arXiv subjects

Changxin Liu

Publications and source records attributed to Changxin Liu.

At least 19 recordsLinked to original sources

arXiv2026

Byzantine-Resilient Consensus via Active Reputation Learning

This paper proposes a Byzantine-resilient consensus framework that simultaneously pursues two tightly coupled objectives: actively identifying Byzantine agents and guaranteeing resilient consensus among normal agents. Unlike existing methods that treat adversary mitigation as a passive filtering process, our approach embeds an active reputation learning mechanism into the consensus loop. Agents evaluate neighbors' behaviors using outlier-robust loss functions and historical information, and construct a reputation vector on a probability simplex via a mechanism that balances loss minimization with diversity-preserving exploration, representing dynamic beliefs over neighbor trustworthiness. These reputations are then used to form weighted local updates that suppress adversarial influence and improve agreement among normal agents, thereby reducing the bias in local loss evaluations and enabling more reliable subsequent reputation estimation. This learning-control co-design yields a closed-loop dual objective: improved consensus states enhance Byzantine identifiability, while refined reputations in turn improve consensus. A range of distributed systems experiments, benchmarking against classical resilient consensus methods, demonstrate superior Byzantine detection accuracy and significantly more reliable and scalable consensus.

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arXiv2026

Accelerating Byzantine-Robust Distributed Learning with Compressed Communication via Double Momentum and Variance Reduction

In collaborative and distributed learning, Byzantine robustness reflects a major facet of optimization algorithms. Such distributed algorithms are often accompanied by transmitting a large number of parameters, so communication compression is essential for an effective solution. In this paper, we propose Byz-DM21, a novel Byzantine-robust and communication-efficient stochastic distributed learning algorithm. Our key innovation is a novel gradient estimator based on a double-momentum mechanism, integrating recent advancements in error feedback techniques. Using this estimator, we design both standard and accelerated algorithms that eliminate the need for large batch sizes while maintaining robustness against Byzantine workers. We prove that the Byz-DM21 algorithm has a smaller neighborhood size and converges to $\varepsilon$-stationary points in $\mathcal{O}(\varepsilon^{-4})$ iterations. To further enhance efficiency, we introduce a distributed variant called Byz-VR-DM21, which incorporates local variance reduction at each node to progressively eliminate variance from random approximations. We show that Byz-VR-DM21 provably converges to $\varepsilon$-stationary points in $\mathcal{O}(\varepsilon^{-3 })$ iterations. Additionally, we extend our results to the case where the functions satisfy the Polyak-{\L}ojasiewicz condition. Finally, numerical experiments demonstrate the effectiveness of the proposed method.

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arXiv2025

Projected Gradient Descent for Constrained Decision-Dependent Optimization

This paper considers the decision-dependent optimization problem, where the data distributions react in response to decisions affecting both the objective function and linear constraints. We propose a new method termed repeated projected gradient descent (RPGD), which iteratively projects points onto evolving feasible sets throughout the optimization process. To analyze the impact of varying projection sets, we show a Lipschitz continuity property of projections onto varying sets with an explicitly given Lipschitz constant. Leveraging this property, we provide sufficient conditions for the convergence of RPGD to the constrained equilibrium point. Compared to the existing dual ascent method, RPGD ensures continuous feasibility throughout the optimization process and reduces the computational burden. We validate our results through numerical experiments on a market problem and dynamic pricing problem.

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arXiv2025

Decentralized Optimization with Amplified Privacy via Efficient Communication

Decentralized optimization is crucial for multi-agent systems, with significant concerns about communication efficiency and privacy. This paper explores the role of efficient communication in decentralized stochastic gradient descent algorithms for enhancing privacy preservation. We develop a novel algorithm that incorporates two key features: random agent activation and sparsified communication. Utilizing differential privacy, we demonstrate that these features reduce noise without sacrificing privacy, thereby amplifying the privacy guarantee and improving accuracy. Additionally, we analyze the convergence and the privacy-accuracy-communication trade-off of the proposed algorithm. Finally, we present experimental results to illustrate the effectiveness of our algorithm.

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arXiv2025

Distributed model predictive control without terminal cost under inexact distributed optimization

This paper presents a novel distributed model predictive control (MPC) formulation without terminal cost and a corresponding distributed synthesis approach for distributed linear discrete-time systems with coupled constraints. The proposed control scheme introduces an explicit stability condition as an additional constraint based on relaxed dynamic programming. As a result, contrary to other related approaches, system stability with the developed controller does not rely on designing a terminal cost. A distributed synthesis approach is then introduced to handle the stability constraint locally within each local agent. To solve the underlying optimization problem for distributed MPC, a violation-free distributed optimization approach is developed, using constraint tightening to ensure feasibility throughout iterations. A numerical example demonstrates that the proposed distributed MPC approach ensures closed-loop stability for each feasible control sequence, with each agent computing its control input in parallel.

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arXiv2025

Federated Cubic Regularized Newton Learning with Sparsification-amplified Differential Privacy

This paper investigates the use of the cubic-regularized Newton method within a federated learning framework while addressing two major concerns that commonly arise in federated learning: privacy leakage and communication bottleneck. We introduce a federated learning algorithm called Differentially Private Federated Cubic Regularized Newton (DP-FCRN). By leveraging second-order techniques, our algorithm achieves lower iteration complexity compared to first-order methods. We also incorporate noise perturbation during local computations to ensure privacy. Furthermore, we employ sparsification in uplink transmission, which not only reduces the communication costs but also amplifies the privacy guarantee. Specifically, this approach reduces the necessary noise intensity without compromising privacy protection. We analyze the convergence properties of our algorithm and establish the privacy guarantee. Finally, we validate the effectiveness of the proposed algorithm through experiments on a benchmark dataset.

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arXiv2025

A continuous-time violation-free multi-agent optimization algorithm and its applications to safe distributed control

In this work, we propose a continuous-time distributed optimization algorithm with guaranteed zero coupling constraint violation and apply it to safe distributed control in the presence of multiple control barrier functions (CBF). The optimization problem is defined over a network that collectively minimizes a separable cost function with coupled linear constraints. An equivalent optimization problem with auxiliary decision variables and a decoupling structure is proposed. A sensitivity analysis demonstrates that the subgradient information can be computed using local information. This then leads to a subgradient algorithm for updating the auxiliary variables. A case with sparse coupling constraints is further considered, and it is shown to have better memory and communication efficiency. For the specific case of a CBF-induced time-varying quadratic program (QP), an update law is proposed that achieves finite-time convergence. Numerical results involving a static resource allocation problem and a safe coordination problem for a multi-agent system demonstrate the efficiency and effectiveness of our proposed algorithms.

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arXiv2024

Enhancing Privacy in Federated Learning through Local Training

In this paper we propose the federated learning algorithm Fed-PLT to overcome the challenges of (i) expensive communications and (ii) privacy preservation. We address (i) by allowing for both partial participation and local training, which significantly reduce the number of communication rounds between the central coordinator and computing agents. The algorithm matches the state of the art in the sense that the use of local training demonstrably does not impact accuracy. Additionally, agents have the flexibility to choose from various local training solvers, such as (stochastic) gradient descent and accelerated gradient descent. Further, we investigate how employing local training can enhance privacy, addressing point (ii). In particular, we derive differential privacy bounds and highlight their dependence on the number of local training epochs. We assess the effectiveness of the proposed algorithm by comparing it to alternative techniques, considering both theoretical analysis and numerical results from a classification task.

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arXiv2024

Asynchronous Distributed Optimization with Delay-free Parameters

Existing asynchronous distributed optimization algorithms often use diminishing step-sizes that cause slow practical convergence, or use fixed step-sizes that depend on and decrease with an upper bound of the delays. Not only are such delay bounds hard to obtain in advance, but they also tend to be large and rarely attained, resulting in unnecessarily slow convergence. This paper develops asynchronous versions of two distributed algorithms, Prox-DGD and DGD-ATC, for solving consensus optimization problems over undirected networks. In contrast to alternatives, our algorithms can converge to the fixed point set of their synchronous counterparts using step-sizes that are independent of the delays. We establish convergence guarantees for convex and strongly convex problems under both partial and total asynchrony. We also show that the convergence speed of the two asynchronous methods adjusts to the actual level of asynchrony rather than being constrained by the worst-case. Numerical experiments demonstrate a strong practical performance of our asynchronous algorithms.

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arXiv2024

Byzantine-Robust and Communication-Efficient Distributed Learning via Compressed Momentum Filtering

Distributed learning has become the standard approach for training large-scale machine learning models across private data silos. While distributed learning enhances privacy preservation and training efficiency, it faces critical challenges related to Byzantine robustness and communication reduction. Existing Byzantine-robust and communication-efficient methods rely on full gradient information either at every iteration or at certain iterations with a probability, and they only converge to an unnecessarily large neighborhood around the solution. Motivated by these issues, we propose a novel Byzantine-robust and communication-efficient stochastic distributed learning method that imposes no requirements on batch size and converges to a smaller neighborhood around the optimal solution than all existing methods, aligning with the theoretical lower bound. Our key innovation is leveraging Polyak Momentum to mitigate the noise caused by both biased compressors and stochastic gradients, thus defending against Byzantine workers under information compression. We provide proof of tight complexity bounds for our algorithm in the context of non-convex smooth loss functions, demonstrating that these bounds match the lower bounds in Byzantine-free scenarios. Finally, we validate the practical significance of our algorithm through an extensive series of experiments, benchmarking its performance on both binary classification and image classification tasks.

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arXiv2024

Privacy-Preserving Set-Based Estimation Using Differential Privacy and Zonotopes

For large-scale cyber-physical systems, the collaboration of spatially distributed sensors is often needed to perform the state estimation process. Privacy concerns arise from disclosing sensitive measurements to a cloud estimator. To solve this issue, we propose a differentially private set-based estimation protocol that guarantees true state containment in the estimated set and differential privacy for the sensitive measurements throughout the set-based state estimation process within the central and local differential privacy models. Zonotopes are employed in the proposed differentially private set-based estimator, offering computational advantages in set operations. We consider a plant of a non-linear discrete-time dynamical system with bounded modeling uncertainties, sensors that provide sensitive measurements with bounded measurement uncertainties, and a cloud estimator that predicts the system's state. The privacy-preserving noise perturbs the centers of measurement zonotopes, thereby concealing the precise position of these zonotopes, i.e., ensuring privacy preservation for the sets containing sensitive measurements. Compared to existing research, our approach achieves less privacy loss and utility loss through the central and local differential privacy models by leveraging a numerically optimized truncated noise distribution. The proposed estimator is perturbed by weaker noise than the analytical approaches in the literature to guarantee the same level of privacy, therefore improving the estimation utility. Numerical and comparison experiments with truncated Laplace noise are presented to support our approach.

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arXiv2024

A survey on secure decentralized optimization and learning

Decentralized optimization has become a standard paradigm for solving large-scale decision-making problems and training large machine learning models without centralizing data. However, this paradigm introduces new privacy and security risks, with malicious agents potentially able to infer private data or impair the model accuracy. Over the past decade, significant advancements have been made in developing secure decentralized optimization and learning frameworks and algorithms. This survey provides a comprehensive tutorial on these advancements. We begin with the fundamentals of decentralized optimization and learning, highlighting centralized aggregation and distributed consensus as key modules exposed to security risks in federated and distributed optimization, respectively. Next, we focus on privacy-preserving algorithms, detailing three cryptographic tools and their integration into decentralized optimization and learning systems. Additionally, we examine resilient algorithms, exploring the design and analysis of resilient aggregation and consensus protocols that support these systems. We conclude the survey by discussing current trends and potential future directions.

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arXiv2024

Achieving violation-free distributed optimization under coupling constraints

Constraint satisfaction is a critical component in a wide range of engineering applications, including but not limited to safe multi-agent control and economic dispatch in power systems. This study explores violation-free distributed optimization techniques for problems characterized by separable objective functions and coupling constraints. First, we incorporate auxiliary decision variables together with a network-dependent linear mapping to each coupling constraint. For the reformulated problem, we show that the projection of its feasible set onto the space of primal variables is identical to that of the original problem, which is the key to achieving all-time constraint satisfaction. Upon treating the reformulated problem as a min-min optimization problem with respect to auxiliary and primal variables, we demonstrate that the gradients in the outer minimization problem have a locally computable closed-form. Then, two violation-free distributed optimization algorithms are developed and their convergence under reasonable assumptions is analyzed. Finally, the proposed algorithm is applied to implement a control barrier function based controller in a distributed manner, and the results verify its effectiveness.

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arXiv2024

Near-Optimal Resilient Aggregation Rules for Distributed Learning Using 1-Center and 1-Mean Clustering with Outliers

Byzantine machine learning has garnered considerable attention in light of the unpredictable faults that can occur in large-scale distributed learning systems. The key to secure resilience against Byzantine machines in distributed learning is resilient aggregation mechanisms. Although abundant resilient aggregation rules have been proposed, they are designed in ad-hoc manners, imposing extra barriers on comparing, analyzing, and improving the rules across performance criteria. This paper studies near-optimal aggregation rules using clustering in the presence of outliers. Our outlier-robust clustering approach utilizes geometric properties of the update vectors provided by workers. Our analysis show that constant approximations to the 1-center and 1-mean clustering problems with outliers provide near-optimal resilient aggregators for metric-based criteria, which have been proven to be crucial in the homogeneous and heterogeneous cases respectively. In addition, we discuss two contradicting types of attacks under which no single aggregation rule is guaranteed to improve upon the naive average. Based on the discussion, we propose a two-phase resilient aggregation framework. We run experiments for image classification using a non-convex loss function. The proposed algorithms outperform previously known aggregation rules by a large margin with both homogeneous and heterogeneous data distributions among non-faulty workers. Code and appendix are available at https://github.com/jerry907/AAAI24-RASHB.

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arXiv2023

Constrained Optimization with Decision-Dependent Distributions

In this paper we deal with stochastic optimization problems where the data distributions change in response to the decision variables. Traditionally, the study of optimization problems with decision-dependent distributions has assumed either the absence of constraints or fixed constraints. This work considers a more general setting where the constraints can also dynamically adjust in response to changes in the decision variables. Specifically, we consider linear constraints and analyze the effect of decision-dependent distributions in both the objective function and constraints. Firstly, we establish a sufficient condition for the existence of a constrained equilibrium point, at which the distributions remain invariant under retraining. Morevoer, we propose and analyze two algorithms: repeated constrained optimization and repeated dual ascent. For each algorithm, we provide sufficient conditions for convergence to the constrained equilibrium point. Furthermore, we explore the relationship between the equilibrium point and the optimal point for the constrained decision-dependent optimization problem. Notably, our results encompass previous findings as special cases when the constraints remain fixed. To show the effectiveness of our theoretical analysis, we provide numerical experiments on both a market problem and a dynamic pricing problem for parking based on real-world data.

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arXiv2023

Delay-agnostic Asynchronous Distributed Optimization

Existing asynchronous distributed optimization algorithms often use diminishing step-sizes that cause slow practical convergence, or fixed step-sizes that depend on an assumed upper bound of delays. Not only is such a delay bound hard to obtain in advance, but it is also large and therefore results in unnecessarily slow convergence. This paper develops asynchronous versions of two distributed algorithms, DGD and DGD-ATC, for solving consensus optimization problems over undirected networks. In contrast to alternatives, our algorithms can converge to the fixed-point set of their synchronous counterparts using step-sizes that are independent of the delays. We establish convergence guarantees under both partial and total asynchrony. The practical performance of our algorithms is demonstrated by numerical experiments.

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arXiv2023

Secure State Estimation against Sparse Attacks on a Time-varying Set of Sensors

This paper studies the problem of secure state estimation of a linear time-invariant (LTI) system with bounded noise in the presence of sparse attacks on an unknown, time-varying set of sensors. In other words, at each time, the attacker has the freedom to choose an arbitrary set of no more that $p$ sensors and manipulate their measurements without restraint. To this end, we propose a secure state estimation scheme and guarantee a bounded estimation error subject to $2p$-sparse observability and a mild, technical assumption that the system matrix has no degenerate eigenvalues. The proposed scheme comprises a design of decentralized observer for each sensor based on the local observable subspace decomposition. At each time step, the local estimates of sensors are fused by solving an optimization problem to obtain a secure estimation, which is then followed by a local detection-and-resetting process of the decentralized observers. The estimation error is shown to be upper-bounded by a constant which is determined only by the system parameters and noise magnitudes. Moreover, we optimize the detector threshold to ensure that the benign sensors do not trigger the detector. The efficacy of the proposed algorithm is demonstrated by its application on a benchmark example of IEEE 14-bus system.

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arXiv2023

Distributed Empirical Risk Minimization With Differential Privacy

This work studies the distributed empirical risk minimization (ERM) problem under differential privacy (DP) constraint. Standard distributed algorithms achieve DP typically by perturbing all local subgradients with noise, leading to significantly degenerated utility. To tackle this issue, we develop a class of private distributed dual averaging (DDA) algorithms, which activates a fraction of nodes to perform optimization. Such subsampling procedure provably amplifies the DP guarantee, thereby achieving an equivalent level of DP with reduced noise. We prove that the proposed algorithms have utility loss comparable to centralized private algorithms for both general and strongly convex problems. When removing the noise, our algorithm attains the optimal O(1/t) convergence for non-smooth stochastic optimization. Finally, experimental results on two benchmark datasets are given to verify the effectiveness of the proposed algorithms.

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