Eco-panda: A Computationally Economic, Geometrically Converging Dual Optimization Method on Time-varying Undirected Graphs | IEEE Conference Publication | IEEE Xplore

Eco-panda: A Computationally Economic, Geometrically Converging Dual Optimization Method on Time-varying Undirected Graphs


Abstract:

In this paper we consider distributed convex optimization over time-varying undirected graphs. We propose a linearized version of primarily averaged network dual ascent (...Show More

Abstract:

In this paper we consider distributed convex optimization over time-varying undirected graphs. We propose a linearized version of primarily averaged network dual ascent (PANDA) that keeps the advantages of PANDA while requiring less computational costs. The proposed method, economic primarily averaged network dual ascent (Eco-PANDA), provably converges at R-linear rate to the optimal point given that the agents' objective functions are strongly convex and have Lipschitz continuous gradients. Therefore, the method is competitive, in terms of type of rate, with both DIGing and PANDA. The proposed method halves the communication costs of methods like DIGing while still converging R-linearly and having the same per iterate complexity.
Date of Conference: 12-17 May 2019
Date Added to IEEE Xplore: 17 April 2019
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Conference Location: Brighton, UK
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1. INTRODUCTION

In this paper we solve convex optimization problems of the form \begin{equation*}\mathop {\min }\limits_{{\mathbf{\bar x}} \in {{\mathbb{R}}^p}} \sum\limits_{i = 1}^n {{f_i}} ({\mathbf{\bar x}})\tag{1}\end{equation*} in a decentralized manner within a network of n agents. Agent i possesses exclusive knowledge of its private objective function fi. Problems of the form of (1) naturally arise in applications such as distributed estimation and control [7], [8], [9], [10], decentralized source localization [11], power grids [12], [13] and distributed learning [14], [15], [16]. Methods to solve problems of the form (1) in a decentralized manner over static networks have received a lot of attention in the last few years. If the individual objective functions, fi, are strongly convex and have Lipschitz continuous gradients, linearly converging methods such as the decentralized exact first-order algorithm (EX-TRA) [17] have previously been proposed. In some applications, the agents may be communicating via wireless links. Due to the random nature of the wireless channel the communication links can be unreliable. This justifies the need for procedures according to which the agents cooperate to solve the optimization problem in (1) over time varying networks. DIGing [2] is the first known method to have established linear convergence over time-varying networks. However, DIGing requires the exchange of both the primal variables and the gradients at each iteration.

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