arXiv subjects

Deming Yuan

Publications and source records attributed to Deming Yuan.

21 records · Page 2Linked to original sources

arXiv2019

Distributed Randomized Gradient-Free Mirror Descent Algorithm for Constrained Optimization

This paper is concerned with multi-agent optimization problem. A distributed randomized gradient-free mirror descent (DRGFMD) method is developed by introducing a randomized gradient-free oracle in the mirror descent scheme where the non-Euclidean Bregman divergence is used. The classical gradient descent method is generalized without using subgradient information of objective functions. The proposed algorithm is the first distributed non-Euclidean zeroth-order method which achieves an $O(1/\sqrt{T})$ convergence rate, recovering the best known optimal rate of distributed compact constrained convex optimization. Also, the DRGFMD algorithm achieves an $O(\ln T/T)$ convergence rate for the strongly convex constrained optimization case. The rate matches the best known non-compact constraint result. Moreover, a decentralized reciprocal weighted average approximating sequence is investigated and first used in distributed algorithm. A class of convergence rates are also achieved for the algorithm with weighted averaging (DRGFMD-WA). The technique on constructing the decentralized weighted average sequence provides new insight in searching for minimizers in distributed algorithms.

math.OC↗

arXiv2019

Distributed Online Linear Regression

We study online linear regression problems in a distributed setting, where the data is spread over a network. In each round, each network node proposes a linear predictor, with the objective of fitting the \emph{network-wide} data. It then updates its predictor for the next round according to the received local feedback and information received from neighboring nodes. The predictions made at a given node are assessed through the notion of regret, defined as the difference between their cumulative network-wide square errors and those of the best off-line network-wide linear predictor. Various scenarios are investigated, depending on the nature of the local feedback (full information or bandit feedback), on the set of available predictors (the decision set), and the way data is generated (by an oblivious or adaptive adversary). We propose simple and natural distributed regression algorithms, involving, at each node and in each round, a local gradient descent step and a communication and averaging step where nodes aim at aligning their predictors to those of their neighbors. We establish regret upper bounds typically in ${\cal O}(T^{3/4})$ when the decision set is unbounded and in ${\cal O}(\sqrt{T})$ in case of bounded decision set.

cs.LG↗

arXiv2018

Optimal Distributed Stochastic Mirror Descent for Strongly Convex Optimization

In this paper we consider convergence rate problems for stochastic strongly-convex optimization in the non-Euclidean sense with a constraint set over a time-varying multi-agent network. We propose two efficient non-Euclidean stochastic subgradient descent algorithms based on the Bregman divergence as distance-measuring function rather than the Euclidean distances that were employed by the standard distributed stochastic projected subgradient algorithms. For distributed optimization of nonsmooth and strongly convex functions whose only stochastic subgradients are available, the first algorithm recovers the best previous known rate of O(ln(T)/T) (where T is the total number of iterations). The second algorithm is an epoch variant of the first algorithm that attains the optimal convergence rate of O(1/T), matching that of the best previously known centralized stochastic subgradient algorithm. Finally, we report some simulation results to illustrate the proposed algorithms.

math.OC↗