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Smoothing Gradient Tracking for Decentralized Optimization over the Stiefel Manifold with Non-Smooth Regularizers

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Smoothing Gradient Tracking for Decentralized Optimization o...

IEEE Conference on Decision and Control

作者： Lei Wang Xin Liu State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China and University of Chinese Academy of Sciences Beijing China

Recently, decentralized optimization over the Stiefel manifold has attracted tremendous attentions due to its wide range of applications in various fields. Existing methods rely on the gradients to update variables, which are not applicable to the objective functions with non-smooth regularizers, such as sparse PCA. In this paper, to the best of our knowledge, we propose the first decentralized algorithm for non-smooth optimization over Stiefel manifolds. Our algorithm approximates the non-smooth part of objective function by its Moreau envelope, and then existing algorithms for smooth optimization can be deployed. We establish the convergence guarantee with the iteration complexity of $\mathcal{O}$ (∊ 4 ). Numerical experiments conducted under the decentralized setting demonstrate the effectiveness and efficiency of our algorithm.

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Realizing record efficiencies for ultra-thin organic photovoltaics through step-by-step optimizations of silver nanowire transparent electrodes

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FlexMat

FlexMat 2024年第3期1卷 221-233页

作者： Xiangjun Zheng Yiming Wang Tianyi Chen Yibo Kong Xiaoling Wu Cun Zhou Qun Luo Chang-Qi Ma Lijian Zuo Minmin Shi Hongzheng Chen State Key Laboratory of Silicon and Advanced Semiconductor Materials MOE Key Laboratory of Macromolecular Synthesis and Functionalization Department of Polymer Science and Engineering Zhejiang University Hangzhou China Printable Electronics Research Center Suzhou Institute of Nano-Tech and Nano-Bionics Chinese Academy of Sciences (CAS) Suzhou China Zhejiang University-Hangzhou Global Scientific and Technological Innovation Center Hangzhou China

Ultra-thin (also known as ultra-flexible) organic photovoltaics (OPVs) represent a strong contender among emerging photovoltaic technologies. However, due to the imbalance between the optical and electrical properties of indium tin oxide (ITO)-free transparent electrodes, the ultra-thin OPVs often exhibit lower efficiency compared to the brittle yet more balanced rigid ITO counterparts. Here, we design and fabricate an advanced ultra-thin OPV, which involves a thoroughly optimized silver nanowires (AgNWs) transparent electrode (named AZAT) with excellent optical, electrical and mechanical properties. Specifically, the high-kinetic energy spray-coating method successfully yields a curve-shaped, tightly connected and uniformly distributed AgNWs film, complemented by a capping layer of zinc oxide:aluminum-doped zinc oxide (ZnO:AZO) to improve charge collection capability. Simultaneously, the transparency of the electrode is enhanced through precise optical optimization. Thus, we implant the AZAT-based devices on 1.3 μm polyimide substrates and demonstrate ultra-thin OPVs with a record efficiency of 18.46% and a power density of 40.31 W g −1 , which is the highest value for PV technologies. Encouragingly, the AZAT electrode also enables the 10.0 cm 2 device to exhibit a high efficiency of 15.67%. These results provide valuable insights for the development of ultra-thin OPVs with high efficiency, low cost, superior flexibility, and up-scaling capacity.

关键词： AgNWs transparent electrode ITO-free devices large-area devices ultra-flexible organic photovoltaics ultra-thin organic photovoltaics

Efficient Global Algorithms for Transmit Beamforming Design in ISAC Systems

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arXiv 2024年

作者： Wu, Jiageng Wang, Zhiguo Liu, Ya-Feng Liu, Fan The School of Mathematics Jilin University Changchun130012 China The College of Mathematics Sichuan University Sichuan Chengdu610064 China The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The Department of Electrical and Electronic Engineering Southern University of Science and Technology Shenzhen518055 China

In this paper, we propose a multi-input multi-output transmit beamforming optimization model for joint radar sensing and multi-user communications, where the design of the beamformers is formulated as an optimization problem whose objective is a weighted combination of the sum rate and the Cramér-Rao bound, subject to the transmit power budget. Obtaining the global solution for the formulated nonconvex problem is a challenging task, since the sum-rate maximization problem itself (even without considering the sensing metric) is known to be NP-hard. The main contributions of this paper are threefold. Firstly, we derive an optimal closed-form solution to the formulated problem in the single-user case and the multi-user case where the channel vectors of different users are orthogonal. Secondly, for the general multi-user case, we propose a novel branch and bound (B&B) algorithm based on the McCormick envelope relaxation. The proposed algorithm is guaranteed to find the globally optimal solution to the formulated problem. Thirdly, we design a graph neural network (GNN) based pruning policy to determine irrelevant nodes that can be directly pruned in the proposed B&B algorithm, thereby significantly reducing the number of unnecessary enumerations therein and improving its computational efficiency. Simulation results show the efficiency of the proposed vanilla and GNN-based accelerated B&B algorithms. Copyright © 2024, The Authors. All rights reserved.

关键词： Computational efficiency

Stochastic optimization over expectation-formulated generalized Stiefel manifold

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arXiv 2024年

作者： Jiang, Linshuo Xiao, Nachuan Liu, Xin State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences China The Institute of Operations Research and Analytics National University of Singapore Singapore

In this paper, we consider a class of stochastic optimization problems over the expectation-formulated generalized Stiefel manifold (SOEGS), where the objective function f is continuously differentiable. We propose a novel constraint dissolving penalty function with a customized penalty term (CDFCP), which maintains the same order of differentiability as f. Our theoretical analysis establishes the global equivalence between CDFCP and SOEGS, in the sense that they share the same first-order and second-order stationary points under mild conditions. These results on equivalence enable the direct implementation of various stochastic optimization approaches to solve SOEGS. In particular, we develop a stochastic gradient algorithm and its accelerated variant by incorporating an adaptive step size strategy. Furthermore, we prove their O(Ε−4) sample complexity for finding an Ε-stationary point of CDFCP. Comprehensive numerical experiments show the efficiency and robustness of our proposed algorithms. Copyright © 2024, The Authors. All rights reserved.

关键词： Optimization algorithms

Decentralized Stochastic Subgradient-based Methods for Nonsmooth Nonconvex Optimization

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arXiv 2024年

作者： Zhang, Siyuan Xiao, Nachuan Liu, Xin State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences China The Institute of Operations Research and Analytics National University of Singapore Singapore

In this paper, we concentrate on decentralized optimization problems with nonconvex and nonsmooth objective functions, especially on the decentralized training of nonsmooth neural networks. We introduce a unified framework to analyze the global convergence of decentralized stochastic subgradient-based methods. We prove the global convergence of our proposed framework under mild conditions, by establishing that the generated sequence asymptotically approximates the trajectories of its associated differential inclusion. Furthermore, we establish that our proposed framework covers a wide range of existing efficient decentralized subgradient-based methods, including decentralized stochastic subgradient descent (DSGD), DSGD with gradient-tracking technique (DSGD-T), and DSGD with momentum (DSGD-M). In addition, we introduce the sign map to regularize the update directions in DSGD-M, and show it is enclosed in our proposed framework. Consequently, our convergence results establish, for the first time, global convergence of these methods when applied to nonsmooth nonconvex objectives. Preliminary numerical experiments demonstrate that our proposed framework yields highly efficient decentralized subgradient-based methods with convergence guarantees in the training of nonsmooth neural networks. Copyright © 2024, The Authors. All rights reserved.

关键词： Lyapunov functions

Numerical Solution for Nonlinear 4D Variational Data Assimilation (4D-Var) via ADMM

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arXiv 2024年

作者： Li, Bowen Shi, Bin State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

The four-dimensional variational data assimilation (4D-Var) has emerged as an important methodology, widely used in numerical weather prediction, oceanographic modeling, and climate forecasting. Classical unconstrained gradient-based algorithms often struggle with local minima, making their numerical performance highly sensitive to the initial guess. In this study, we exploit the separable structure of the 4D-Var problem to propose a practical variant of the alternating direction method of multipliers (ADMM), referred to as the linearized multi-block ADMM with regularization. Unlike classical first-order optimization methods that primarily focus on initial conditions, our approach derives the Euler-Lagrange equation for the entire dynamical system, enabling more comprehensive and effective utilization of observational data. When the initial condition is poorly chosen, the arg min operation steers the iteration towards the observational data, thereby reducing sensitivity to the initial guess. The quadratic subproblems further simplify the solution process, while the parallel structure enhances computational efficiency, especially when utilizing modern hardware. To validate our approach, we demonstrate its superior performance using the Lorenz system, even in the presence of noisy observational data. Furthermore, we showcase the effectiveness of the linearized multi-block ADMM with regularization in solving the 4D-Var problems for the viscous Burgers’ equation, across various numerical schemes, including finite difference, finite element, and spectral methods. Finally, we illustrate the recovery of dynamics under noisy observational data in a 2D turbulence scenario, particularly focusing on vorticity concentration, highlighting the robustness of our algorithm in handling complex physical phenomena. © 2024, CC BY-NC-ND.

关键词： Weather forecasting

Bounded-DWA: An Efficient Local Planner for Ackermann-driven Vehicles on Sandy Terrain

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Bounded-DWA: An Efficient Local Planner for Ackermann-driven...

IEEE International Conference on Real-time computing and Robotics (RCAR)

作者： Ke Gong Zhiyuan Xu Xinyu Zhang Shanghai Key Laboratory of Trustworthy Computing Engineering Research Center of Software/Hardware Co-Design Technology and Application (MoE) and School of Software Engineering East China Normal University Shanghai Midea Group China

We present a new dynamic window approach (DWA) for mobile vehicles equipped with Ackermann steering geometry that adheres to Ackermann kinematic constraints. By integrating these constraints with the sampling window in DWA, we can further reduce and bound the sampling range and enhance the efficiency of the DWA when a mobile vehicle moves on sandy terrain. Furthermore, we improve the evaluation function to optimize the selected trajectory. Our algorithm is successfully validated in ROS and Gazebo through comparison with other existing local planner such as the original DWA and TEB algorithms. We also successfully deploy our Bounded-DWA in the application of coverage path planning, where tree-planting robots traverse on sandy terrain.

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The Distributionally Robust Optimization Model of Sparse Principal Component Analysis

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arXiv 2025年

作者： Wang, Lei Liu, Xin Chen, Xiaojun Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences Beijing China

We consider sparse principal component analysis (PCA) under a stochastic setting where the underlying probability distribution of the random parameter is uncertain. This problem is formulated as a distributionally robust optimization (DRO) model based on a constructive approach to capturing uncertainty in the covariance matrix, which constitutes a nonsmooth constrained min-max optimization problem. We further prove that the inner maximization problem admits a closed-form solution, reformulating the original DRO model into an equivalent minimization problem on the Stiefel manifold. This transformation leads to a Riemannian optimization problem with intricate nonsmooth terms, a challenging formulation beyond the reach of existing algorithms. To address this issue, we devise an efficient smoothing manifold proximal gradient algorithm. We prove the Riemannian gradient consistency and global convergence of our algorithm to a stationary point of the nonsmooth minimization problem. Moreover, we establish the iteration complexity of our algorithm. Finally, numerical experiments are conducted to validate the effectiveness and scalability of our algorithm, as well as to highlight the necessity and rationality of adopting the DRO model for sparse PCA. Copyright © 2025, The Authors. All rights reserved.

关键词： Optimization algorithms

Continual Learning with Bayesian Model Based on a Fixed Pre-Trained Feature Extractor

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SSRN

SSRN 2022年

作者： Yang, Yang Cui, Zhiying Xu, Junjie Zhong, Changhong Zheng, Wei-Shi Wang, Ruixuan School of Computer Science and Engineering Sun Yat-sen University China Key Laboratory of Machine Intelligence and Advanced Computing MOE

Deep learning has shown its human-level performance in various applications. However, current deep learning models are characterised by catastrophic forgetting of old knowledge when learning new classes. This poses a challenge particularly in intelligent diagnosis systems where initially only training data of a limited number of diseases are available. In this case, updating the intelligent system with data of new diseases would inevitably downgrade its performance on previously learned diseases. Inspired by the process of learning new knowledge in human brains, we propose a Bayesian generative model for continual learning built on a fixed pre-trained feature extractor. In this model, knowledge of each old class can be compactly represented by a collection of statistical distributions, e.g. with Gaussian mixture models, and naturally kept from forgetting in continual learning over time. Unlike existing class-incremental learning methods, the proposed approach is not sensitive to the continual learning process and can be additionally well applied to the data-incremental learning scenario. Experiments on multiple medical and natural image classification tasks showed that the proposed approach outperforms state-of-the-art approaches which even keep some images of old classes during continual learning of new classes. © 2022, The Authors. All rights reserved.

关键词： Intelligent systems