7 research outputs found
Snake: a Stochastic Proximal Gradient Algorithm for Regularized Problems over Large Graphs
A regularized optimization problem over a large unstructured graph is
studied, where the regularization term is tied to the graph geometry. Typical
regularization examples include the total variation and the Laplacian
regularizations over the graph. When applying the proximal gradient algorithm
to solve this problem, there exist quite affordable methods to implement the
proximity operator (backward step) in the special case where the graph is a
simple path without loops. In this paper, an algorithm, referred to as "Snake",
is proposed to solve such regularized problems over general graphs, by taking
benefit of these fast methods. The algorithm consists in properly selecting
random simple paths in the graph and performing the proximal gradient algorithm
over these simple paths. This algorithm is an instance of a new general
stochastic proximal gradient algorithm, whose convergence is proven.
Applications to trend filtering and graph inpainting are provided among others.
Numerical experiments are conducted over large graphs
Distributed feedback-aided subspace concurrent opportunistic communications
© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This paper deals with the distributed subspace agreement problem for opportunistic communications in time division duplex (TDD) distributed networks. Since scenario-adapted opportunistic transmission schemes rely on locally sampled observations from the wireless environment, degrees-of-freedom (DoF) sensed as available at any node may differ. Transmitting information without agreeing the common active subspace may incur in a performance loss due to noise enhancement, energy loss and inter-system interference. In this context, we propose two subspace concurrence schemes with and without side information about neighboring user's DoF.Peer ReviewedPostprint (published version
Federated Variance-Reduced Stochastic Gradient Descent with Robustness to Byzantine Attacks
This paper deals with distributed finite-sum optimization for learning over
networks in the presence of malicious Byzantine attacks. To cope with such
attacks, most resilient approaches so far combine stochastic gradient descent
(SGD) with different robust aggregation rules. However, the sizeable
SGD-induced stochastic gradient noise makes it challenging to distinguish
malicious messages sent by the Byzantine attackers from noisy stochastic
gradients sent by the 'honest' workers. This motivates us to reduce the
variance of stochastic gradients as a means of robustifying SGD in the presence
of Byzantine attacks. To this end, the present work puts forth a Byzantine
attack resilient distributed (Byrd-) SAGA approach for learning tasks involving
finite-sum optimization over networks. Rather than the mean employed by
distributed SAGA, the novel Byrd- SAGA relies on the geometric median to
aggregate the corrected stochastic gradients sent by the workers. When less
than half of the workers are Byzantine attackers, the robustness of geometric
median to outliers enables Byrd-SAGA to attain provably linear convergence to a
neighborhood of the optimal solution, with the asymptotic learning error
determined by the number of Byzantine workers. Numerical tests corroborate the
robustness to various Byzantine attacks, as well as the merits of Byrd- SAGA
over Byzantine attack resilient distributed SGD