20,180 research outputs found
Stochastic Subgradient Algorithms for Strongly Convex Optimization over Distributed Networks
We study diffusion and consensus based optimization of a sum of unknown
convex objective functions over distributed networks. The only access to these
functions is through stochastic gradient oracles, each of which is only
available at a different node, and a limited number of gradient oracle calls is
allowed at each node. In this framework, we introduce a convex optimization
algorithm based on the stochastic gradient descent (SGD) updates. Particularly,
we use a carefully designed time-dependent weighted averaging of the SGD
iterates, which yields a convergence rate of
after gradient updates for each node on
a network of nodes. We then show that after gradient oracle calls, the
average SGD iterate achieves a mean square deviation (MSD) of
. This rate of convergence is optimal as it
matches the performance lower bound up to constant terms. Similar to the SGD
algorithm, the computational complexity of the proposed algorithm also scales
linearly with the dimensionality of the data. Furthermore, the communication
load of the proposed method is the same as the communication load of the SGD
algorithm. Thus, the proposed algorithm is highly efficient in terms of
complexity and communication load. We illustrate the merits of the algorithm
with respect to the state-of-art methods over benchmark real life data sets and
widely studied network topologies
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
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