arXiv subjects

Wenying Xu

Publications and source records attributed to Wenying Xu.

4 recordsLinked to original sources

arXiv2026

Entropy-Regularized Reinforcement Learning for Linear-Quadratic Stackelberg Differential Games in Regime-Switching Diffusion Models

Stackelberg differential games (SDGs) provide a powerful framework for hierarchical decision-making in stochastic and continuous-time environments, yet their solution remains computationally challenging due to the complexity of traditional dynamic programming and Hamilton-Jacobi-Bellman-Isaacs (HJBI) methods, especially in high-dimensional systems. This paper proposes an entropy-regularized reinforcement learning (ERRL) approach for linear-quadratic SDGs (LQ-SDGs) within a continuous-time diffusion framework governed by Markovian regime switching. The key innovation lies in deriving exploratory weakly-coupled HJBI equations with entropy regularization, which promotes stochastic policies that actively avoid suboptimal equilibria -- a limitation of classical SDG methods. Neural networks are integrated to approximate regime-dependent value functions and solve high-dimensional partial differential equations (PDEs) efficiently, while a novel sampling technique enhances computational tractability. Numerical results demonstrate the effectiveness of the framework compared to conventional approaches, particularly in escaping suboptimal traps through exploratory policies. The study highlights the critical role of entropy regularization and neural network approximations in achieving robust solutions for hierarchical decision-making problems under abrupt environmental shifts.

cs.LG↗

arXiv2026

Bundle EXTRA for Decentralized Optimization

Decentralized primal-dual methods are widely used for solving decentralized optimization problems, but their updates often rely on the potentially crude first-order Taylor approximations of the objective functions, which can limit convergence speed. To overcome this, we replace the first-order Taylor approximation in the primal update of EXTRA, which can be interpreted as a primal-dual method, with a more accurate multi-cut bundle model, resulting in a fully decentralized bundle EXTRA method. The bundle model incorporates historical information to improve the approximation accuracy, potentially leading to faster convergence. Under mild assumptions, we show that a KKT residual converges to zero. Numerical experiments on decentralized least-squares problems demonstrate that, compared to EXTRA, the bundle EXTRA method converges faster and is more robust to step-size choices.

math.OC↗

arXiv2026

Local adapt-then-combine algorithms for distributed nonsmooth optimization: Achieving provable communication acceleration

This paper is concerned with the distributed composite optimization problem over networks, where agents aim to minimize a sum of local smooth components and a common nonsmooth term. Leveraging the probabilistic local updates mechanism, we propose a communication-efficient Adapt-Then-Combine (ATC) framework, FlexATC, unifying numerous ATC-based distributed algorithms. Under stepsizes independent of the network topology and the number of local updates, we establish sublinear and linear convergence rates for FlexATC in convex and strongly convex settings, respectively. Remarkably, in the strong convex setting, the linear rate is decoupled from the objective functions and network topology, and FlexATC permits communication to be skipped in most iterations without any deterioration of the linear rate. In addition, the proposed unified theory demonstrates for the first time that local updates provably lead to communication acceleration for ATC-based distributed algorithms. Numerical experiments further validate the efficacy of the proposed framework and corroborate the theoretical results.

math.OC↗

arXiv2023

Decentralized ADMM with Compressed and Event-Triggered Communication

This paper focuses on the decentralized optimization problem, where agents in a network cooperate to minimize the sum of their local objective functions by information exchange and local computation. Based on the alternating direction method of multipliers (ADMM), we propose CC-DQM, a communication-efficient decentralized second-order optimization algorithm that combines compressed communication with event-triggered communication. Specifically, agents are allowed to transmit the compressed message only when the current primal variables have changed greatly compared to its last estimate. Moreover, to relieve the computation cost, the update of Hessian is scheduled by the trigger condition. To maintain exact linear convergence under compression, we compress the difference between the information to be transmitted and its estimate by a general contractive compressor. Theoretical analysis shows that CC-DQM can still achieve an exact linear convergence, despite the existence of compression error and intermittent communication, if the objective functions are strongly convex and smooth. Finally, we validate the performance of CC-DQM by numerical experiments.

math.OC↗