1,955 research outputs found
Distributed Partitioned Big-Data Optimization via Asynchronous Dual Decomposition
In this paper we consider a novel partitioned framework for distributed
optimization in peer-to-peer networks. In several important applications the
agents of a network have to solve an optimization problem with two key
features: (i) the dimension of the decision variable depends on the network
size, and (ii) cost function and constraints have a sparsity structure related
to the communication graph. For this class of problems a straightforward
application of existing consensus methods would show two inefficiencies: poor
scalability and redundancy of shared information. We propose an asynchronous
distributed algorithm, based on dual decomposition and coordinate methods, to
solve partitioned optimization problems. We show that, by exploiting the
problem structure, the solution can be partitioned among the nodes, so that
each node just stores a local copy of a portion of the decision variable
(rather than a copy of the entire decision vector) and solves a small-scale
local problem
A randomized primal distributed algorithm for partitioned and big-data non-convex optimization
In this paper we consider a distributed optimization scenario in which the
aggregate objective function to minimize is partitioned, big-data and possibly
non-convex. Specifically, we focus on a set-up in which the dimension of the
decision variable depends on the network size as well as the number of local
functions, but each local function handled by a node depends only on a (small)
portion of the entire optimization variable. This problem set-up has been shown
to appear in many interesting network application scenarios. As main paper
contribution, we develop a simple, primal distributed algorithm to solve the
optimization problem, based on a randomized descent approach, which works under
asynchronous gossip communication. We prove that the proposed asynchronous
algorithm is a proper, ad-hoc version of a coordinate descent method and thus
converges to a stationary point. To show the effectiveness of the proposed
algorithm, we also present numerical simulations on a non-convex quadratic
program, which confirm the theoretical results
A randomized primal distributed algorithm for partitioned and big-data non-convex optimization
In this paper we consider a distributed opti- mization scenario in which the aggregate objective function to minimize is partitioned, big-data and possibly non-convex. Specifically, we focus on a set-up in which the dimension of the decision variable depends on the network size as well as the number of local functions, but each local function handled by a node depends only on a (small) portion of the entire optimiza- tion variable. This problem set-up has been shown to appear in many interesting network application scenarios. As main paper contribution, we develop a simple, primal distributed algorithm to solve the optimization problem, based on a randomized descent approach, which works under asynchronous gossip communication. We prove that the proposed asynchronous algorithm is a proper, ad-hoc version of a coordinate descent method and thus converges to a stationary point. To show the effectiveness of the proposed algorithm, we also present numerical simulations on a non-convex quadratic program, which confirm the theoretical results
Distributed Big-Data Optimization via Block Communications
We study distributed multi-agent large-scale optimization problems, wherein
the cost function is composed of a smooth possibly nonconvex sum-utility plus a
DC (Difference-of-Convex) regularizer. We consider the scenario where the
dimension of the optimization variables is so large that optimizing and/or
transmitting the entire set of variables could cause unaffordable computation
and communication overhead. To address this issue, we propose the first
distributed algorithm whereby agents optimize and communicate only a portion of
their local variables. The scheme hinges on successive convex approximation
(SCA) to handle the nonconvexity of the objective function, coupled with a
novel block-signal tracking scheme, aiming at locally estimating the average of
the agents' gradients. Asymptotic convergence to stationary solutions of the
nonconvex problem is established. Numerical results on a sparse regression
problem show the effectiveness of the proposed algorithm and the impact of the
block size on its practical convergence speed and communication cost
Distributed Big-Data Optimization via Block-Iterative Convexification and Averaging
In this paper, we study distributed big-data nonconvex optimization in
multi-agent networks. We consider the (constrained) minimization of the sum of
a smooth (possibly) nonconvex function, i.e., the agents' sum-utility, plus a
convex (possibly) nonsmooth regularizer. Our interest is in big-data problems
wherein there is a large number of variables to optimize. If treated by means
of standard distributed optimization algorithms, these large-scale problems may
be intractable, due to the prohibitive local computation and communication
burden at each node. We propose a novel distributed solution method whereby at
each iteration agents optimize and then communicate (in an uncoordinated
fashion) only a subset of their decision variables. To deal with non-convexity
of the cost function, the novel scheme hinges on Successive Convex
Approximation (SCA) techniques coupled with i) a tracking mechanism
instrumental to locally estimate gradient averages; and ii) a novel block-wise
consensus-based protocol to perform local block-averaging operations and
gradient tacking. Asymptotic convergence to stationary solutions of the
nonconvex problem is established. Finally, numerical results show the
effectiveness of the proposed algorithm and highlight how the block dimension
impacts on the communication overhead and practical convergence speed
A Distributed Asynchronous Method of Multipliers for Constrained Nonconvex Optimization
This paper presents a fully asynchronous and distributed approach for
tackling optimization problems in which both the objective function and the
constraints may be nonconvex. In the considered network setting each node is
active upon triggering of a local timer and has access only to a portion of the
objective function and to a subset of the constraints. In the proposed
technique, based on the method of multipliers, each node performs, when it
wakes up, either a descent step on a local augmented Lagrangian or an ascent
step on the local multiplier vector. Nodes realize when to switch from the
descent step to the ascent one through an asynchronous distributed logic-AND,
which detects when all the nodes have reached a predefined tolerance in the
minimization of the augmented Lagrangian. It is shown that the resulting
distributed algorithm is equivalent to a block coordinate descent for the
minimization of the global augmented Lagrangian. This allows one to extend the
properties of the centralized method of multipliers to the considered
distributed framework. Two application examples are presented to validate the
proposed approach: a distributed source localization problem and the parameter
estimation of a neural network.Comment: arXiv admin note: substantial text overlap with arXiv:1803.0648
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