47 research outputs found
FROST -- Fast row-stochastic optimization with uncoordinated step-sizes
In this paper, we discuss distributed optimization over directed graphs,
where doubly-stochastic weights cannot be constructed. Most of the existing
algorithms overcome this issue by applying push-sum consensus, which utilizes
column-stochastic weights. The formulation of column-stochastic weights
requires each agent to know (at least) its out-degree, which may be impractical
in e.g., broadcast-based communication protocols. In contrast, we describe
FROST (Fast Row-stochastic-Optimization with uncoordinated STep-sizes), an
optimization algorithm applicable to directed graphs that does not require the
knowledge of out-degrees; the implementation of which is straightforward as
each agent locally assigns weights to the incoming information and locally
chooses a suitable step-size. We show that FROST converges linearly to the
optimal solution for smooth and strongly-convex functions given that the
largest step-size is positive and sufficiently small.Comment: Submitted for journal publication, currently under revie
A Unified Contraction Analysis of a Class of Distributed Algorithms for Composite Optimization
We study distributed composite optimization over networks: agents minimize
the sum of a smooth (strongly) convex function, the agents' sum-utility, plus a
non-smooth (extended-valued) convex one. We propose a general algorithmic
framework for such a class of problems and provide a unified convergence
analysis leveraging the theory of operator splitting. Our results unify several
approaches proposed in the literature of distributed optimization for special
instances of our formulation. Distinguishing features of our scheme are: (i)
when the agents' functions are strongly convex, the algorithm converges at a
linear rate, whose dependencies on the agents' functions and the network
topology are decoupled, matching the typical rates of centralized optimization;
(ii) the step-size does not depend on the network parameters but only on the
optimization ones; and (iii) the algorithm can adjust the ratio between the
number of communications and computations to achieve the same rate of the
centralized proximal gradient scheme (in terms of computations). This is the
first time that a distributed algorithm applicable to composite optimization
enjoys such properties.Comment: To appear in the Proc. of the 2019 IEEE International Workshop on
Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 19
Distributed Nonconvex Multiagent Optimization Over Time-Varying Networks
We study nonconvex distributed optimization in multiagent networks where the
communications between nodes is modeled as a time-varying sequence of arbitrary
digraphs. We introduce a novel broadcast-based distributed algorithmic
framework for the (constrained) minimization of the sum of a smooth (possibly
nonconvex and nonseparable) function, i.e., the agents' sum-utility, plus a
convex (possibly nonsmooth and nonseparable) regularizer. The latter is usually
employed to enforce some structure in the solution, typically sparsity. The
proposed method hinges on Successive Convex Approximation (SCA) techniques
coupled with i) a tracking mechanism instrumental to locally estimate the
gradients of agents' cost functions; and ii) a novel broadcast protocol to
disseminate information and distribute the computation among the agents.
Asymptotic convergence to stationary solutions is established. A key feature of
the proposed algorithm is that it neither requires the double-stochasticity of
the consensus matrices (but only column stochasticity) nor the knowledge of the
graph sequence to implement. To the best of our knowledge, the proposed
framework is the first broadcast-based distributed algorithm for convex and
nonconvex constrained optimization over arbitrary, time-varying digraphs.
Numerical results show that our algorithm outperforms current schemes on both
convex and nonconvex problems.Comment: Copyright 2001 SS&C. Published in the Proceedings of the 50th annual
Asilomar conference on signals, systems, and computers, Nov. 6-9, 2016, CA,
US