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arXiv 2024年

作者： Bilel, Bensaid Université de Bordeaux 351 cours de la Libération TalenceF 33 405 France

The classical Armijo backtracking algorithm [4] achieves the optimal complexity for smooth functions like gradient descent but without any hyperparameter tuning. However, the smoothness assumption is not suitable for Deep Learning optimization. In this work, we show that some variants of the Armijo optimizer achieves acceleration and optimal complexities under assumptions more suited for Deep Learning: the (L0, L1) smoothness condition [26] and analyticity [5]. New dependences on the smoothness constants and the initial gap are established. The results theoretically highlight the powerful efficiency of Armijo-like conditions for highly non-convex problems. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

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Markovian Foundations for Quasi-Stochastic Approximation in Two Timescales: Extended Version

arXiv

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arXiv 2024年

作者： Lauand, Caio Kalil Meyn, Sean The Department of Electrical and Computer Engineering University of Florida GainesvilleFL United States

Many machine learning and optimization algorithms can be cast as instances of stochastic approximation (SA). The convergence rate of these algorithms is known to be slow, with the optimal mean squared error (MSE) of order O(n−1). In prior work it was shown that MSE bounds approaching O(n−4) can be achieved through the framework of quasi-stochastic approximation (QSA);essentially SA with careful choice of deterministic exploration. These results are extended to two time-scale algorithms, as found in policy gradient methods of reinforcement learning and extremum seeking control. The extensions are made possible in part by a new approach to analysis, allowing for the interpretation of two timescale algorithms as instances of single timescale QSA, made possible by the theory of negative Lyapunov exponents for QSA. The general theory is illustrated with applications to extremum seeking control (ESC). Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

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DETERMINING THE OPTIMAL SAMPLING SET SIZE FOR RANDOM SEARCH 13

DETERMINING THE OPTIMAL SAMPLING SET SIZE FOR RANDOM SEARCH

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Simulation Conference

作者： Chenbo Zhu Jie Xu Chun-Hung Chen Loo Hay Lee Jianqiang Hu Fudan University Shanghai China George Mason University Fairfax Virginia National University of Singapore Singapore

ISBN: (纸本)9781479920778

Random search is a core component of many well known simulation optimization algorithms such as nested partition and COMPASS. Given a fixed computation budget, a critical decision is how many solutions to sample from a search area, which directly determines the number of simulation replications for each solution assuming that each solution receives the same number of simulation replications. This is another instance of the exploration vs. exploitation tradeoff in simulation optimization. Modeling the performance profile of all solutions in the search area as a normal distribution, we propose a method to (approximately) optimally determine the size of the sampling set and the number of simulation replications and use numerical experiments to demonstrate its performance.

关键词： Solutions simulating optimization algorithms compasses Gaussian distribution numerical invariant Core Assembly

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optimization of Antennas in Communication Systems: Digital Modulation Analysis

Optimization of Antennas in Communication Systems: Digital M...

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SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference

作者： Guilherme Franco Santos Samuel Gomes Quintanilha Robert Kley Lagano Marco Antonio Brasil Terada Rafael Rabelo Nunes Dept. of Electrical Engineering University of Brasilia Centro Universitario Estacio de Brasilia Faculdade Atenas

ISBN: (纸本)9781467394932

This paper focus on studying techniques that allow optimization of a communication system by analyzing the patterns of antenna configurations and digital modulations. Antenna design methods are discussed, taking into account parameters such as the number of elements in arrays and modulation types. Computer simulations are made with the use of LTE system simulation and antenna packages freely available. The main goal is to investigate if the modulation scheme influences the antenna design.

关键词： Antenna synthesis optimization algorithms Digital modulations Wireless communication systems Electromagnetic compatibility and interference

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A Decentralized Resource Allocation Approach for Sharing Renewable Energy among Interconnected Smart Homes

A Decentralized Resource Allocation Approach for Sharing Ren...

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IEEE Annual Conference on Decision and Control

作者： Raffaele Carli Mariagrazia Dotoli Department of Electrical and Information Engineering of the Polytechnic of Bari Bari Italy

ISBN: (纸本)9781479978878

The paper deals with the scheduling of energy activities of a group of interconnected users that buy energy from a producer and share a renewable energy source. The scheduling problem is stated and solved with a twofold goal. First, the model is formulated to ensure social welfare-optimal allocation of the energy produced from the shared renewable energy generator. Second, the model aims at cost-optimal planning of users' controllable appliances taking into account a realistic time-varying quadratic pricing of the energy bought from the distribution network. The solution approach relies on a decentralized optimization algorithm that is composed by a two-level iterative procedure combining Gauss-Seidel decomposition with competitive game formulation. A case study simulated in different scenarios demonstrates that the approach allows exploiting the potential of renewable energy sources' sharing to reduce individual users' energy consumption costs, limiting the peak average ratio of energy profiles and complying with the customer's energy needs.

关键词： Renewable energy Energy sources Resource utilization renewable energy sources Smart homes Decentralized Power grids optimization algorithms actor management of resources

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On Top-k Selection in Multi-Armed Bandits and Hidden Bipartite Graphs 15

On Top-k Selection in Multi-Armed Bandits and Hidden Biparti...

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Annual Conference on Neural Information Processing Systems

作者： Wei Cao Jian Li Yufei Tao Zhize Li Tsinghua University Chinese University of Hong Kong

ISBN: (纸本)9781510825024

This paper discusses how to efficiently choose from n unknown distributions the k ones whose means are the greatest by a certain metric, up to a small relative error. We study the topic under two standard settings-multi-armed bandits and hidden bipartite graphs-which differ in the nature of the input distributions. In the former setting, each distribution can be sampled (in the i.i.d. manner) an arbitrary number of times, whereas in the latter, each distribution is defined on a population of a finite size m (and hence, is fully revealed after m samples). For both settings, we prove lower bounds on the total number of samples needed, and propose optimal algorithms whose sample complexities match those lower bounds.

关键词： Lower bound Bipartite graph TWO-COMPONENT optimization algorithms relative errors

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Performance of Variational algorithms for Local Hamiltonian Problems on Random Regular Graphs

arXiv

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arXiv 2024年

作者： Marwaha, Kunal She, Adrian Sud, James University of Chicago United States University of Toronto Canada

We design two variational algorithms to optimize specific 2-local Hamiltonians defined on graphs. Our algorithms are inspired by the Quantum Approximate optimization Algorithm. We develop formulae to analyze the energy achieved by these algorithms with high probability over random regular graphs in the infinite-size limit, using techniques from [Bas+22a]. The complexity of evaluating these formulae scales exponentially with the number of layers of the algorithms, so our numerical evaluation is limited to a small constant number of layers. We compare these algorithms to simple classical approaches and a state-of-the-art worst-case algorithm. We find that the symmetry inherent to these specific variational algorithms presents a major obstacle to successfully optimizing the Quantum MaxCut (QMC) Hamiltonian on general graphs. Nonetheless, the algorithms outperform known methods to optimize the EPR Hamiltonian of [Kin23] on random regular graphs, and the QMC Hamiltonian when the graphs are also bipartite. As a special case, we show that with just five layers of our algorithm, we can already prepare states within 1.62% error of the ground state energy for QMC on an infinite 1D ring, corresponding to the antiferromagnetic Heisenberg spin chain. © 2024, CC BY.

关键词： optimization algorithms

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Strategies for optimizing double-bracket quantum algorithms

arXiv

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arXiv 2024年

作者： Xiaoyue, Li Robbiati, Matteo Pasquale, Andrea Pedicillo, Edoardo Wright, Andrew Carrazza, Stefano Gluza, Marek School of Physical and Mathematical Sciences Nanyang Technological University 21 Nanyang Link Singapore637371 Singapore Geneva1211 Switzerland TIF Lab Dipartimento di Fisica Università degli Studi diMilano Italy Quantum Research Centre Technology Innovation Institute Abu Dhabi United Arab Emirates INFN Sezione di Milano Milan Italy Lausanne Switzerland

Recently double-bracket quantum algorithms have been proposed as a way to compile circuits for approximating eigenstates. Physically, they consist of appropriately composing evolutions under an input Hamiltonian together with diagonal evolutions. Here, we present strategies to optimize the choice of the double-bracket evolutions to enhance the diagonalization efficiency. This can be done by finding optimal generators and durations of the evolutions. We present numerical results regarding the preparation of double-bracket iterations, both in ideal cases where the algorithm’s setup provides analytical convergence guarantees and in more heuristic cases, where we use an adaptive and variational approach to optimize the generators of the evolutions. As an example, we discuss the efficacy of these optimization strategies when considering a spin-chain Hamiltonian as the target. To propose algorithms that can be executed starting today, fully aware of the limitations of the quantum technologies at our disposal, we finally present a selection of diagonal evolution parametrizations that can be directly compiled into CNOTs and single-qubit rotation gates. We discuss the advantages and limitations of this compilation and propose a way to take advantage of this approach when used in synergy with other existing methods. © 2024, CC BY.

关键词： optimization algorithms

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A Set-Based Discrete Differential Evolution Algorithm

A Set-Based Discrete Differential Evolution Algorithm

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IEEE International Conference on Systems, Man, and Cybernetics

作者： Yu Liu Wei-Neng Chen Zhi-Hui Zhan Ying Lin Yue-Jiao Gong Jun Zhang Department of Computer Science Sun Yat-sen University Key Laboratory of Machine Intelligence and Sensor Network Ministry of Education Key Laboratory of Software Technology Education Department of Guangdong Province P.R. China

ISBN: (纸本)9781479906505

The TSP problem is considered as classical discrete optimization grouping problem, which is widely used in practice, but it is real a difficult NP problem. Simultaneously differential evolution (DE) algorithm has been proven to be a powerful optimization algorithm. Since the mutation process of DE contains a series of arithmetic operators operating on continuous space, few algorithms based on DE solve this problem nicely and the advantages of DE in continuous space cannot be used to solve TSP. To take full advantages of the strengths of DE, this paper proposes a set-based DE (S-DE) which completely follows the procedure of the original DE. We present a representation scheme to characterize the discrete problem space and by redefining its basic concept and all related operators in mutation, DE can operate directly on the original set space of the discrete optimization problems instead of performing a space transformation. In that way, the searching features of DE in continuous space is kept. In experiment, we test the performance of our proposed S-DE and the results show it is very promising.

关键词： component Discrete Differential algorithm Sebased COP TSP MT CARD16 gene discrete element optimization algorithms Total suspended particles evolutionary algorithm arithmetic operator NP problem CONTINUOUS SPACE differential evolution algorithms

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Sampling-based Learning Control for Quantum Systems with Hamiltonian Uncertainties

Sampling-based Learning Control for Quantum Systems with Ham...

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IEEE Annual Conference on Decision and Control

作者： Daoyi Dong Chunlin Chen Ruixing Long Bo Qi Ian R. Petersen School of Information Technology and Electrical Engineering University of New South Wales at the Australian Defence Force Academy Canberra ACT 2600 Australia Department of Control and System Engineering Nanjing University Nanjing 210093 China Department of Chemistry Princeton University Princeton New Jersey 08544 USA Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

ISBN: (纸本)9781467357159

Robust control design for quantum systems has been recognized as a key task in the development of practical quantum technology. In this paper, we present a systematic numerical methodology of sampling-based learning control (SLC) for control design of quantum systems with Hamiltonian uncertainties. The SLC method includes two steps of "training" and "testing and evaluation". In the training step, an augmented system is constructed by sampling uncertainties according to possible distributions of uncertainty parameters. A gradient flow based learning and optimization algorithm is adopted to find the control for the augmented system. In the process of testing and evaluation, a number of samples obtained through sampling the uncertainties are tested to evaluate the control performance. Numerical results demonstrate the success of the SLC approach. The SLC method has potential applications for robust control design of quantum systems.

关键词： design control learning control quanta AUGMENTED SYSTEM Uncertainty Gradient flow Hamiltonian control performance Robust control optimization algorithms

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