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A Novel Approach to statistical comparison of meta-heuristic stochastic optimization algorithms using deep statistics

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INFORMATION SCIENCES 2017年 417卷 186-215页

作者： Eftimov, Tome Korosec, Peter Seljak, Barbara Korousic Jozef Stefan Inst Comp Syst Dept Jamova Cesta 39 Ljubljana 1000 Slovenia Jozef Stefan Int Postgrad Sch Jamova Cesta 39 Ljubljana 1000 Slovenia Fac Math Nat Sci & Informat Technol Glagoljaska Ulica 8 Koper 6000 Slovenia

In this paper a novel approach for making a statistical comparison of meta-heuristic stochastic optimization algorithms over multiple single-objective problems is introduced, where a new ranking scheme is proposed to obtain data for multiple problems. The main contribution of this approach is that the ranking scheme is based on the whole distribution, instead of using only one statistic to describe the distribution, such as average or median. Averages are sensitive to outliers (i.e., the poor runs of the stochastic optimization algorithms) and consequently medians are sometimes used. However, using the common approach with either averages or medians, the results can be affected by the ranking scheme that is used by some standard statistical tests. This happens when the differences between the averages or medians are in some 6-neighborhood and the algorithms obtain different ranks though they should be ranked equally given the small differences that exist between them. The experimental results obtained on Black-Box Benchmarking 2015, show that our approach gives more robust results compared to the common approach in cases when the results are affected by outliers or by a misleading ranking scheme. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Statistical comparison stochastic optimization algorithms Single objective function Ranking scheme Multiple problem analysis

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DSCTool: A web-service-based framework for statistical comparison of stochastic optimization algorithms

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APPLIED SOFT COMPUTING 2020年 87卷 105977-000页

作者： Eftimov, Tome Petelin, Gasper Korosec, Peter Jozef Stefan Inst Comp Syst Dept Ljubljana 1000 Slovenia Stanford Univ Dept Biomed Data Sci Stanford CA 94305 USA Stanford Univ Ctr Populat Hlth Sci Stanford CA 94305 USA Univ Ljubljana Fac Comp & Informat Sci Ljubljana 1000 Slovenia

DSCTool is a statistical tool for comparing performance of stochastic optimization algorithms on a single benchmark function (i.e. single-problem analysis) or a set of benchmark functions (i.e., multiple-problem analysis). DSCTool implements a recently proposed approach, called Deep Statistical Comparison (DSC), and its variants. DSC ranks optimization algorithms by comparing distributions of obtained solutions for a problem instead of using a simple descriptive statistic such as the mean or the median. The rankings obtained for an individual problem give the relations between the performance of the applied algorithms. To compare optimization algorithms in the multiple-problem scenario, an appropriate statistical test must be applied to the rankings obtained for a set of problems. The main advantage of DSCTool are its REST web services, which means all its functionalities can be accessed from any programming language. In this paper, we present the DSCTool in detail with examples for its usage. (C) 2019 The Author( s). Published by Elsevier B.V.

关键词： Statistical tool Benchmarking stochastic optimization algorithms DSCTool Web service

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Understanding Exploration and Exploitation Powers of Meta-heuristic stochastic optimization algorithms through Statistical Analysis 19

Understanding Exploration and Exploitation Powers of Meta-he...

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Genetic and Evolutionary Computation Conference (GECCO)

作者： Eftimov, Tome Korosec, Peter Jozef Stefan Inst Comp Syst Dept Ljubljana Slovenia Stanford Univ Ctr Populat Hlth Sci Palo Alto CA 94304 USA Univ Primorska Fac Math Nat Sci & Informat Technol Koper Slovenia

ISBN: (纸本)9781450367486

Understanding of exploration and exploitation powers of metaheuristic stochastic optimization algorithms is very important for algorithm developers. For this reason, we have recently proposed an approach for making a statistical comparison of meta-heuristic stochastic optimization algorithms according to the distribution of the solutions in the search space, which is also presented in this paper. Its main contribution is the support to identify exploration and exploitation powers of the compared algorithms. This is especially important when dealing with multimodal search spaces, which consist of many local optima with similar values, and large-scale continuous optimization problems, where it is hard to understand the reasons for the differences in performances. Experimental results showed that our recently proposed approach gives very promising results.

关键词： Statistical analysis stochastic optimization algorithms

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Identifying practical significance through statistical comparison of meta-heuristic stochastic optimization algorithms

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APPLIED SOFT COMPUTING 2019年 85卷 105862-000页

作者： Eftimov, Tome Korosec, Peter Jozef Stefan Inst Comp Syst Dept Ljubljana 1000 Slovenia Stanford Univ Palo Alto CA 94305 USA

In this paper, we propose an extension of a recently proposed Deep Statistical Comparison (DSC) approach, called practical Deep Statistical Comparison (pDSC), which takes into account practical significance when making a statistical comparison of meta-heuristic stochastic optimization algorithms for single-objective optimization. For achieving practical significance, two variants of the standard DSC ranking scheme are proposed. The first is called sequential pDSC, and takes into account practical significance by preprocessing of the independent optimization runs in a sequential order. The second is called Monte Carlo pDSC, and avoids any dependency of practical significance with regard to the ordering of optimization runs. The analysis of identifying practical significance on benchmark tests for single-objective problems, shows that for some cases, both variants of pDSC compared to the Chess Rating System for Evolutionary algorithms (CRS4EAs) approach give different conclusions. Preprocessing for practical significance is carried out in a similar way, but there are cases when the conclusion for practical significance differ, which comes from the different statistical concepts used to identify practical significance. (C) 2019 The Author(s). Published by Elsevier B.V.

关键词： Benchmarking Practical significance Ranking scheme Single objective problem Statistical comparison stochastic optimization algorithms

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algorithms of Robust stochastic optimization Based on Mirror Descent Method

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AUTOMATION AND REMOTE CONTROL 2019年第9期80卷 1607-1627页

作者： Nazin, A., V Nemirovsky, A. S. Tsybakov, A. B. Juditsky, A. B. Russian Acad Sci Trapeznikov Inst Control Sci Moscow Russia Georgia Inst Technol Atlanta GA 30332 USA ENSAE CREST Palaiseau France Univ Grenoble Alpes Grenoble France

We propose an approach to the construction of robust non-Euclidean iterative algorithms by convex composite stochastic optimization based on truncation of stochastic gradients. For such algorithms, we establish sub-Gaussian confidence bounds under weak assumptions about the tails of the noise distribution in convex and strongly convex settings. Robust estimates of the accuracy of general stochastic algorithms are also proposed.

关键词： robust iterative algorithms stochastic optimization algorithms convex composite stochastic optimization mirror descent method robust confidence sets

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Adaptive coordinate sampling for stochastic primal-dual optimization

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2022年第1期29卷 24-47页

作者： Liu, Huikang Wang, Xiaolu So, Anthony Man-Cho Imperial Coll London Imperial Coll Business Sch London SW7 2BX England Chinese Univ Hong Kong Dept Syst Engn & Engn Management Hong Kong Peoples R China

We consider the regularized empirical risk minimization (ERM) of linear predictors, which arises in a variety of problems in machine learning and statistics. After reformulating the original ERM as a bilinear saddle-point problem, we can apply stochastic primal-dual methods to solve it. Sampling the primal or dual coordinates with a fixed nonuniform distribution is usually employed to accelerate the convergence of the algorithm, but such a strategy only exploits the global information of the objective function. To capture its local structures, we propose an adaptive importance sampling strategy that chooses the coordinates based on delicately designed nonuniform and nonstationary distributions. When our adaptive coordinate sampling strategy is applied to the stochastic Primal-Dual Coordinate (SPDC), we prove that the resulting algorithm enjoys linear convergence. Moreover, we show that the ideal form of our adaptive sampling exhibits strictly sharper convergence rate under certain conditions compared with the vanilla SPDC. We also extend our sampling strategy to other algorithms including Doubly stochastic Primal-Dual Coordinate (DSPDC) and stochastic Primal-Dual with O(1) per-iteration cost and Variance Reduction (SPD1-VR), where both primal and dual coordinates are randomly sampled. Our experiment results show that the proposed strategy significantly improves the convergence performance of the methods when compared with existing sampling strategies.

关键词： primal-dual methods stochastic optimization algorithms adaptive importance sampling machine learning

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System-level post-optimization of Delta-Sigma modulators using finite difference stochastic approximation

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ANALOG INTEGRATED CIRCUITS AND SIGNAL PROCESSING 2016年第1期88卷 31-42页

作者： Tang, Hua Univ Minnesota Dept Elect & Comp Engn Duluth MN 55812 USA

Traditional methods for system-level design of Delta-Sigma (a dagger I ) pound modulators typically assume linear modeling of the modulator, in which quantization noise is modeled as additive independent white noise. But it is well known that the a dagger I pound modulator is a non-linear system and linear modeling is only an approximation. Also, circuit-level non-idealities, which may greatly change the modulator behavior, are typically neglected at system-level design. As a result, system-level modulator designs obtained from traditional methods may not be realistically optimal. This paper presents a system-level post-optimization method for a dagger I pound modulators so that modulator designs initially obtained from traditional methods are post-optimized considering non-linear and non-ideal characteristics of a dagger I pound modulators including both quantization noise and circuit-level non-idealities. The post-optimization algorithm is based on Finite Difference stochastic Approximation due to the stochastic nature of modeling of some circuit-level non-idealities in system-level design. During the post-optimization run, each candidate design is simulated for performance measures and stability has always been a must constraint. Results on two a dagger I pound modulators have shown that post-optimized modulator designs outperform the original designs from traditional methods.

关键词： Delta-Sigma modulators System-level design Post-optimization Quantizer non-linearity Circuit-level non-idealities Behavioral modeling Noise stochastic optimization algorithms

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Log-Linear Convergence and Divergence of the Scale-Invariant (1+1)-ES in Noisy Environments

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ALGORITHMICA 2011年第3期59卷 425-460页

作者： Jebalia, Mohamed Auger, Anne Hansen, Nikolaus LRI Paris Sud Univ TAO Team INRIA Saclay Ile de France F-91405 Orsay France

Noise is present in many real-world continuous optimization problems. stochastic search algorithms such as Evolution Strategies (ESs) have been proposed as effective search methods in such contexts. In this paper, we provide a mathematical analysis of the convergence of a (1+1)-ES on unimodal spherical objective functions in the presence of noise. We prove for a multiplicative noise model that for a positive expected value of the noisy objective function, convergence or divergence happens depending on the infimum of the support of the noise. Moreover, we investigate convergence rates and show that log-linear convergence is preserved in presence of noise. This result is a strong theoretical foundation of the robustness of ESs with respect to noise.

关键词： Numerical optimization Noisy optimization stochastic optimization algorithms Evolution strategies Convergence Convergence rates Markov chains Borel-Cantelli lemma

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stochastic heavy ball

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ELECTRONIC JOURNAL OF STATISTICS 2018年第1期12卷 461-529页

作者： Gadat, Sebastien Panloup, Fabien Saadane, Sofiane Univ Toulouse Toulouse Sch Econ UMR 5604 Toulouse France Univ Angers Lab Angevin Rech Math UMR 6093 Angers France Univ Toulouse Inst Math Toulouse UMR 5219 Toulouse France

This paper deals with a natural stochastic optimization procedure derived from the so-called Heavy-ball method differential equation, which was introduced by Polyak in the 1960s with his seminal contribution [Pol64]. The Heavy-ball method is a second-order dynamics that was investigated to minimize convex functions f. The family of second-order methods recently received a large amount of attention, until the famous contribution of Nesterov [Nes83], leading to the explosion of large-scale optimization problems. This work provides an in-depth description of the stochastic heavy-ball method, which is an adaptation of the deterministic one when only unbiased evalutions of the gradient are available and used throughout the iterations of the algorithm. We first describe some almost sure convergence results in the case of general non-convex coercive functions f. We then examine the situation of convex and strongly convex potentials and derive some non-asymptotic results about the stochastic heavy-ball method. We end our study with limit theorems on several rescaled algorithms.

关键词： stochastic optimization algorithms second-order methods random dynamical systems

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MINIMIZING EXPECTED MAKESPANS ON UNIFORM PROCESSOR SYSTEMS

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ADVANCES IN APPLIED PROBABILITY 1987年第1期19卷 177-201页

作者： COFFMAN, EG FLATTO, L GAREY, MR WEBER, RR UNIV CAMBRIDGE QUEENS COLL CAMBRIDGE CB3 9ETENGLAND

We study the problem of scheduling n given jobs on m uniform processors to minimize expected makespan (maximum finishing time). Job execution times are not known in advance, but are known to be exponentially distributed, with identical rate parameters depending solely on the executing processor. For m = 2 and 3, we show that there exist optimal scheduling rules of a certain threshold type, and we show how the required thresholds can be easily determined. We conjecture that similar threshold rules suffice for m > 3 but are unable to prove this. However, for m > 3 we do obtain a general bound on problem size that permits Bellman equations to be used to construct an optimal scheduling rule for any given set of m rate parameters, with the memory required to represent that scheduling rule being independent of the number of remaining jobs.

关键词： SCHEDULING SCHEDULING stochastic optimization algorithms

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