A Coordinate Descent Primal-Dual Algorithm and Application to Distributed Asynchronous Optimization

• Published in: IEEE transactions on automatic control 2016-10, Vol.61 (10), p.2947-2957
• Main Authors: Bianchi, Pascal, Hachem, Walid, Iutzeler, Franck
• Format: Article
• Language: English
• Subjects: Consensus algorithms; Convergence; Convex functions; coordinate descent; Cost function; distributed optimization; Mathematics; Minimization; Optimization algorithms; Optimization and Control; primal-dual algorithm; Statistics; Yttrium
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2015.2512043

Based on the idea of randomized coordinate descent of α-averaged operators, a randomized primal-dual optimization algorithm is introduced, where a random subset of coordinates is updated at each iteration. The algorithm builds upon a variant of a recent (deterministic) algorithm proposed by Vũ and Condat that includes the well-known Alternating Direction Method of Multipliers as a particular case. The obtained algorithm is used to solve asynchronously a distributed optimization problem. A network of agents, each having a separate cost function containing a differentiable term, seek to find a consensus on the minimum of the aggregate objective. The method yields an algorithm where at each iteration, a random subset of agents wake up, update their local estimates, exchange some data with their neighbors, and go idle. Numerical results demonstrate the attractive performance of the method. The general approach can be naturally adapted to other situations where coordinate descent convex optimization algorithms are used with a random choice of the coordinates.