arXiv subjects

Antai Xie

Publications and source records attributed to Antai Xie.

8 recordsLinked to original sources

arXiv2026

Compressed Momentum-based Single-Point Zeroth-Order Algorithm for Stochastic Distributed Nonconvex Optimization

This paper studies a compressed momentum-based single-point zeroth-order algorithm for stochastic distributed nonconvex optimization, aiming to alleviate communication overhead and address the unavailability of explicit gradient information. In the developed framework, each agent has access only to stochastic zeroth-order information of its local objective function, performs local stochastic updates with momentum, and exchanges compressed updates with its neighbors. We theoretically prove that the proposed algorithm can achieve the exact solution with diminishing step sizes and can achieve a sublinear convergence rate towards a neighborhood of the stationary point with fixed step sizes. Numerical experiments validate the effectiveness and communication efficiency of the proposed algorithm.

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arXiv2026

Compressed Distributed Stochastic Nonconvex Optimization with Differential Privacy

This paper studies distributed stochastic nonconvex optimization problems with compressed communication and differential privacy, in which each agent aims to minimize the sum of all agents' cost functions by using local compressed information exchange. To this end, we propose a compressed distributed stochastic gradient descent algorithm, which is robust under a general class of compression operators that allow both relative and absolute compression errors. We then show that the proposed algorithm finds the first-order stationary point for smooth nonconvex functions with the linear speedup convergence rate $\mathcal{O}(1/\sqrt{nT})$ and converges to the optimum if the global cost function additionally satisfies the Polyak--Łojasiewicz (P--Ł) condition with the convergence rate $\mathcal{O}(1/(nT^θ)),θ\in(0,1)$, where $T$ is the total number of iterations and $n$ is the number of agents. Furthermore, if the P--Ł~constant is known in advance, we show that the proposed algorithm achieves a convergence rate $\mathcal{O}(1/(nT))$. Finally, we show that the proposed algorithm is able to achieve $(0,δ)$-differential privacy without sacrificing convergence accuracy. Numerical experiments are carried out to

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arXiv2025

Initial State Privacy of Nonlinear Systems on Riemannian Manifolds

In this paper, we investigate initial state privacy protection for discrete-time nonlinear closed systems. By capturing Riemannian geometric structures inherent in such privacy challenges, we refine the concept of differential privacy through the introduction of an initial state adjacency set based on Riemannian distances. A new differential privacy condition is formulated using incremental output boundedness, enabling the design of time-varying Laplacian noise to achieve specified privacy guarantees. The proposed framework extends beyond initial state protection to also cover system parameter privacy, which is demonstrated as a special application.

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arXiv2025

A Communication-Efficient and Differentially-Private Distributed Generalized Nash Equilibrium Seeking Algorithm for Aggregative Games

This paper studies the distributed generalized Nash equilibrium seeking problem for aggregative games with coupling constraints, where each player optimizes its strategy depending on its local cost function and the estimated strategy aggregation. The information transmission in distributed networks may go beyond bandwidth capacity and eventuate communication bottlenecks. Therefore, we propose a novel communication-efficient distributed generalized Nash equilibrium seeking algorithm, in which the communication efficiency is improved by event-triggered communication and information compression methods. The proposed algorithm saves the transmitted rounds and bits of communication simultaneously. Specifically, by developing precise step size conditions, the proposed algorithm ensures provable convergence, and is proven to achieve $(0,δ)$-differential privacy with a stochastic quantization scheme. In the end, simulation results verify the effectiveness of the proposed algorithm.

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arXiv2024

Differentially Private and Communication-Efficient Distributed Nonconvex Optimization Algorithms

This paper studies the privacy-preserving distributed optimization problem under limited communication, where each agent aims to keep its cost function private while minimizing the sum of all agents' cost functions. To this end, we propose two differentially private distributed algorithms under compressed communication. We show that the proposed algorithms achieve sublinear convergence for smooth (possibly nonconvex) cost functions and linear convergence when the global cost function additionally satisfies the Polyak-Łojasiewicz condition, even for a general class of compressors with bounded relative compression error. Furthermore, we rigorously prove that the proposed algorithms ensure $ε$-differential privacy. Unlike methods in the literature, the analysis of privacy under the proposed algorithms do not rely on the specific forms of compressors. Simulations are presented to demonstrate the effectiveness of our proposed approach.

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arXiv2024

Autonomous vehicle decision and control through reinforcement learning with traffic flow randomization

Most of the current studies on autonomous vehicle decision-making and control tasks based on reinforcement learning are conducted in simulated environments. The training and testing of these studies are carried out under rule-based microscopic traffic flow, with little consideration of migrating them to real or near-real environments to test their performance. It may lead to a degradation in performance when the trained model is tested in more realistic traffic scenes. In this study, we propose a method to randomize the driving style and behavior of surrounding vehicles by randomizing certain parameters of the car-following model and the lane-changing model of rule-based microscopic traffic flow in SUMO. We trained policies with deep reinforcement learning algorithms under the domain randomized rule-based microscopic traffic flow in freeway and merging scenes, and then tested them separately in rule-based microscopic traffic flow and high-fidelity microscopic traffic flow. Results indicate that the policy trained under domain randomization traffic flow has significantly better success rate and calculative reward compared to the models trained under other microscopic traffic flows.

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arXiv2024

A Communication-Efficient Stochastic Gradient Descent Algorithm for Distributed Nonconvex Optimization

This paper studies distributed nonconvex optimization problems with stochastic gradients for a multi-agent system, in which each agent aims to minimize the sum of all agents' cost functions by using local compressed information exchange. We propose a distributed stochastic gradient descent (SGD) algorithm, suitable for a general class of compressors. We show that the proposed algorithm achieves the linear speedup convergence rate $\mathcal{O}(1/\sqrt{nT})$ for smooth nonconvex functions, where $T$ and $n$ are the number of iterations and agents, respectively. If the global cost function additionally satisfies the Polyak--Łojasiewicz condition, the proposed algorithm can linearly converge to a neighborhood of the global optimum, regardless of whether the stochastic gradient is unbiased or not. Numerical experiments are carried out to verify the efficiency of our algorithm.

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arXiv2023

Compressed Differentially Private Distributed Optimization with Linear Convergence

This paper addresses the problem of differentially private distributed optimization under limited communication, where each agent aims to keep their cost function private while minimizing the sum of all agents' cost functions. In response, we propose a novel Compressed differentially Private distributed Gradient Tracking algorithm (CPGT). We demonstrate that CPGT achieves linear convergence for smooth and strongly convex cost functions, even with a class of biased but contractive compressors, and achieves the same accuracy as the idealized communication algorithm. Additionally, we rigorously prove that CPGT ensures differential privacy. Simulations are provided to validate the effectiveness of the proposed algorithm.

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