In this work, we show that for linearly constrained optimization problems the primal-dual hybrid gradient algorithm, analyzed by Chambolle and Pock [3], can be written as an entirely primal algorithm. This allows us to prove convergence of the iterates even in the degenerate cases when the linear system is inconsistent or when the strong duality … Read more
We consider a multi-player optimization where each player has her own optimization problem and the individual problems are connected by a cardinality constraint on their shared resources. We give distributed algorithms that allow each player to solve their own optimization problem and still achieve a global optimization solution for problems that possess a concavity property. … Read more
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this problem either do not work well in the distributed setting or work only for specific regularizers. Our algorithm uses successive quadratic approximations, and we describe how to … Read more
Methods for distributed optimization have received significant attention in recent years owing to their wide applicability in various domains including machine learning, robotics and sensor networks. A distributed optimization method typically consists of two key components: communication and computation. More specifically, at every iteration (or every several iterations) of a distributed algorithm, each node in … Read more
Designing distributed algorithms for empirical risk minimization (ERM) has become an active research topic in recent years because of the practical need to deal with the huge volume of data. In this paper, we propose a general framework for training an ERM model via solving its dual problem in parallel over multiple machines. Our method … Read more
This paper presents novel convergence results for the Augmented Lagrangian based Alternating Direction Inexact Newton method (ALADIN) in the context of distributed convex optimization. It is shown that ALADIN converges for a large class of convex optimization problems from any starting point to minimizers without needing line-search or other globalization routines. Under additional regularity assumptions, … Read more
We consider distributed optimization problems where networked nodes cooperatively minimize the sum of their locally known convex costs. A popular class of methods to solve these problems are the distributed gradient methods, which are attractive due to their inexpensive iterations, but have a drawback of slow convergence rates. This motivates the incorporation of second-order information … Read more
We consider distributed optimization where $N$ nodes in a connected network minimize the sum of their local costs subject to a common constraint set. We propose a distributed projected gradient method where each node, at each iteration $k$, performs an update (is active) with probability $p_k$, and stays idle (is inactive) with probability $1-p_k$. Whenever … Read more
We consider distributed convex optimization problems originated from sample average approximation of stochastic optimization, or empirical risk minimization in machine learning. We assume that each machine in the distributed computing system has access to a local empirical loss function, constructed with i.i.d. data sampled from a common distribution. We propose a communication-efficient distributed algorithm to … Read more
In this paper, we investigate a parallel subspace correction framework for composite convex optimization. The variables are first divided into a few blocks based on certain rules. At each iteration, the algorithms solve a suitable subproblem on each block simultaneously, construct a search direction by combining their solutions on all blocks, then identify a new … Read more