1,010 research outputs found
Distributed Multi-Agent Optimization with State-Dependent Communication
We study distributed algorithms for solving global optimization problems in
which the objective function is the sum of local objective functions of agents
and the constraint set is given by the intersection of local constraint sets of
agents. We assume that each agent knows only his own local objective function
and constraint set, and exchanges information with the other agents over a
randomly varying network topology to update his information state. We assume a
state-dependent communication model over this topology: communication is
Markovian with respect to the states of the agents and the probability with
which the links are available depends on the states of the agents. In this
paper, we study a projected multi-agent subgradient algorithm under
state-dependent communication. The algorithm involves each agent performing a
local averaging to combine his estimate with the other agents' estimates,
taking a subgradient step along his local objective function, and projecting
the estimates on his local constraint set. The state-dependence of the
communication introduces significant challenges and couples the study of
information exchange with the analysis of subgradient steps and projection
errors. We first show that the multi-agent subgradient algorithm when used with
a constant stepsize may result in the agent estimates to diverge with
probability one. Under some assumptions on the stepsize sequence, we provide
convergence rate bounds on a "disagreement metric" between the agent estimates.
Our bounds are time-nonhomogeneous in the sense that they depend on the initial
starting time. Despite this, we show that agent estimates reach an almost sure
consensus and converge to the same optimal solution of the global optimization
problem with probability one under different assumptions on the local
constraint sets and the stepsize sequence
Primal Recovery from Consensus-Based Dual Decomposition for Distributed Convex Optimization
Dual decomposition has been successfully employed in a variety of distributed
convex optimization problems solved by a network of computing and communicating
nodes. Often, when the cost function is separable but the constraints are
coupled, the dual decomposition scheme involves local parallel subgradient
calculations and a global subgradient update performed by a master node. In
this paper, we propose a consensus-based dual decomposition to remove the need
for such a master node and still enable the computing nodes to generate an
approximate dual solution for the underlying convex optimization problem. In
addition, we provide a primal recovery mechanism to allow the nodes to have
access to approximate near-optimal primal solutions. Our scheme is based on a
constant stepsize choice and the dual and primal objective convergence are
achieved up to a bounded error floor dependent on the stepsize and on the
number of consensus steps among the nodes
A Distributed Newton Method for Network Utility Maximization
Most existing work uses dual decomposition and subgradient methods to solve
Network Utility Maximization (NUM) problems in a distributed manner, which
suffer from slow rate of convergence properties. This work develops an
alternative distributed Newton-type fast converging algorithm for solving
network utility maximization problems with self-concordant utility functions.
By using novel matrix splitting techniques, both primal and dual updates for
the Newton step can be computed using iterative schemes in a decentralized
manner with limited information exchange. Similarly, the stepsize can be
obtained via an iterative consensus-based averaging scheme. We show that even
when the Newton direction and the stepsize in our method are computed within
some error (due to finite truncation of the iterative schemes), the resulting
objective function value still converges superlinearly to an explicitly
characterized error neighborhood. Simulation results demonstrate significant
convergence rate improvement of our algorithm relative to the existing
subgradient methods based on dual decomposition.Comment: 27 pages, 4 figures, LIDS report, submitted to CDC 201
An Online Parallel and Distributed Algorithm for Recursive Estimation of Sparse Signals
In this paper, we consider a recursive estimation problem for linear
regression where the signal to be estimated admits a sparse representation and
measurement samples are only sequentially available. We propose a convergent
parallel estimation scheme that consists in solving a sequence of
-regularized least-square problems approximately. The proposed scheme
is novel in three aspects: i) all elements of the unknown vector variable are
updated in parallel at each time instance, and convergence speed is much faster
than state-of-the-art schemes which update the elements sequentially; ii) both
the update direction and stepsize of each element have simple closed-form
expressions, so the algorithm is suitable for online (real-time)
implementation; and iii) the stepsize is designed to accelerate the convergence
but it does not suffer from the common trouble of parameter tuning in
literature. Both centralized and distributed implementation schemes are
discussed. The attractive features of the proposed algorithm are also
numerically consolidated.Comment: Part of this work has been presented at The Asilomar Conference on
Signals, Systems, and Computers, Nov. 201
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