arXiv subjects

Zichong Ou

Publications and source records attributed to Zichong Ou.

8 recordsLinked to original sources

arXiv2026

A Unifying Primal-Dual Proximal Framework for Distributed Nonconvex Optimization

We consider distributed nonconvex optimization over an undirected network, where each node privately possesses its local objective and communicates exclusively with its neighboring nodes, striving to collectively achieve a common optimal solution. To handle the nonconvexity of the objective, we linearize the augmented Lagrangian function and introduce a time-varying proximal term. This approach leads to a Unifying Primal-Dual Proximal (UPP) framework that unifies a variety of existing first-order and second-order methods. Building on this framework, we further derive two specialized realizations with different communication strategies, namely UPP-MC and UPP-SC. We prove that both UPP-MC and UPP-SC achieve stationary solutions for nonconvex smooth problems at a sublinear rate. Furthermore, under the additional Polyak-Łojasiewics (P-Ł) condition, UPP-MC is linearly convergent to the global optimum. These convergence results provide new or improved guarantees for many existing methods that can be viewed as specializations of UPP-MC or UPP-SC. To further optimize the mixing process, we incorporate Chebyshev acceleration into UPP-SC, resulting in UPP-SC-OPT, which attains an optimal communication complexity bound. Extensive experiments across diverse network topologies demonstrate that our proposed algorithms outperform state-of-the-art methods in both convergence speed and communication efficiency.

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arXiv2026

Robust Distributed Nonconvex Optimization Enabling Communication Acceleration and Privacy Protection

This paper addresses a distributed nonconvex optimization problem over multi-agent networks, where each agent exchanges its local information solely with its neighbors. Given that most existing distributed nonconvex optimization algorithms are susceptible to information leakage during inter agent communications, we propose a Robust Proximal Primal dual algorithm, referred to as RPP, to enhance the security of information transmission. In contrast to many existing approaches that directly transmit local variables throughout the network, we introduce carefully designed random noises to obfuscate sensitive local information. This not only preserves privacy but also demonstrates the noise robustness of our proposed algorithm. We establish a sublinear rate at which RPP converges to a stationary solution. Moreover, by incorporating Chebyshev acceleration, an accelerated variant of RPP is developed and achieves the optimal communication complexity bound for the algorithms that allow for exchanging local deci sions at each iteration. The superior convergence performance of RPP is validated through a few numerical experiments, which also indicate that, within an appropriate range, the introduced perturbations do not impede the convergence speed of RPP.

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arXiv2025

Globally-Constrained Decentralized Optimization with Variable Coupling

Many realistic decision-making problems in networked scenarios, such as formation control and collaborative task offloading, often involve complicatedly entangled local decisions, which, however, have not been sufficiently investigated yet. Motivated by this, we study a class of decentralized optimization problems with a variable coupling structure that is new to the literature. Specifically, we consider a network of nodes collaborating to minimize a global objective subject to a collection of global inequality and equality constraints, which are formed by the local objective and constraint functions of the nodes. On top of that, we allow such local functions of each node to depend on not only its own decision variable but the decisions of its neighbors as well. To address this problem, we propose a decentralized projected primal-dual algorithm. It first incorporates a virtual-queue technique with a primal-dual-primal scheme, and then linearizes the non-separable objective and constraint functions to enable decentralized implementation. Under mild conditions, we derive $O(1/k)$ convergence rates for both objective error and constraint violations. Finally, two numerical experiments corroborate our theoretical results and illustrate the competitive performance of the proposed algorithm.

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arXiv2025

Distributed Nonconvex Optimization with Double Privacy Protection and Exact Convergence

Motivated by the pervasive lack of privacy protection in existing distributed nonconvex optimization methods, this paper proposes a decentralized proximal primal-dual algorithm enabling double protection of privacy ($\text{DPP}^2$) for minimizing nonconvex sum-utility functions over multi-agent networks, which ensures zero leakage of critical local information during inter-agent communications. We develop a two-tier privacy protection mechanism that first merges the primal and dual variables by means of a variable transformation, followed by embedding an additional random perturbation to further obfuscate the transmitted information. We theoretically establish that $\text{DPP}^2$ ensures differential privacy for local objectives while achieving exact convergence under nonconvex settings. Specifically, $\text{DPP}^2$ converges sublinearly to a stationary point and attains a linear convergence rate under the additional Polyak-Łojasiewicz (P-Ł) condition. Finally, a numerical example demonstrates the superiority of $\text{DPP}^2$ over a number of state-of-the-art algorithms, showcasing the faster, exact convergence achieved by $\text{DPP}^2$ under the same level of differential privacy.

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arXiv2024

A Zeroth-Order Proximal Algorithm for Consensus Optimization

This paper considers a consensus optimization problem, where all the nodes in a network, with access to the zeroth-order information of its local objective function only, attempt to cooperatively achieve a common minimizer of the sum of their local objectives. To address this problem, we develop ZoPro, a zeroth-order proximal algorithm, which incorporates a zeroth-order oracle for approximating Hessian and gradient into a recently proposed, high-performance distributed second-order proximal algorithm. We show that the proposed ZoPro algorithm, equipped with a dynamic stepsize, converges linearly to a neighborhood of the optimum in expectation, provided that each local objective function is strongly convex and smooth. Extensive simulations demonstrate that ZoPro converges faster than several state-of-the-art distributed zeroth-order algorithms and outperforms a few distributed second-order algorithms in terms of running time for reaching given accuracy.

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arXiv2024

A Mixing-Accelerated Primal-Dual Proximal Algorithm for Distributed Nonconvex Optimization

In this paper, we develop a distributed mixing-accelerated primal-dual proximal algorithm, referred to as MAP-Pro, which enables nodes in multi-agent networks to cooperatively minimize the sum of their nonconvex, smooth local cost functions in a decentralized fashion. The proposed algorithm is constructed upon minimizing a computationally inexpensive augmented-Lagrangian-like function and incorporating a time-varying mixing polynomial to expedite information fusion across the network. The convergence results derived for MAP-Pro include a sublinear rate of convergence to a stationary solution and, under the Polyak-Łojasiewics (P-Ł) condition, a linear rate of convergence to the global optimal solution. Additionally, we may embed the well-noted Chebyshev acceleration scheme in MAP-Pro, which generates a specific sequence of mixing polynomials with given degrees and enhances the convergence performance based on MAP-Pro. Finally, we illustrate the competitive convergence speed and communication efficiency of MAP-Pro via a numerical example.

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arXiv2023

A Distributed Buffering Drift-Plus-Penalty Algorithm for Coupling Constrained Optimization

This paper focuses on distributed constrained optimization over time-varying directed networks, where all agents cooperate to optimize the sum of their locally accessible objective functions subject to a coupled inequality constraint consisting of all their local constraint functions. To address this problem, we develop a buffering drift-plus-penalty algorithm, referred to as B-DPP. The proposed B-DPP algorithm utilizes the idea of drift-plus-penalty minimization in centralized optimization to control constraint violation and objective error, and adapts it to the distributed setting. It also innovatively incorporates a buffer variable into local virtual queue updates to acquire flexible and desirable tracking of constraint violation. We show that B-DPP achieves $O(1/\sqrt{t})$ rates of convergence to both optimality and feasibility, which outperform the alternative methods in the literature. Moreover, with a proper buffer parameter, B-DPP is capable of reaching feasibility within a finite number of iterations, which is a pioneering result in the area. Simulations on a resource allocation problem over 5G virtualized networks demonstrate the competitive convergence performance and efficiency of B-DPP.

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arXiv2022

A Stochastic Second-Order Proximal Method for Distributed Optimization

In this paper, we propose a distributed stochastic second-order proximal method that enables agents in a network to cooperatively minimize the sum of their local loss functions without any centralized coordination. The proposed algorithm, referred to as St-SoPro, incorporates a decentralized second-order approximation into an augmented Lagrangian function, and then randomly samples the local gradients and Hessian matrices of the agents, so that it is computationally and memory-wise efficient, particularly for large-scale optimization problems. We show that for globally restricted strongly convex problems, the expected optimality error of St-SoPro asymptotically drops below an explicit error bound at a linear rate, and the error bound can be arbitrarily small with proper parameter settings. Simulations over real machine learning datasets demonstrate that St-SoPro outperforms several state-of-the-art distributed stochastic first-order methods in terms of convergence speed as well as computation and communication costs.

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