arXiv subjects

Daniel W. C. Ho

Publications and source records attributed to Daniel W. C. Ho.

24 records · Page 2Linked to original sources

arXiv2019

Zeroth-Order Stochastic Block Coordinate Type Methods for Nonconvex Optimization

We study (constrained) nonconvex (composite) optimization problems where the decision variables vector can be split into blocks of variables. Random block projection is a popular technique to handle this kind of problem for its remarkable reduction of the computational cost from the projection. However, this powerful method has not been proposed for the situation that first-order information is prohibited and only zeroth-order information is available. In this paper, we propose to develop different classes of zeroth-order stochastic block coordinate type methods. Zeroth-order block coordinate descent (ZS-BCD) is proposed for solving unconstrained nonconvex optimization problem. For composite optimization, we establish the zeroth-order stochastic block mirror descent (ZS-BMD) and its associated two-phase method to achieve the complexity bound for finding $(ε,Λ)$-solution. Furthermore, we also establish zeroth-order stochastic block coordinate conditional gradient (ZS-BCCG) method for nonconvex (composite) optimization. By implementing ZS-BCCG method, in each iteration, only (approximate) linear programming subproblem needs to be solved on a random block instead of a rather costly projection subproblem on the whole decision space, in contrast to the existing traditional stochastic approximation methods. In what follows, an approximate ZS-BCCG method and corresponding two-phase ZS-BCCG method are proposed. This is also the first time that a two-phase BCCG method has been developed to achieve the $(ε, Λ)$-solution of nonconvex composite optimization problem. To the best of our knowledge, the proposed results in this paper are new in stochastic nonconvex (composite) optimization literature.

math.OC↗

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↗

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↗

arXiv2018

A New Approach to Linear/Nonlinear Distributed Fusion Estimation Problem

Disturbance noises are always bounded in a practical system, while fusion estimation is to best utilize multiple sensor data containing noises for the purpose of estimating a quantity--a parameter or process. However, few results are focused on the information fusion estimation problem under bounded noises. In this paper, we study the distributed fusion estimation problem for linear time-varying systems and nonlinear systems with bounded noises, where the addressed noises do not provide any statistical information, and are unknown but bounded. When considering linear time-varying fusion systems with bounded noises, a new local Kalman-like estimator is designed such that the square error of the estimator is bounded as time goes to $\infty$. A novel constructive method is proposed to find an upper bound of fusion estimation error, then a convex optimization problem on the design of an optimal weighting fusion criterion is established in terms of linear matrix inequalities, which can be solved by standard software packages. Furthermore, according to the design method of linear time-varying fusion systems, each local nonlinear estimator is derived for nonlinear systems with bounded noises by using Taylor series expansion, and a corresponding distributed fusion criterion is obtained by solving a convex optimization problem. Finally, target tracking system and localization of a mobile robot are given to show the advantages and effectiveness of the proposed methods.

eess.SY↗

arXiv2011

Evolution of cooperation in multilevel public goods games with community structures

In a community-structured population, public goods games (PGG) occur both within and between communities. Such type of PGG is referred as multilevel public goods games (MPGG). We propose a minimalist evolutionary model of the MPGG and analytically study the evolution of cooperation. We demonstrate that in the case of sufficiently large community size and community number, if the imitation strength within community is weak, i.e., an individual imitates another one in the same community almost randomly, cooperation as well as punishment are more abundant than defection in the long run; if the imitation strength between communities is strong, i.e., the more successful strategy in two individuals from distinct communities is always imitated, cooperation and punishment are also more abundant. However, when both of the two imitation intensities are strong, defection becomes the most abundant strategy in the population. Our model provides insight into the investigation of the large-scale cooperation in public social dilemma among contemporary communities.

q-bio.PE↗

arXiv2010

Consensus over a Random Network Generated by i.i.d. Stochastic Matrices

Our goal is to find a necessary and sufficient condition on the consensus over a random network, generated by i.i.d. stochastic matrices. We show that the consensus problem in three different convergence modes (almost surely, in probability, and in L1) are equivalent, thus have the same necessary and sufficient condition. We obtain the necessary and sufficient condition through the stability in a projected subspace.

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