Distributed Stochastic Optimization over Time-Varying Noisy Network

This paper is concerned with distributed stochastic multi-agent optimization problem over a class of time-varying network with slowly decreasing communication noise effects. This paper considers the problem in composite optimization setting which is more general in noisy network optimization. It is noteworthy that existing methods for noisy network optimization are Euclidean projection based. We present two related different classes of non-Euclidean methods and investigate their convergence behavior. One is distributed stochastic composite mirror descent type method (DSCMD-N) which provides a more general algorithm framework than former works in this literature. As a counterpart, we also consider a composite dual averaging type method (DSCDA-N) for noisy network optimization. Some main error bounds for DSCMD-N and DSCDA-N are obtained. The trade-off among stepsizes, noise decreasing rates, convergence rates of algorithm is analyzed in detail. To the best of our knowledge, this is the first work to analyze and derive convergence rates of optimization algorithm in noisy network optimization. We show that an optimal rate of $O(1/\sqrt{T})$ in nonsmooth convex optimization can be obtained for proposed methods under appropriate communication noise condition. Moveover, convergence rates in different orders are comprehensively derived in both expectation convergence and high probability convergence sense.Comment: 27 page

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.Comment: 9 pages, 3 figure

Variance-constrained control for uncertain stochastic systems with missing measurements

Copyright [2005] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we are concerned with a new control problem for uncertain discrete-time stochastic systems with missing measurements. The parameter uncertainties are allowed to be norm-bounded and enter into the state matrix. The system measurements may be unavailable (i.e., missing data) at any sample time, and the probability of the occurrence of missing data is assumed to be known. The purpose of this problem is to design an output feedback controller such that, for all admissible parameter uncertainties and all possible incomplete observations, the system state of the closed-loop system is mean square bounded, and the steady-state variance of each state is not more than the individual prescribed upper bound. We show that the addressed problem can be solved by means of algebraic matrix inequalities. The explicit expression of the desired robust controllers is derived in terms of some free parameters, which may be exploited to achieve further performance requirements. An illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach

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.Comment: 6 pages, 4 figures, Accepted by EP

Estimates on Learning Rates for Multi-Penalty Distribution Regression

This paper is concerned with functional learning by utilizing two-stage sampled distribution regression. We study a multi-penalty regularization algorithm for distribution regression under the framework of learning theory. The algorithm aims at regressing to real valued outputs from probability measures. The theoretical analysis on distribution regression is far from maturity and quite challenging, since only second stage samples are observable in practical setting. In the algorithm, to transform information from samples, we embed the distributions to a reproducing kernel Hilbert space $\mathcal{H}_K$ associated with Mercer kernel $K$ via mean embedding technique. The main contribution of the paper is to present a novel multi-penalty regularization algorithm to capture more features of distribution regression and derive optimal learning rates for the algorithm. The work also derives learning rates for distribution regression in the nonstandard setting $f_{\rho}\notin\mathcal{H}_K$, which is not explored in existing literature. Moreover, we propose a distribution regression-based distributed learning algorithm to face large-scale data or information challenge. The optimal learning rates are derived for the distributed learning algorithm. By providing new algorithms and showing their learning rates, we improve the existing work in different aspects in the literature

Robust finite-horizon filtering for stochastic systems with missing measurements

Copyright [2005] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this letter, we consider the robust finite-horizon filtering problem for a class of discrete time-varying systems with missing measurements and norm-bounded parameter uncertainties. The missing measurements are described by a binary switching sequence satisfying a conditional probability distribution. An upper bound for the state estimation error variance is first derived for all possible missing observations and all admissible parameter uncertainties. Then, a robust filter is designed, guaranteeing that the variance of the state estimation error is not more than the prescribed upper bound. It is shown that the desired filter can be obtained in terms of the solutions to two discrete Riccati difference equations, which are of a form suitable for recursive computation in online applications. A simulation example is presented to show the effectiveness of the proposed approach by comparing to the traditional Kalman filtering method