arXiv subjects

Daniel W. C. Ho

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

At least 19 recordsLinked to original sources

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

Primal-dual policy learning for mean-field stochastic LQR problem

Integrating data-driven techniques with mechanism-driven insights has recently gained popularity as a powerful learning approach to solving traditional LQR problems for designing intelligent controllers in complex dynamic systems. However, the theoretical understanding of various reinforcement learning algorithms needs further exploration to enhance their efficiency and safety. In this article, by means of primal-dual optimization tools, we study the partially model-free design of the mean-field stochastic LQR (MF-SLQR) controller using a policy learning approach. Firstly, by designing appropriate optimizing variables, the considered MF-SLQR problem is transformed into a new static nonconvex constrained optimization problem with equivalence preserved in certain senses. After that, the equivalent formulation of the duality results is constructed via finding the solution of the generalized Lyapunov equation. Then, the strong duality is analyzed, based on which we establish a primal-dual algorithm by Karush-Kuhn-Tucker conditions. More importantly, a partially model-free implementation is also presented, which has a direct connection with the classical policy iteration algorithm. Finally, we use a high-dimensional example to validate our methods.

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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

Real-time Estimation of DoS Duration and Frequency for Security Control

In this paper, we develop a new denial-of-service (DoS) estimator, enabling defenders to identify duration and frequency parameters of any DoS attacker, except for three edge cases, exclusively using real-time data. The key advantage of the estimator lies in its capability to facilitate security control in a wide range of practical scenarios, even when the attacker's information is previously unknown. We demonstrate the advantage and application of our new estimator in the context of two classical control scenarios, namely consensus of multi-agent systems and impulsive stabilization of nonlinear systems, for illustration.

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arXiv2024

Stability Analysis of Distributed Estimators for Large-Scale Interconnected Systems: Time-Varying and Time-Invariant Cases

This paper studies a distributed estimation problem for time-varying/time-invariant large-scale interconnected systems (LISs). A fully distributed estimator is presented by recursively solving a distributed modified Riccati equation (DMRE) with decoupling variables. By partitioning the LIS based on the transition matrix's block structure, it turns out that the stability of the subsystem is independent of the global LIS if the decoupling variable is selected as the number of out-neighbors. Additionally, it is revealed that any LIS can be equivalently represented by a Markov system. Based on this insight, we show that the stability decoupling above can also be achieved if the decoupling variable equals the number of in-neighbors. Then, the distributed estimator is proved to be stable if the DMRE remains uniformly bounded. When the LIS is considered time-invariant, and by analyzing the spectral radius of a linear operator, it is proved that the DMRE is uniformly bounded if and only if a linear matrix inequality is feasible. Based on the boundedness result, we also show that the distributed estimator converges to a unique steady state for any initial condition. Finally, simulations verify the effectiveness of the proposed methods.

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arXiv2024

Distributed Stochastic Block Coordinate Descent for Time-Varying Multi-Agent Optimization

In this paper, a class of large-scale distributed nonsmooth convex optimization problem over time-varying multi-agent network is investigated. Specifically, the decision space which can be split into several blocks of convex set is considered. We present a distributed block coordinate descent (DSBCD) method in which for each node, information communication with other agents and a block Bregman projection are performed in each iteration. In contrast to existing work, we do not require the projection is operated on the whole decision space. Instead, in each step, distributed projection procedure is performed on only one random block. The explicit formulation of the convergence level depending on random projection probabilities and network parameters is achieved. An expected $O(1/\sqrt{T})$ rate is achieved. In addition, we obtain an explicit $\mathcal{O}(b^2/ε^2)$ complexity bound with target accuracy $ε$ and characteristic constant factor $b$. The complexity with dependency on $ε$ and $b$ is shown to be the best known in this literature.

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arXiv2024

A Safety Modulator Actor-Critic Method in Model-Free Safe Reinforcement Learning and Application in UAV Hovering

This paper proposes a safety modulator actor-critic (SMAC) method to address safety constraint and overestimation mitigation in model-free safe reinforcement learning (RL). A safety modulator is developed to satisfy safety constraints by modulating actions, allowing the policy to ignore safety constraint and focus on maximizing reward. Additionally, a distributional critic with a theoretical update rule for SMAC is proposed to mitigate the overestimation of Q-values with safety constraints. Both simulation and real-world scenarios experiments on Unmanned Aerial Vehicles (UAVs) hovering confirm that the SMAC can effectively maintain safety constraints and outperform mainstream baseline algorithms.

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arXiv2023

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 $f_ρ\notin\mathcal{H}_K$, 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.

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arXiv2023

Synchronization of multiple rigid body systems: a survey

The multi-agent system has been a hot topic in the past few decades owing to its lower cost, higher robustness, and higher flexibility. As a particular multi-agent system, the multiple rigid body system received a growing interest for its wide applications in transportation, aerospace, and ocean exploration. Due to the non-Euclidean configuration space of attitudes and the inherent nonlinearity of the dynamics of rigid body systems, synchronization of multiple rigid body systems is quite challenging. This paper aims to present an overview of the recent progress in synchronization of multiple rigid body systems from the view of two fundamental problems. The first problem focuses on attitude synchronization, while the second one focuses on cooperative motion control in that rotation and translation dynamics are coupled. Finally, a summary and future directions are given in the conclusion.

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arXiv2022

Secure Fusion Estimation Against FDI Sensor Attacks in Cyber-Physical Systems

This paper is concerned with the problem of secure multi-sensors fusion estimation for cyber-physical systems, where sensor measurements may be tampered with by false data injection (FDI) attacks. In this work, it is considered that the adversary may not be able to attack all sensors. That is, several sensors remain not being attacked. In this case, new local reorganized subsystems including the FDI attack signals and un-attacked sensor measurements are constructed by the augmentation method. Then, a joint Kalman fusion estimator is designed under linear minimum variance sense to estimate the system state and FDI attack signals simultaneously. Finally, illustrative examples are employed to show the effectiveness and advantages of the proposed methods.

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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

Distributed Estimation for Interconnected Systems with Arbitrary Coupling Structures

This paper is concerned with the problem of distributed estimation for time-varying interconnected dynamic systems with arbitrary coupling structures. To guarantee the robustness of the designed estimators, novel distributed stability conditions are proposed with only local information and the information from neighbors. Then, simplified stability conditions which do not require timely exchange of neighbors' estimator gain information is further developed for systems with delayed communication. By merging these subsystem-level stability conditions and the optimization-based estimator gain design, the distributed, stable and optimal estimators are proposed. Quite notably, these optimization solutions can be easily obtained by standard software packages, and it is also shown that the designed estimators are scalable in the sense of adding or subtracting subsystems. Finally, an illustrative example is employed to show the effectiveness of the proposed methods.

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arXiv2021

Delay-Dependent Distributed Kalman Fusion Estimation with Dimensionality Reduction in Cyber-Physical Systems

This paper studies the distributed dimensionality reduction fusion estimation problem with communication delays for a class of cyber-physical systems (CPSs). The raw measurements are preprocessed in each sink node to obtain the local optimal estimate (LOE) of a CPS, and the compressed LOE under dimensionality reduction encounters with communication delays during the transmission. Under this case, a mathematical model with compensation strategy is proposed to characterize the dimensionality reduction and communication delays. This model also has the property to reduce the information loss caused by the dimensionality reduction and delays. Based on this model, a recursive distributed Kalman fusion estimator (DKFE) is derived by optimal weighted fusion criterion in the linear minimum variance sense. A stability condition for the DKFE, which can be easily verified by the exiting software, is derived. In addition, this condition can guarantee that estimation error covariance matrix of the DKFE converges to the unique steady-state matrix for any initial values, and thus the steady-state DKFE (SDKFE) is given. Notice that the computational complexity of the SDKFE is much lower than that of the DKFE. Moreover, a probability selection criterion for determining the dimensionality reduction strategy is also presented to guarantee the stability of the DKFE. Two illustrative examples are given to show the advantage and effectiveness of the proposed methods.

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arXiv2021

Polynomial-Time Algorithms for Structurally Observable Graphs by Controlling Minimal Vertices

The aim of this paper is to characterize an important class of marked digraphs, called structurally observable graphs (SOGs), and to solve two minimum realization problems. To begin with, by exploring structural observability of large-scale Boolean networks (LSBNs), an underlying type of SOGs is provided based on a recent observability criterion of conjunctive BNs. Besides, SOGs are also proved to have important applicability to structural observability of general discrete-time systems. Further, two minimum realization strategies are considered to induce an SOG from an arbitrarily given digraph by marking and controlling the minimal vertices, respectively. It indicates that one can induce an observable system by means of adding the minimal sensors or modifying the adjacency relation of minimal vertices. Finally, the structural observability of finite-field networks, and the minimum pinned node theorem for Boolean networks are displayed as application and simulation. The most salient superiority is that the designed algorithms are polynomial time and avoid exhaustive brute-force searches. It means that our results can be applied to deal with the observability of large-scale systems (particularly, LSBNs), whose observability analysis and the minimum controlled node theorem are known as intractable problems.

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arXiv2021

Distributed Constrained Optimization with Delayed Subgradient Information over Time-Varying Network under Adaptive Quantization

In this paper, we consider a distributed constrained optimization problem with delayed subgradient information over the time-varying communication network, where each agent can only communicate with its neighbors and the communication channel has a limited data rate. We propose an adaptive quantization method to address this problem. A mirror descent algorithm with delayed subgradient information is established based on the theory of Bregman divergence. With non-Euclidean Bregman projection-based scheme, the proposed method essentially generalizes many previous classical Euclidean projection-based distributed algorithms. Through the proposed adaptive quantization method, the optimal value without any quantization error can be obtained. Furthermore, comprehensive analysis on convergence of the algorithm is carried out and our results show that the optimal convergence rate $O(1/\sqrt{T})$ can be obtained under appropriate conditions. Finally, numerical examples are presented to demonstrate the effectiveness of our algorithm and theoretical results.

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arXiv2021

Robust Kernel-based Distribution Regression

Regularization schemes for regression have been widely studied in learning theory and inverse problems. In this paper, we study distribution regression (DR) which involves two stages of sampling, and aims at regressing from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS). Recently, theoretical analysis on DR has been carried out via kernel ridge regression and several learning behaviors have been observed. However, the topic has not been explored and understood beyond the least square based DR. By introducing a robust loss function $l_σ$ for two-stage sampling problems, we present a novel robust distribution regression (RDR) scheme. With a windowing function $V$ and a scaling parameter $σ$ which can be appropriately chosen, $l_σ$ can include a wide range of popular used loss functions that enrich the theme of DR. Moreover, the loss $l_σ$ is not necessarily convex, hence largely improving the former regression class (least square) in the literature of DR. The learning rates under different regularity ranges of the regression function $f_ρ$ are comprehensively studied and derived via integral operator techniques. The scaling parameter $σ$ is shown to be crucial in providing robustness and satisfactory learning rates of RDR.

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arXiv2020

A New Approach to Pinning Control of Boolean Networks

Boolean networks (BNs) are discrete-time systems where nodes are inter-connected (here we call such connection rule among nodes as network structure), and the dynamics of each gene node is determined by logical functions. In this paper, we propose a new approach on pinning control design for global stabilization of BNs based on BNs' network structure, named as network-structure-based distributed pinning control. By deleting the minimum number of edges, the network structure becomes acyclic. Then, an efficient distributed pinning control is designed to achieve global stabilization. Compared with existing literature, the design of pinning control is not based on the state transition matrix of BNs. Hence, the computational complexity in this paper is reduced from $O(2^n\times 2^n)$ to $O(2\times 2^K)$, where $n$ is the number of nodes and $K\leq n$ is the largest number of in-neighbors of nodes. In addition, without using state transition matrix, global state information is no longer needed, the design of pinning control is just based on neighbors' local information, which is easier to be implemented. The proposed method is well demonstrated by several biological networks with different sizes. The results are shown to be simple and concise, while the traditional pinning control can not be applied for BNs with such a large dimension.

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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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