arXiv subjects

Deming Yuan

Publications and source records attributed to Deming Yuan.

At least 19 recordsLinked to original sources

arXiv2026

Differential Privacy on Affine Manifolds: Geometrically Confined Privacy in Linear Dynamical Systems

In this paper, we present a comprehensive framework for differential privacy over affine manifolds and validate its usefulness in the contexts of differentially private cloud-based control and average consensus. We consider differential privacy mechanisms for linear queries when the input data are constrained to lie on affine manifolds, a structural property that is assumed to be available as prior knowledge to adversaries. In this setting, the definition of neighborhood adjacency must be formulated with respect to the intrinsic geometry of the manifolds. We demonstrate that such affine-manifold constraints can fundamentally alter the attainable privacy levels relative to the unconstrained case. In particular, we derive necessary and sufficient conditions under which differential privacy can be realized via structured noise injection mechanisms, wherein correlated Gaussian or Laplace noise distributions, rather than i.i.d. perturbations, are calibrated to the dataset. Based on these characterizations, we develop explicit noise calibration procedures that guarantee the tight realization of any prescribed privacy budget with a matching noise magnitude. Finally, we show that the proposed framework admits direct applications to linear dynamical systems ranging from differentially private cloud-based control to privacy-preserving average consensus, all of which naturally involve affine-manifold constraints. The established theoretical results are illustrated through numerical examples.

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arXiv2025

Generic Frameworks for Distributed Functional Optimization and Learning over Time-Varying Networks

In this paper, we establish a distributed functional optimization (DFO) theory over time-varying networks. The vast majority of existing distributed optimization theories are developed based on Euclidean decision variables. However, for many scenarios in machine learning and statistical learning, such as reproducing kernel spaces or probability measure spaces that use functions or probability measures as fundamental variables, the development of existing distributed optimization theories exhibit obvious theoretical and technical deficiencies. This paper addresses these issues by developing a novel general DFO theory on Banach spaces, allowing functional learning problems in the aforementioned scenarios to be incorporated into our framework for resolution. We study both convex and nonconvex DFO problems and rigorously establish a comprehensive convergence theory of distributed functional mirror descent and distributed functional gradient descent algorithm to solve them. Satisfactory convergence rates are fully derived. The work has provided generic analyzing frameworks for DFO. The established theory is shown to have crucial application value in the kernel-based distributed learning theory over networks.

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arXiv2025

Distributed Stochastic Optimization under Heavy-Tailed Noise: A Federated Mirror Descent Approach with High Probability Convergence

We study the distributed stochastic optimization (DSO) problem under a heavy-tailed noise condition by utilizing a multi-agent system. Despite the extensive research on DSO algorithms used to solve DSO problems under light-tailed noise conditions (such as Gaussian noise), there is a significant lack of study of DSO algorithms in the context of heavy-tailed random noise. Classical DSO approaches in a heavy-tailed setting may present poor convergence behaviors. Therefore, developing DSO methods in the context of heavy-tailed noises is of importance. This work follows this path and we consider the setting that the gradient noises associated with each agent can be heavy-tailed, potentially having unbounded variance. We propose a clipped federated stochastic mirror descent algorithm to solve the DSO problem. We rigorously present a convergence theory and show that, under appropriate rules on the stepsize and the clipping parameter associated with the local noisy gradient influenced by the heavy-tailed noise, the algorithm is able to achieve satisfactory high probability convergence.

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arXiv2025

Distributed Online Stochastic Convex-Concave Optimization: Dynamic Regret Analyses under Single and Multiple Consensus Steps

This paper considers the distributed online convex-concave optimization with constraint sets over a multiagent network, in which each agent autonomously generates a series of decision pairs through a designable mechanism to cooperatively minimize the global loss function. To this end, under no-Euclidean distance metrics, we propose a distributed online stochastic mirror descent convex-concave optimization algorithm with time-varying predictive mappings. Taking dynamic saddle point regret as a performance metric, it is proved that the proposed algorithm achieves the regret upper-bound in $\mathcal{O}(\max \{T^{\theta_1}, T^{\theta_2} (1+V_T ) \})$ for the general convex-concave loss function, where $\theta_1, \theta_2 \in(0,1)$ are the tuning parameters, $T$ is the total iteration time, and $V_T$ is the path-variation. Surely, this algorithm guarantees the sublinear convergence, provided that $V_T$ is sublinear. Moreover, aiming to achieve better convergence, we further investigate a variant of this algorithm by employing the multiple consensus technique. The obtained results show that the appropriate setting can effectively tighten the regret bound to a certain extent. Finally, the efficacy of the proposed algorithms is validated and compared through the simulation example of a target tracking problem.

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arXiv2025

High-Probability Convergence Theory for Distributed Composite Optimization with Sub-Weibull Noises

With the rapid development of distributed optimization (DO) theory, the distributed stochastic gradient methods (DSGMs) occupy an important position. Although the theory of different DSGMs has been widely established, the main-stream results of existing work are still derived under the condition of light-tailed stochastic gradient noises. Increasing examples from various fields, indicate that, the light-tailed noise model is overly idealized in many practical instances, failing to capture the complexity and variability of noises in real-world scenarios, such as the presence of outliers or extreme values from data science and statistical learning. To address this issue, we propose a new DO framework that incorporates stochastic gradients under sub-Weibull randomness. We study a distributed composite stochastic mirror descent scheme with sub-Weibull gradient noise (DCSMD-SW) for solving a convex distributed composite optimization (DCO) problem over the time-varying multi-agent network. By investigating sub-Weibull randomness in DCSMD for the first time, we show that the algorithm is applicable in some common heavier-tailed noise environments while also guaranteeing good convergence properties. We comprehensively study the convergence performance of DCSMD-SW. Satisfactory high-probability convergence rates are derived for DCSMD-SW without any smoothness requirement. The work also offers a unified analytical framework for several critical cases of both algorithms and noise environments.

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arXiv2024

Distributed Optimization by Network Flows with Spatio-Temporal Compression

Several data compressors have been proposed in distributed optimization frameworks of network systems to reduce communication overhead in large-scale applications. In this paper, we demonstrate that effective information compression may occur over time or space during sequences of node communications in distributed algorithms, leading to the concept of spatio-temporal compressors. This abstraction classifies existing compressors and inspires new compressors as spatio-temporal compressors, with their effectiveness described by constructive stability criteria from nonlinear system theory. Subsequently, we incorporate these spatio-temporal compressors directly into standard continuous-time consensus flows and distributed primal-dual flows, establishing conditions ensuring exponential convergence. Additionally, we introduce a novel observer-based distributed primal-dual continuous flow integrated with spatio-temporal compressors, which provides broader convergence conditions. These continuous flows achieve exponential convergence to the global optimum when the objective function is strongly convex and can be discretized using Euler approximations. Finally, numerical simulations illustrate the versatility of the proposed spatio-temporal compressors and verify the convergence of

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arXiv2024

Spatio-Temporal Communication Compression in Distributed Prime-Dual Flows

In this paper, we study distributed prime-dual flows for multi-agent optimization with spatio-temporal compressions. The central aim of multi-agent optimization is for a network of agents to collaboratively solve a system-level optimization problem with local objective functions and node-to-node communication by distributed algorithms. The scalability of such algorithms crucially depends on the complexity of the communication messages, and a number of communication compressors for distributed optimization have recently been proposed in the literature. First of all, we introduce a general spatio-temporal compressor characterized by the stability of the resulting dynamical system along the vector field of the compressor. We show that several important distributed optimization compressors such as the greedy sparsifier, the uniform quantizer, and the scalarizer all fall into the category of this spatio-temporal compressor. Next, we propose two distributed prime-dual flows with the spatio-temporal compressors being applied to local node states and local error states, respectively, and prove (exponential) convergence of the node trajectories to the global optimizer for (strongly) convex cost functions. Finally, a few numerical examples are present to illustrate our theoretical results.

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arXiv2024

Distributed Solvers for Network Linear Equations with Scalarized Compression

Distributed computing is fundamental to multi-agent systems, with solving distributed linear equations as a typical example. In this paper, we study distributed solvers for network linear equations over a network with node-to-node communication messages compressed as scalar values. Our key idea lies in a dimension compression scheme that includes a dimension-compressing vector and a data unfolding step. The compression vector applies to individual node states as an inner product to generate a real-valued message for node communication. In the unfolding step, such scalar message is then plotted along the subspace generated by the compression vector for the local computations. We first present a compressed consensus flow that relies only on such scalarized communication, and show that linear convergence can be achieved with well excited signals for the compression vector. We then employ such a compressed consensus flow as a fundamental consensus subroutine to develop distributed continuous-time and discrete-time solvers for network linear equations, and prove their linear convergence properties under scalar node communications. With scalar communications, a direct benefit would be the reduced node-to-node communication channel burden for distributed computing. Numerical examples are presented to illustrate the effectiveness of the established theoretical results.

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arXiv2023

Improved Dynamic Regret of Distributed Online Multiple Frank-Wolfe Convex Optimization

In this paper, we consider a distributed online convex optimization problem over a time-varying multi-agent network. The goal of this network is to minimize a global loss function through local computation and communication with neighbors. To effectively handle the optimization problem with a high-dimensional and structural constraint set, we develop a distributed online multiple Frank-Wolfe algorithm to avoid the expensive computational cost of projection operation. The dynamic regret bounds are established as $\mathcal{O}(T^{1-γ}+H_T)$ with the linear oracle number $\mathcal{O} (T^{1+γ})$, which depends on the horizon (total iteration number) $T$, the function variation $H_T$, and the tuning parameter $0<γ<1$. In particular, when the prior knowledge of $H_T$ and $T$ is available, the bound can be enhanced to $\mathcal{O} (1+H_T)$. Moreover, we illustrate the significant advantages of the multiple iteration technique and reveal a trade-off between dynamic regret bound, computational cost, and communication cost. Finally, the performance of our algorithm is verified and compared through the distributed online ridge regression problems with two constraint sets.

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arXiv2023

Riemannian Optimistic Algorithms

In this paper, we consider Riemannian online convex optimization with dynamic regret. First, we propose two novel algorithms, namely the Riemannian Online Optimistic Gradient Descent (R-OOGD) and the Riemannian Adaptive Online Optimistic Gradient Descent (R-AOOGD), which combine the advantages of classical optimistic algorithms with the rich geometric properties of Riemannian manifolds. We analyze the dynamic regrets of the R-OOGD and R-AOOGD in terms of regularity of the sequence of cost functions and comparators. Next, we apply the R-OOGD to Riemannian zero-sum games, leading to the Riemannian Optimistic Gradient Descent Ascent algorithm (R-OGDA). We analyze the average iterate and best-iterate of the R-OGDA in seeking Nash equilibrium for a two-player, zero-sum, g-convex-concave games. We also prove the last-iterate convergence of the R-OGDA for g-strongly convex-strongly concave problems. Our theoretical analysis shows that all proposed algorithms achieve results in regret and convergence that match their counterparts in Euclidean spaces. Finally, we conduct several experiments to verify our theoretical findings.

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arXiv2023

Quantized Distributed Online Projection-free Convex Optimization

This paper considers online distributed convex constrained optimization over a time-varying multi-agent network. Agents in this network cooperate to minimize the global objective function through information exchange with their neighbors and local computation. Since the capacity or bandwidth of communication channels often is limited, a random quantizer is introduced to reduce the transmission bits. Through incorporating this quantizer, we develop a quantized distributed online projection-free optimization algorithm, which can achieve the saving of communication resources and computational costs. For different parameter settings of the quantizer, we establish the corresponding dynamic regret upper bounds of the proposed algorithm and reveal the trade-off between the convergence performance and the quantization effect. Finally, the theoretical results are illustrated by the simulation of distributed online linear regression problem.

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arXiv2023

Dynamic Regret of Distributed Online Frank-Wolfe Convex Optimization

This paper considers distributed online convex constrained optimization, in which various agents in a multi-agent system cooperate to minimize a global cost function through communicating with neighbors over a time-varying network. When the constraint set of optimization problem is high-dimensional and complicated, the computational cost of the projection operation often becomes prohibitive. To handle this problem, we develop a distributed online Frank-Wolfe optimization algorithm combining with gradient tracking technique. We rigorously establish the dynamic regret bound of the proposed optimization algorithm as $\mathcal{O}(\sqrt{T(1+H_T)}+D_T)$, which explicitly depends on the iteration round $T$, function variation $H_T$, and gradient variation $D_T$. Finally, the theoretical results are verified and compared in the case of distributed online ridge regression problems.

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arXiv2022

Distributed Stochastic Constrained Composite Optimization over Time-Varying Network with a Class of Communication Noise

This paper is concerned with distributed stochastic multi-agent constrained optimization problem over time-varying network with a class of communication noise. This paper considers the problem in composite optimization setting which is more general in the literature of noisy network optimization. It is noteworthy that the mainstream existing methods for noisy network optimization are Euclidean projection based. Based on Bregman projection-based mirror descent scheme, we present a non-Euclidean method and investigate their convergence behavior. This method is the distributed stochastic composite mirror descent type method (DSCMD-N) which provides a more general algorithm framework. Some new error bounds for DSCMD-N are obtained. 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 also show that an optimal rate of $O(1/\sqrt{T})$ in nonsmooth convex optimization can be obtained for the proposed method under appropriate communication noise condition. Moreover, novel convergence results are comprehensively derived in expectation convergence, high probability convergence, and almost surely sense.

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arXiv2022

Push-sum Distributed Dual Averaging for Convex Optimization in Multi-agent Systems with Communication Delays

The distributed convex optimization problem over the multi-agent system is considered in this paper, and it is assumed that each agent possesses its own cost function and communicates with its neighbours over a sequence of time-varying directed graphs. However, due to some reasons there exist communication delays while agents receive information from other agents, and we are going to seek the optimal value of the sum of agents' loss functions in this case. We desire to handle this problem with the push-sum distributed dual averaging (PS-DDA) algorithm. It is proved that this algorithm converges and the error decays at a rate $\mathcal{O}\left(T^{-0.5}\right)$ with proper step size, where $T$ is iteration span. The main result presented in this paper also illustrates the convergence of the proposed algorithm is related to the maximum value of the communication delay on one edge. We finally apply the theoretical results to numerical simulations to show the PS-DDA algorithm's performance.

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arXiv2021

Towards Online Optimization for Power Grids

In this note, we discuss potential advantages in extending distributed optimization frameworks to enhance support for power grid operators managing an influx of online sequential decisions. First, we review the state-of-the-art distributed optimization frameworks for electric power systems, and explain how distributed algorithms deliver scalable solutions. Next, we introduce key concepts and paradigms for online optimization, and present a distributed online optimization framework highlighting important performance characteristics. Finally, we discuss the connection and difference between offline and online distributed optimization, showcasing the suitability of such optimization techniques for power grid applications.

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arXiv2021

Dynamics of Opinions with Bounded Confidence in Social Cliques: Emergence of Fluctuations

In this paper, we study the evolution of opinions over social networks with bounded confidence in social cliques. Node initial opinions are independently and identically distributed; at each time step, nodes review the average opinions of a randomly selected local clique. The clique averages may represent local group pressures on peers. Then nodes update their opinions under bounded confidence: only when the difference between an agent individual opinion and the corresponding local clique pressure is below a threshold, this agent opinion is updated according to the DeGroot rule as a weighted average of the two values. As a result, this opinion dynamics is a generalization of the classical Deffuant-Weisbuch model in which only pairwise interactions take place. First of all, we prove conditions under which all node opinions converge to finite limits. We show that in the limits the event that all nodes achieve a consensus, and the event that all nodes achieve pairwise distinct limits, i.e., social disagreements, are both nontrivial events. Next, we show that opinion fluctuations may take place in the sense that at least one agent in the network fails to hold a converging opinion trajectory. In fact, we prove that this fluctuation event happens with a strictly positive probability, and also constructively present an initial value event under which the fluctuation event arises with probability one. These results add to the understanding of the role of bounded confidence in social opinion dynamics, and the possibility of fluctuation reveals that bringing in cliques in Deffuant-Weisbuch models have fundamentally changed the behavior of such opinion dynamical processes.

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arXiv2020

Distributed Mirror Descent for Online Composite Optimization

In this paper, we consider an online distributed composite optimization problem over a time-varying multi-agent network that consists of multiple interacting nodes, where the objective function of each node consists of two parts: a loss function that changes over time and a regularization function. This problem naturally arises in many real-world applications ranging from wireless sensor networks to signal processing. We propose a class of online distributed optimization algorithms that are based on approximate mirror descent, which utilize the Bregman divergence as distance-measuring function that includes the Euclidean distances as a special case. We consider two standard information feedback models when designing the algorithms, that is, full-information feedback and bandit feedback. For the full-information feedback model, the first algorithm attains an average regularized regret of order $\mathcal{O}(1/\sqrt{T})$ with the total number of rounds $T$. The second algorithm, which only requires the information of the values of the loss function at two predicted points instead of the gradient information, achieves the same average regularized regret as that of the first algorithm. Simulation results of a distributed online regularized linear regression problem are provided to illustrate the performance of the proposed algorithms.

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arXiv2019

Distributed Online Optimization with Long-Term Constraints

We consider distributed online convex optimization problems, where the distributed system consists of various computing units connected through a time-varying communication graph. In each time step, each computing unit selects a constrained vector, experiences a loss equal to an arbitrary convex function evaluated at this vector, and may communicate to its neighbors in the graph. The objective is to minimize the system-wide loss accumulated over time. We propose a decentralized algorithm with regret and cumulative constraint violation in $\mathcal{O}(T^{\max\{c,1-c\} })$ and $\mathcal{O}(T^{1-c/2})$, respectively, for any $c\in (0,1)$, where $T$ is the time horizon. When the loss functions are strongly convex, we establish improved regret and constraint violation upper bounds in $\mathcal{O}(\log(T))$ and $\mathcal{O}(\sqrt{T\log(T)})$. These regret scalings match those obtained by state-of-the-art algorithms and fundamental limits in the corresponding centralized online optimization problem (for both convex and strongly convex loss functions). In the case of bandit feedback, the proposed algorithms achieve a regret and constraint violation in $\mathcal{O}(T^{\max\{c,1-c/3 \} })$ and $\mathcal{O}(T^{1-c/2})$ for any $c\in (0,1)$. We numerically illustrate the performance of our algorithms for the particular case of distributed online regularized linear regression problems.

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