and clustering objectives.Comment: Accepted to be published in AAAI 2021. The Code is available at: https://github.com/imtiazziko/Variational-Fair-Clusterin