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2nd Russian Supercomputing Days Conference (RuSCDays)

作者： Evtushenko, Yury Golubeva, Yana Orlov, Yury Posypkin, Mikhail FRC CSC RAS Dorodnicyn Comp Ctr Moscow Russia

ISBN: (纸本)9783319556680;9783319556697

The branch-and-bound (B&B) is a fundamental algorithmic scheme for a large variety of global optimization methods. For many problems B&B requires the amount of computing resources far beyond the power of a single-CPU workstation thus making parallelization almost inevitable. The approach proposed in this paper allows one to evaluate load balancing algorithms for parallel B&B with various numbers of processors, sizes of the search tree, the characteristics of the supercomputer's interconnect. The proposed approach was implemented as a special tool that simulates the process of resolution of the optimization problem by B&B method as a stochastic tree branching process. Data exchanges are modeled using the concept of logical time. The user-friendly graphical interface can render both real traces and ones produced by the simulator. It provides efficient visualization of the CPU's load, data exchanges and progress of the optimization process.

关键词： Performance analysis and simulation Parallel computing Global optimization branch-and-bound methods Load balancing

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Adversarial Robustness Guarantees for Gaussian Processes

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JOURNAL OF MACHINE LEARNING RESEARCH 2022年第1期23卷 1-55页

作者： Patane, Andrea Blaas, Arno Laurenti, Luca Cardelli, Luca Roberts, Stephen Kwiatkowska, Marta Univ Oxford Dept Comp Sci Oxford OX1 3QG England Univ Oxford Dept Engn Sci Oxford OX2 6ED England

Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications. Such scenarios demand that GP decisions are not only accurate, but also robust to perturbations. In this paper we present a frame-work to analyse adversarial robustness of GPs, defined as invariance of the model's decision to bounded perturbations. Given a compact subset of the input space T subset of Rd, a point x* and a GP, we provide provable guarantees of adversarial robustness of the GP by comput-ing lower and upper bounds on its prediction range in T. We develop a branch-and-bound scheme to refine the bounds and show, for any epsilon > 0, that our algorithm is guaranteed to converge to values epsilon-close to the actual values in finitely many iterations. The algorithm is anytime and can handle both regression and classification tasks, with analytical formulation for most kernels used in practice. We evaluate our methods on a collection of synthetic and standard benchmark data sets, including SPAM, MNIST and FashionMNIST. We study the effect of approximate inference techniques on robustness and demonstrate how our method can be used for interpretability. Our empirical results suggest that the adversarial robustness of GPs increases with accurate posterior estimation.

关键词： Gaussian processes adversarial robustness non-linear optimisation Bayesian learning branch-and-bound methods

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Discrete MMSE Precoding for Multiuser MIMO Systems With PSK Modulation

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2022年第10期21卷 8817-8831页

作者： Lopes, Erico S. P. Landau, Lukas T. N. Pontifical Catholic Univ Rio de Janeiro Ctr Studies Telecommun BR-22453900 Rio De Janeiro Brazil

We propose an optimal MMSE precoding technique using quantized signals with constant envelope. Unlike the existing MMSE design that relies on 1-bit resolution, the proposed approach employs uniform phase quantization and the bounding step in the branch-and-bound method is different in terms of considering the most restrictive relaxation of the nonconvex problem, which is then utilized for a suboptimal design also. We also propose robust MMSE designs where we exploit second order statistics of a channel state information mismatch. Moreover, unlike prior studies, we propose three different soft detection methods and an iterative detection and decoding scheme that allow the utilization of channel coding in conjunction with low-resolution precoding. Besides an exact approach for computing the extrinsic information, we propose two approximations with reduced computational complexity. Numerical simulations show that utilizing the MMSE criterion instead of the established maximum-minimum distance to the decision threshold yields a lower bit-error-rate in many scenarios. Furthermore, when using the MMSE criterion, a smaller number of bound evaluations in the branch-and-bound method is required for low and medium SNR. Finally, results based on an LDPC block code indicate that the proposed receive processing schemes yield a lower bit-error-rate compared to the conventional design.

关键词： Precoding Quantization (signal) Wireless communication Signal processing algorithms Modulation MIMO communication Iterative decoding Precoding low-resolution quantization phase quantization MIMO systems branch-and-bound methods MMSE constant envelope log-likelihood-ratios soft detection iterative detection and decoding

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Adversarial robustness guarantees for Gaussian processes

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2022年第1期23卷 6524-6578页

作者： Andrea Patanè Arno Blaas Luca Laurenti Luca Cardelli Stephen Roberts Marta Kwiatkowska Department of Computer Science University of Oxford Oxford UK Department of Engineering Science University of Oxford Oxford UK

Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications. Such scenarios demand that GP decisions are not only accurate, but also robust to perturbations. In this paper we present a framework to analyse adversarial robustness of GPs, defined as invariance of the model's decision to bounded perturbations. Given a compact subset of the input space T ⊆ ℝd, a point x* and a GP, we provide provable guarantees of adversarial robustness of the GP by computing lower and upper bounds on its prediction range in T. We develop a branch-and-bound scheme to refine the bounds and show, for any ε > 0, that our algorithm is guaranteed to converge to values ε-close to the actual values in finitely many iterations. The algorithm is anytime and can handle both regression and classification tasks, with analytical formulation for most kernels used in practice. We evaluate our methods on a collection of synthetic and standard benchmark data sets, including SPAM, MNIST and FashionMNIST. We study the effect of approximate inference techniques on robustness and demonstrate how our method can be used for interpretability. Our empirical results suggest that the adversarial robustness of GPs increases with accurate posterior estimation.

关键词： Gaussian processes adversarial robustness non-linear optimisation Bayesian learning branch-and-bound methods

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Optimal Precoding for Multiuser MIMO Systems With Phase Quantization and PSK Modulation via branch-and-bound

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IEEE WIRELESS COMMUNICATIONS LETTERS 2020年第9期9卷 1393-1397页

作者： Lopes, Erico S. P. Landau, Lukas T. N. Pontificia Univ Catolica Rio De Janeiro Ctr Estudos Telecomunicacoes BR-22453900 Rio De Janeiro Brazil

With an increasing number of antennas in MIMO systems, the energy consumption and costs of the corresponding front ends become relevant. In this context, a promising approach is the consideration of low-resolution data converters. In this letter we propose an optimal precoding algorithm constrained to constant envelope signals and phase quantization that maximizes the minimum distance to the decision threshold at the receivers using a branch-and-bound strategy. The proposed algorithm is superior to the existing methods in terms of bit error rate. Numerical results show that the proposed approach has significantly lower complexity than exhaustive search.

关键词： Precoding Quantization (signal) Phase shift keying Transmitting antennas MIMO communication Upper bound Energy consumption Precoding low-resolution quantization MIMO systems branch-and-bound methods

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branch-and-bound Precoding for Multiuser MIMO Systems With 1-Bit Quantization

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IEEE WIRELESS COMMUNICATIONS LETTERS 2017年第6期6卷 770-773页

作者： Landau, Lukas T. N. de Lamare, Rodrigo C. Pontificia Univ Catolica Rio de Janeiro Ctr Estudos Telecomunicacoes BR-22453900 Rio De Janeiro Brazil

Multiple-antenna systems is a key technique for serving multiple users in future wireless systems. For low energy consumption and hardware complexity we first consider transmit symbols with constant magnitude and then 1-bit digital-to-analog converters (DACs). We propose precoding designs which maximize the minimum distance to the decision threshold at the receiver. The precoding design with 1-bit DAC corresponds to a discrete optimization problem, which we solve exactly with a branch-and-bound strategy. We alternatively present an approximation based on relaxation. Our results show that the proposed branch-and-bound approach has polynomial complexity. The proposed methods outperform existing precoding methods with 1-bit DAC in terms of uncoded bit error rate and sum-rate. The performance loss in comparison to infinite DAC resolution is small.

关键词： Precoding 1-bit quantization MIMO systems branch-and-bound methods

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Lattice preconditioning for the real relaxation branch-and-bound approach for integer least squares problems

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JOURNAL OF GLOBAL OPTIMIZATION 2014年第2-3期59卷 227-242页

作者： Anjos, Miguel F. Chang, Xiao-Wen Ku, Wen-Yang Gerad Montreal PQ H3C 3A7 Canada Ecole Polytech Montreal PQ H3C 3A7 Canada McGill Univ Sch Comp Sci Montreal PQ H3A 0E9 Canada Univ Toronto Dept Mech & Ind Engn Toronto ON M5S 3G8 Canada

The integer least squares problem is an important problem that arises in numerous applications. We propose a real relaxation-based branch-and-bound (RRBB) method for this problem. First, we define a quantity called the distance to integrality, propose it as a measure of the number of nodes in the RRBB enumeration tree, and provide computational evidence that the size of the RRBB tree is proportional to this distance. Since we cannot know the distance to integrality a priori, we prove that the norm of the Moore-Penrose generalized inverse of the matrix of coefficients is a key factor for bounding this distance, and then we propose a preconditioning method to reduce this norm using lattice reduction techniques. We also propose a set of valid box constraints that help accelerate the RRBB method. Our computational results show that the proposed preconditioning significantly reduces the size of the RRBB enumeration tree, that the preconditioning combined with the proposed set of box constraints can significantly reduce the computational time of RRBB, and that the resulting RRBB method can outperform the Schnorr and Eucher method, a widely used method for solving integer least squares problems, on some types of problem data.

关键词： Integer least squares branch-and-bound methods Lattice reduction Preconditioning Box constraints

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A solution algorithm for non-convex mixed integer optimization problems with only few continuous variables

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2014年第2期232卷 266-275页

作者： Schoebel, Anita Scholz, Daniel Univ Gottingen Inst Numer & Angew Math Gottingen Germany

Geometric branch-and-bound techniques are well-known solution algorithms for non-convex continuous global optimization problems with box constraints. Several approaches can be found in the literature differing mainly in the bounds used. The aim of this paper is to extend geometric branch-and-bound methods to mixed integer optimization problems, i.e. to objective functions with some continuous and some integer variables. Mixed-integer non-linear and non-convex optimization problems are extremely hard, containing several classes of NP-hard problems as special cases. We identify for which type of mixed integer non-linear problems our method can be applied efficiently, derive several bounding operations and analyze their rates of convergence theoretically. Moreover, we show that the accuracy of any algorithm for solving the problem with fixed integer variables can be transferred to the mixed integer case. Our results are demonstrated theoretically and experimentally using the truncated Weber problem and the p-median problem. For both problems we succeed in finding exact optimal solutions. (c) 2013 Elsevier B.V. All rights reserved.

关键词： Global optimization Combinatorial optimization Non-convex optimization Mixed-integer optimization branch-and-bound methods Facility location problems

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A framework for parallel large-scale global optimization

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COMPUTER SCIENCE-RESEARCH AND DEVELOPMENT 2009年第3-4期23卷 211-215页

作者： Evtushenko, Yuri Posypkin, Mikhail Sigal, Israel Russian Acad Sci Dorodnicyn Comp Ctr RU-119333 Moscow Russia Russian Acad Sci Inst Syst Anal Prospect 60-letija Oktyabrya9 Moscow Russia

The paper describes the design and implementation of BNB-Solver, an object-oriented framework for discrete and continuous parallel global optimization. The framework supports exact branch-and-bound algorithms, heuristic methods and hybrid approaches. BNB-Solver provides a support for distributed and shared memory architectures. The implementation for distributed memory machines is based on MPI and thus can run on almost any computational cluster. In order to take advantages of multicore processors we provide a separate multi-threaded implementation for shared memory platforms. We introduce a novel collaborative scheme for combining exact and heuristic search methods that provides the support for sophisticated parallel heuristics and convenient balancing between exact and heuristic methods. In the experimental results section we discuss a nonlinear programming solver and a highly efficient knapsack solver that significantly outperforms existing parallel implementations.

关键词： Parallel global optimization branch-and-bound methods Heuristic methods, knapsack problems Nonlinear programming

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Hybrid modelling and optimal control of a Multiproduct Batch Plant

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CONTROL ENGINEERING PRACTICE 2004年第9期12卷 1127-1137页

作者： Potocnik, B Bemporad, A Torrisi, FD Music, G Zupancic, B Univ Ljubljana Fac Elect Engn Lab Modelling Simulat & Control SI-1000 Ljubljana Slovenia Univ Siena Dip Ingn Informaz I-53100 Siena Italy ETH Swiss Fed Inst Technol Automat Control Lab CH-8092 Zurich Switzerland

This paper addresses the problem of optimally selecting the production plan for a Multiproduct Batch Plant. The proposed approach can also be applied to a broader class of optimal control problems for systems with discrete inputs. The plant is modelled as a Discrete Hybrid Automaton (DHA) using the high level modelling language, HYbrid System DEscription Language (HYSDEL), which allows conversion of the DHA model into an Mixed Logical Dynamical (MLD) model. The solution algorithm, which takes into account a model of a hybrid system described as an MLD system, is based on reachability analysis ideas. The algorithm abstracts the behaviour of the hybrid system into a "tree of evolution", where nodes of the tree represent reachable states of the system, and branches connect two nodes if a transition exists between the corresponding states. To each node a cost function value is associated and, based on this value, the tree exploration is driven, searching for the optimal control profile. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： hybrid systems modelling optimal control reachability analysis branch-and-bound methods

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