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Dynamic and Distributed Online Convex optimization for Demand Response of Commercial Buildings

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IEEE CONTROL SYSTEMS LETTERS 2020年第3期4卷 632-637页

作者： Lesage-Landry, Antoine Callaway, Duncan S. Univ Calif Berkeley Energy & Resources Grp Berkeley CA 94720 USA

We extend the regret analysis of the online distributed weighted dual averaging (DWDA) algorithm from Hosseini et al. to the dynamic setting and provide the tightest dynamic regret bound known to date with respect to the time horizon for a distributed online convex optimization (OCO) algorithm. Our bound is linear in the cumulative difference between consecutive optima and does not depend explicitly on the time horizon. We use dynamic-online DWDA (D-ODWDA) and formulate a performance-guaranteed distributed online demand response approach for heating, ventilation, and air-conditioning (HVAC) systems of commercial buildings. We show the performance of our approach for fast timescale demand response in numerical simulations and obtain demand response decisions that closely reproduce the centralized optimal ones.

关键词： Heuristic algorithms Buildings Power system dynamics Fans Real-time systems Convex functions Load management optimization algorithms machine learning power systems

Génération de Matrices de Corrélation avec des Structures de Graphe par Optimisation Convexe

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arXiv 2025年

作者： Fahkar, Ali Polisano, Kévin Gannaz, Irène Achard, Sophie Univ. Grenoble Alpes CNRS Grenoble INP Inria LJK GrenobleF-38000 France Univ. Grenoble Alpes CNRS Grenoble INP G-SCOP Grenoble38000 France

This work deals with the generation of theoretical correlation matrices with specific sparsity patterns, associated to graph structures. We present a novel approach based on convex optimization, offering greater flexibility compared to existing techniques, notably by controlling the mean of the entry distribution in the generated correlation matrices. This allows for the generation of correlation matrices that better represent realistic data and can be used to benchmark statistical methods for graph inference. Copyright © 2025, The Authors. All rights reserved.

关键词： optimization algorithms

Exploring the Performance-Reproducibility Trade-off in Quality-Diversity

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arXiv 2024年

作者： Flageat, Manon Janmohamed, Hannah Lim, Bryan Cully, Antoine Adaptive and Intelligent Robotics Lab Department of Computing Imperial College London United Kingdom

Quality-Diversity (QD) algorithms have exhibited promising results across many domains and applications. However, uncertainty in fitness and behaviour estimations of solutions remains a major challenge when QD is used in complex real-world applications. While several approaches have been proposed to improve the performance in uncertain applications, many fail to address a key challenge: determining how to prioritise solutions that perform consistently under uncertainty, in other words, solutions that are reproducible. Most prior methods improve fitness and reproducibility jointly, ignoring the possibility that they could be contradictory objectives. For example, in robotics, solutions may reliably walk at 90% of the maximum velocity in uncertain environments, while solutions that walk faster are also more prone to falling over. As this is a trade-off, neither one of these two solutions is "better" than the other. Thus, algorithms cannot intrinsically select one solution over the other, but can only enforce given preferences over these two contradictory objectives. In this paper, we formalise this problem as the performance-reproducibility trade-off for uncertain QD. We propose four new a-priori QD algorithms that find optimal solutions for given preferences over the trade-offs. We also propose an a-posteriori QD algorithm for when these preferences cannot be defined in advance. Our results show that our approaches successfully find solutions that satisfy given preferences. Importantly, by simply accounting for this trade-off, our approaches perform better than existing uncertain QD methods. This suggests that considering the performance-reproducibility trade-off unlocks important stepping stones that are usually missed when only performance is optimised. © 2024, CC BY.

关键词： optimization algorithms

Elliptical Wishart distributions: Information geometry, maximum likelihood estimator, performance analysis and statistical learning

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arXiv 2024年

作者： Ayadi, Imen Bouchard, Florent Pascal, Frédéric Université Paris-Saclay CNRS CentraleSupélec Laboratoire des Signaux et Systèmes 3 rue Joliot-Curie Gif-sur-Yvette91190 France

This paper deals with Elliptical Wishart distributions - which generalize the Wishart distribution - in the context of signal processing and machine learning. Two algorithms to compute the maximum likelihood estimator (MLE) are proposed: a fixed point algorithm and a Riemannian optimization method based on the derived information geometry of Elliptical Wishart distributions. The existence and uniqueness of the MLE are characterized as well as the convergence of both estimation algorithms. Statistical properties of the MLE are also investigated such as consistency, asymptotic normality and an intrinsic version of Fisher efficiency. On the statistical learning side, novel classification and clustering methods are designed. For the t-Wishart distribution, the performance of the MLE and statistical learning algorithms are evaluated on both simulated and real EEG and hyperspectral data, showcasing the interest of our proposed methods. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

High-Dimensional Sparse Data Low-rank Representation via Accelerated Asynchronous Parallel Stochastic Gradient Descent

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arXiv 2024年

作者： Hu, Qicong Wu, Hao College of Computer and Information Science Southwest University Chongqing China

Data characterized by high dimensionality and sparsity are commonly used to describe real-world node interactions. Low-rank representation (LR) can map high-dimensional sparse (HDS) data to low-dimensional feature spaces and infer node interactions via modeling data latent associations. Unfortunately, existing optimization algorithms for LR models are computationally inefficient and slowly convergent on large-scale datasets. To address this issue, this paper proposes an Accelerated Asynchronous Parallel Stochastic Gradient Descent (A2PSGD) for High-Dimensional Sparse Data Low-rank Representation with three fold-ideas: a) establishing a lock-free scheduler to simultaneously respond to scheduling requests from multiple threads;b) introducing a greedy algorithm-based load balancing strategy for balancing the computational load among threads;c) incorporating Nesterov's accelerated gradient into the learning scheme to accelerate model convergence. Empirical studies show that A2PSGD outperforms existing optimization algorithms for HDS data LR in both accuracy and training time. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

A preconditioned second-order convex splitting algorithm with a difference of varying convex functions and line search

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arXiv 2024年

作者： Shen, Xinhua Shang, Zaijiu Sun, Hongpeng School of Mathematics Renmin University of China China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Shanghai Institute for Mathematics and Interdisciplinary Sciences Shanghai200092 China

This paper introduces a preconditioned convex splitting algorithm enhanced with line search techniques for nonconvex optimization problems. The algorithm utilizes second-order backward differentiation formulas (BDF) for the implicit and linear components and the Adams-Bashforth scheme for the nonlinear and explicit parts of the gradient flow in variational functions. The proposed algorithm, resembling a generalized difference-of-convex-function approach, involves a changing set of convex functions in each iteration. It integrates the Armijo line search strategy to improve performance. The study also discusses classical preconditioners such as symmetric Gauss-Seidel, Jacobi, and Richardson within this context. The global convergence of the algorithm is established through the Kurdyka-Lojasiewicz properties, ensuring convergence within a finite number of preconditioned iterations. Numerical experiments demonstrate the superiority of the proposed second-order convex splitting with line search over conventional difference-of-convex-function algorithms. © 2024, CC BY-NC-ND.

关键词： optimization algorithms

Complexity order of multiple resource algorithms

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arXiv 2024年

作者： Teh, Run Yan Thenabadu, Manushan Drummond, Peter D. Centre for Quantum Science and Technology Theory Swinburne University of Technology Melbourne3122 Australia

Algorithmic efficiency is essential to reducing energy use and time taken for computational problems. Optimizing efficiency is important for tasks involving multiple resources, for example in stochastic calculations where the size of the random ensemble competes with the time-step. We define the complexity order of an algorithm needing multiple resources as the exponent of inverse total error with respect to the total resources used. The optimum order c is predicted for cases involving competing, factorable resources. As an illustration, this is applied to computing averages in a stochastic differential equation, with numerical examples that agree with earlier literature, as well as with the more general analytic theory that is obtained here. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

Instance-Dependent Confidence and Early Stopping for Reinforcement Learning

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Journal of Machine Learning Research 2023年 24卷

作者： Xia, Eric Khamaru, Koulik Wainwright, Martin J. Jordan, Michael I. Department of EECS Massachusetts Institute of Technology CambridgeMA02139 United States Department of Statistics Rutgers University PiscatawayNJ08854 United States Department of EECS and Mathematics Massachusetts Institute of Technology CambridgeMA02139 United States Department of EECS and Statistics University of California Berkeley BerkeleyCA94720 United States

Reinforcement learning algorithms are known to exhibit a variety of convergence rates depending on the problem structure. Recent years have witnessed considerable progress in developing theory that is instance-dependent, along with algorithms that achieve such instance-optimal guarantees. However, important questions remain in how to utilize such notions for inferential purposes, or for early stopping, so that data and computational resources can be saved for "easy" problems. This paper develops data-dependent procedures that output instance-dependent confidence regions for evaluating and optimizing policies in a Markov decision process. Notably, our procedures require only black-box access to an instance-optimal algorithm, and re-use the samples used in the estimation algorithm itself. The resulting data-dependent stopping rule adapts instance-specific difficulty of the problem and allows for early termination for problems with favorable structure. We highlight benefit of such early stopping rules via some numerical studies. ©2023 Eric Xia, Koulik Khamaru, Martin J. Wainwright, and Michael I. Jordan.

关键词： optimization algorithms

(Almost) Smooth Sailing: Towards Numerical Stability of Neural Networks Through Differentiable Regularization of the Condition Number

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arXiv 2024年

作者： Nenov, Rossen Haider, Daniel Balazs, Peter Acoustics Research Institute Austrian Academy of Sciences Vienna Austria Department of Mathematics University of Vienna Vienna Austria

Maintaining numerical stability in machine learning models is crucial for their reliability and performance. One approach to maintain stability of a network layer is to integrate the condition number of the weight matrix as a regularizing term into the optimization algorithm. However, due to its discontinuous nature and lack of differentiability the condition number is not suitable for a gradient descent approach. This paper introduces a novel regularizer that is provably differentiable almost everywhere and promotes matrices with low condition numbers. In particular, we derive a formula for the gradient of this regularizer which can be easily implemented and integrated into existing optimization algorithms. We show the advantages of this approach for noisy classification and denoising of MNIST images. © 2024, CC BY.

关键词： optimization algorithms