Expander Graph and Communication-Efficient Decentralized Optimization

In this paper, we discuss how to design the graph topology to reduce the communication complexity of certain algorithms for decentralized optimization. Our goal is to minimize the total communication needed to achieve a prescribed accuracy. We discover that the so-called expander graphs are near-optimal choices. We propose three approaches to construct expander graphs for … Read more

Decentralized Consensus Optimization with Asynchrony and Delays

We propose an asynchronous, decentralized algorithm for consensus optimization. The algorithm runs over a network in which the agents communicate with their neighbors and perform local computation. In the proposed algorithm, each agent can compute and communicate independently at different times, for different durations, with the information it has even if the latest information from … Read more

Cyclic Coordinate Update Algorithms for Fixed-Point Problems: Analysis and Applications

Many problems reduce to the fixed-point problem of solving $x=T(x)$. To this problem, we apply the coordinate-update algorithms, which update only one or a few components of $x$ at each step. When each update is cheap, these algorithms are faster than the full fixed-point iteration (which updates all the components). In this paper, we focus … Read more

Coordinate Friendly Structures, Algorithms and Applications

This paper focuses on coordinate update methods, which are useful for solving problems involving large or high-dimensional datasets. They decompose a problem into simple subproblems, where each updates one, or a small block of, variables while fixing others. These methods can deal with linear and nonlinear mappings, smooth and nonsmooth functions, as well as convex … Read more