arXiv subjects

Liang Ran

Publications and source records attributed to Liang Ran.

5 recordsLinked to original sources

arXiv2026

RED-SEGA:Resilient Decentralized Stochastic Proximal Optimization with Gradient Sketching over Time-Varying Networks

Variance reduction is indispensable in Byzantine-resilient decentralized stochastic optimization over multi-agent systems (MASs) for its ability to mitigate gradient noise and thereby enhance the resilient aggregation process. However, most existing Byzantine-resilient decentralized variance-reduced (VR) stochastic gradient algorithms rely on random data sampling, which proves inefficient in data-scarce yet high-dimensional tasks, for instance, image deblurring. This paper pursues an alternative technical line that achieves variance reduction via gradient sketching. To this end, we first formulate a class of structural risk minimization (SRM) problems, where the local objectives are not necessarily decomposable and their gradients may be unavailable. To solve the SRM problems in a decentralized manner, we integrate a gradient-sketching technique into decentralized stochastic proximal gradient descent with gossip communication to propose a decentralized VR stochastic gradient algorithm, dubbed Gossip-SEGA.Since Gossip-SEGA does not provide any resilience against Byzantine attacks, a resilient extension of Gossip-SEGA,namely RED-SEGA,is developed via replacing the weighted average in Gossip-SEGA by a norm-penalized approximation. Theoretically, we derive sufficient conditions for both consensus (among reliable agents) and linear convergence rate of RED-SEGA over time-varying networks. The effectiveness and resilience of the proposed algorithms are validated through numerical experiments.

math.OC↗

arXiv2026

Optimal Decentralized Dynamic Energy Management over Asynchronous Peer-to-Peer Transactive Networks via Operator Splitting

Peer-to-peer (P2P) energy management facilitates decentralized resource allocation among prosumers, improving local hosting capacity for renewables and minimizing energy expenditures while ensuring data privacy through distributed coordination. However, conventional P2P energy management methods are confined to synchronous scheduling paradigms, creating synchronization bottlenecks that fundamentally conflict with the dynamic and decentralized nature of P2P energy management tasks. To bridge this gap, this paper focuses on resolving a class of dynamic energy management problems over asynchronous P2P (Asyn-P2P) transactive networks. We first recast the dynamic energy management problems into a saddle-point problem, and then propose a synchronous decentralized dynamic energy management algorithm, dubbed Syn-DYNA,based on operator splitting theory. To eliminate the global synchronization clock in Syn-DYNA, we introduce a random activation scheme, together with local buffers for latest state tracking, to develop an asynchronous variant of Syn-DYNA, namely Asyn-DYNA. Based on monotone operator theory, theoretical analysis proves a non-asymptotic linear convergence rate for Syn-DYNA and establishes the almost sure convergence ofAsyn-DYNA. Numerical experiments validate effectiveness of Syn-DYNA and Asyn-DYNA algorithms by tackling a dynamic energy management task over P2P transactive networks.

eess.SY↗

arXiv2024

Distributed Generalized Nash Equilibria Seeking Algorithms Involving Synchronous and Asynchronous Schemes

This paper considers a class of noncooperative games in which the feasible decision sets of all players are coupled together by a coupled inequality constraint. Adopting the variational inequality formulation of the game, we first introduce a new local edge-based equilibrium condition and develop a distributed primal-dual proximal algorithm with full information. Considering challenges when communication delays occur, we devise an asynchronous distributed algorithm to seek a generalized Nash equilibrium. This asynchronous scheme arbitrarily activates one player to start new computations independently at different iteration instants, which means that the picked player can use the involved out-dated information from itself and its neighbors to perform new updates. A distinctive attribute is that the proposed algorithms enable the derivation of new distributed forward-backward-like extensions. In theoretical aspect, we provide explicit conditions on algorithm parameters, for instance, the step-sizes to establish a sublinear convergence rate for the proposed synchronous algorithm. Moreover, the asynchronous algorithm guarantees almost sure convergence in expectation under the same step-size conditions and some standard assumptions. An interesting observation is that our analysis approach improves the convergence rate of prior synchronous distributed forward-backward-based algorithms. Finally, the viability and performance of the proposed algorithms are demonstrated by numerical studies on the networked Cournot competition.

cs.GT↗

arXiv2023

Prox-DBRO-VR: A Unified Analysis on Byzantine-Resilient Decentralized Stochastic Composite Optimization with Variance Reduction and Non-Asymptotic Convergence Rates

Decentralized stochastic gradient algorithms efficiently solve large-scale finite-sum optimization problems when all agents in the network are reliable. However, most of these algorithms are not resilient to adverse conditions, such as malfunctioning agents, software bugs, and cyber attacks. This paper aims to handle a class of general composite optimization problems over multi-agent systems (MASs) in the presence of an unknown number of Byzantine agents. Building on a resilient aggregation mechanism and the proximal-gradient mapping method, a Byzantine-resilient decentralized stochastic proximal-gradient algorithmic framework is proposed, dubbed Prox-DBRO-VR, which achieves an optimization and control goal using only local computations and communications. To asymptotically reduce the noise variance arising from local gradient estimation and accelerate the convergence, we incorporate two localized variance-reduced (VR) techniques (SAGA and LSVRG) into Prox-DBRO-VR to design Prox-DBRO-SAGA and Prox-DBRO-LSVRG. By analyzing the contraction relationships among the gradient-learning error, resilient consensus condition, and convergence error in a unified theoretical framework, it is proved that both Prox-DBRO-SAGA and Prox-DBRO-LSVRG, with a well-designed constant (resp., decaying) step-size, converge linearly (resp., sub-linearly) inside an error ball around the optimal solution to the original problem under standard assumptions. A trade-off between convergence accuracy and Byzantine resilience in both linear and sub-linear cases is also characterized. In numerical experiments, the effectiveness and practicability of the proposed algorithms are manifested via resolving a decentralized sparse machine-learning problem under various Byzantine attacks.

math.OC↗

arXiv2009

The relation between 13CO(2-1) line width in molecular clouds and bolometric luminosity of associated IRAS sources

We search for evidence of a relation between properties of young stellar objects (YSOs) and their parent molecular clouds to understand the initial conditions of high-mass star formation. A sample of 135 sources was selected from the Infrared Astronomical Satellite (IRAS) Point Source Catalog, on the basis of their red color to enhance the possibility of discovering young sources. Using the Kolner Observatorium fur SubMillimeter Astronomie (KOSMA) 3-m telescope, a single-point survey in 13CO(2-1) was carried out for the entire sample, and 14 sources were mapped further. Archival mid-infrared (MIR) data were compared with the 13CO emissions to identify evolutionary stages of the sources. A 13CO observed sample was assembled to investigate the correlation between 13CO line width of the clouds and the luminosity of the associated YSOs. We identified 98 sources suitable for star formation analyses for which relevant parameters were calculated. We detected 18 cores from 14 mapped sources, which were identified with eight pre-UC HII regions and one UC HII region, two high-mass cores earlier than pre-UC HII phase, four possible star forming clusters, and three sourceless cores. By compiling a large (360 sources) 13CO observed sample, a good correlation was found between the 13CO line width of the clouds and the bolometric luminosity of the associated YSOs, which can be fitted as a power law: lg(dV13/km/s)=-0.023+0.135lg(Lbol/Lsolar). Results show that luminous (>10^3Lsolar) YSOs tend to be associated with both more massive and more turbulent (dV13>2km/s) molecular cloud structures.

astro-ph.SR↗