Optimization
A Survey of Machine Learning Applied to Computer Architecture Design
Penney, Drew D., Chen, Lizhong
Machine learning has enabled significant benefits in diverse fields, but, with a few exceptions, has had limited impact on computer architecture. Recent work, however, has explored broader applicability for design, optimization, and simulation. Notably, machine learning based strategies often surpass prior state-of-the-art analytical, heuristic, and human-expert approaches. This paper reviews machine learning applied system-wide to simulation and run-time optimization, and in many individual components, including memory systems, branch predictors, networks-on-chip, and GPUs. The paper further analyzes current practice to highlight useful design strategies and identify areas for future work, based on optimized implementation strategies, opportune extensions to existing work, and ambitious long term possibilities. Taken together, these strategies and techniques present a promising future for increasingly automated architectural design.
Military Dog Based Optimizer and its Application to Fake Review
Tripathi, Ashish Kumar, Sharma, Kapil, Bala, Manju
Over the last three decades more then sixty meta-heuristic algorithms have been proposed by the various authors. Such algorithms are inspired from physical phenomena, animal behavior or evolutionary concepts. These algorithms have been widely used for solving the various real world optimization problems. Researchers are continuously working to improve the existing algorithms and also proposing new algorithms that are giving competitive results as compared to the existing algorithms present in the literature. In this paper a novel meta heuristic algorithm based on military dogs squad is introduced. The proposed algorithm mimics the searching capability of the trained military dogs. Military dogs have strong smell senses by which they are able to search the suspicious objects like bombs, wildlife scats, currency, or blood as well as they can communicate with each other by their barking. The performance of the proposed algorithm is tested on 17 benchmark functions and compared with five other meta-heuristics namely particle swarm optimization (PSO), multiverse optimizer (MVO), genetic algorithm (GA), probability based learning (PBIL) and evolutionary strategy (ES). The results are validated in terms of mean and standard deviation of the fitness value. The convergence behavior and consistency of the results have been also validated by plotting convergence graphs and BoxPlots. Further the, proposed algorithm is successfully utilized to solve the real world fake review detection problem. The experimental results demonstrate that the proposed algorithm outperforms the other considered algorithms on the majority of performance parameters.
A Self-consistent-field Iteration for Orthogonal Canonical Correlation Analysis
Zhang, Leihong, Wang, Li, Bai, Zhaojun, Li, Ren-cang
We propose an efficient algorithm for solving orthogonal canonical correlation analysis (OCCA) in the form of trace-fractional structure and orthogonal linear projections. Even though orthogonality has been widely used and proved to be a useful criterion for pattern recognition and feature extraction, existing methods for solving OCCA problem are either numerical unstable by relying on a deflation scheme, or less efficient by directly using generic optimization methods. In this paper, we propose an alternating numerical scheme whose core is the sub-maximization problem in the trace-fractional form with an orthogonal constraint. A customized self-consistent-field (SCF) iteration for this sub-maximization problem is devised. It is proved that the SCF iteration is globally convergent to a KKT point and that the alternating numerical scheme always converges. We further formulate a new trace-fractional maximization problem for orthogonal multiset CCA (OMCCA) and then propose an efficient algorithm with an either Jacobi-style or Gauss-Seidel-style updating scheme based on the same SCF iteration. Extensive experiments are conducted to evaluate the proposed algorithms against existing methods including two real world applications: multi-label classification and multi-view feature extraction. Experimental results show that our methods not only perform competitively to or better than baselines but also are more efficient.
A Mean-Field Theory for Kernel Alignment with Random Features in Generative Adversarial Networks
Khuzani, Masoud Badiei, Shen, Liyue, Shahrampour, Shahin, Xing, Lei
We propose a novel supervised learning method to optimize the kernel in maximum mean discrepancy generative adversarial networks (MMD GANs). Specifically, we characterize a distributionally robust optimization problem to compute a good distribution for the random feature model of Rahimi and Recht to approximate a good kernel function. Due to the fact that the distributional optimization is infinite dimensional, we consider a Monte-Carlo sample average approximation (SAA) to obtain a more tractable finite dimensional optimization problem. We subsequently leverage a particle stochastic gradient descent (SGD) method to solve finite dimensional optimization problems. Based on a mean-field analysis, we then prove that the empirical distribution of the interactive particles system at each iteration of the SGD follows the path of the gradient descent flow on the Wasserstein manifold. We also establish the non-asymptotic consistency of the finite sample estimator. Our empirical evaluation on synthetic data-set as well as MNIST and CIFAR-10 benchmark data-sets indicates that our proposed MMD GAN model with kernel learning indeed attains higher inception scores well as Fr\`{e}chet inception distances and generates better images compared to the generative moment matching network (GMMN) and MMD GAN with untrained kernels.
Online Non-Monotone DR-submodular Maximization
Thang, Nguyen Kim, Srivastav, Abhinav
In this paper, we study problems at the interface of two important fields: \emph{submodular optimization} and \emph{online learning}. Submodular functions play a vital role in modelling cost functions that naturally arise in many areas of discrete optimization. These functions have been studied under various models of computation. Independently, submodularity has been considered in continuous domains. In fact, many problems arising in machine learning and statistics have been modelled using continuous DR-submodular functions. In this work, we are study the problem of maximizing \textit{non-monotone} continuous DR-submodular functions within the framework of online learning. We provide three main results. First, we present an online algorithm (in full-information setting) that achieves an approximation guarantee (depending on the search space) for the problem of maximizing non-monotone continuous DR-submodular functions over a \emph{general} convex domain. To best of our knowledge, no prior approximation algorithm in full-information setting was known for the non-monotone continuous DR submodular functions even for the \emph{down-closed} convex domain. Second, we show that the online stochastic mirror ascent algorithm (in full information setting) achieves an improved approximation ratio of $(1/4)$ for maximizing the non-monotone continuous DR-submodular functions over a \emph{down-closed} convex domain. At last, we extend our second result to the bandit setting where we present the first approximation guarantee of $(1/4)$. To best of our knowledge, no approximation algorithm for non-monotone submodular maximization was known in the bandit setting.
Structured Graph Learning Via Laplacian Spectral Constraints
Kumar, Sandeep, Ying, Jiaxi, Cardoso, Jos'e Vin'icius de M., Palomar, Daniel P.
Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In this paper, we first show that for a set of important graph families it is possible to convert the structural constraints of structure into eigenvalue constraints of the graph Laplacian matrix. Then we introduce a unified graph learning framework, lying at the integration of the spectral properties of the Laplacian matrix with Gaussian graphical modeling that is capable of learning structures of a large class of graph families. The proposed algorithms are provably convergent and practically amenable for large-scale semi-supervised and unsupervised graph-based learning tasks. Extensive numerical experiments with both synthetic and real data sets demonstrate the effectiveness of the proposed methods. An R package containing code for all the experimental results is available at https://cran.r-project.org/package=spectralGraphTopology.
Sign-OPT: A Query-Efficient Hard-label Adversarial Attack
Cheng, Minhao, Singh, Simranjit, Chen, Pin-Yu, Liu, Sijia, Hsieh, Cho-Jui
We study the most practical problem setup for evaluating adversarial robustness of a machine learning system with limited access: the hard-label black-box attack setting for generating adversarial examples, where limited model queries are allowed and only the decision is provided to a queried data input. Several algorithms have been proposed for this problem but they typically require huge amount (>20,000) of queries for attacking one example. Among them, one of the state-of-the-art approaches (Cheng et al., 2019) showed that hard-label attack can be modeled as an optimization problem where the objective function can be evaluated by binary search with additional model queries, thereby a zeroth order optimization algorithm can be applied. In this paper, we adopt the same optimization formulation but propose to directly estimate the sign of gradient at any direction instead of the gradient itself, which enjoys the benefit of single query. Using this single query oracle for retrieving sign of directional derivative, we develop a novel query-efficient Sign-OPT approach for hard-label black-box attack. We provide a convergence analysis of the new algorithm and conduct experiments on several models on MNIST, CIFAR-10 and ImageNet. We find that Sign-OPT attack consistently requires 5X to 10X fewer queries when compared to the current state-of-the-art approaches, and usually converges to an adversarial example with smaller perturbation.
Conditions for Unnecessary Logical Constraints in Kernel Machines
Giannini, Francesco, Maggini, Marco
A main property of support vector machines consists in the fact that only a small portion of the training data is significant to determine the maximum margin separating hyperplane in the feature space, the so called support vectors . In a similar way, in the general scheme of learning from constraints, where possibly several constraints are considered, some of them may turn out to be unnecessary with respect to the learning optimization, even if they are active for a given optimal solution. In this paper we extend the definition of support vector to support constraint and we provide some criteria to determine which constraints can be removed from the learning problem still yielding the same optimal solutions. In particular, we discuss the case of logical constraints expressed by null Lukasiewicz logic, where both inferential and algebraic arguments can be considered. Some theoretical results that characterize the concept of unnecessary constraint are proved and explained by means of examples.
Machine Learning Optimization Algorithms & Portfolio Allocation
Perrin, Sarah, Roncalli, Thierry
Portfolio optimization emerged with the seminal paper of Markowitz (1952). The original mean-variance framework is appealing because it is very efficient from a computational point of view. However, it also has one well-established failing since it can lead to portfolios that are not optimal from a financial point of view. Nevertheless, very few models have succeeded in providing a real alternative solution to the Markowitz model. The main reason lies in the fact that most academic portfolio optimization models are intractable in real life although they present solid theoretical properties. By intractable we mean that they can be implemented for an investment universe with a small number of assets using a lot of computational resources and skills, but they are unable to manage a universe with dozens or hundreds of assets. However, the emergence and the rapid development of robo-advisors means that we need to rethink portfolio optimization and go beyond the traditional mean-variance optimization approach. Another industry has faced similar issues concerning large-scale optimization problems. Machine learning has long been associated with linear and logistic regression models. Again, the reason was the inability of optimization algorithms to solve high-dimensional industrial problems. Nevertheless, the end of the 1990s marked an important turning point with the development and the rediscovery of several methods that have since produced impressive results. The goal of this paper is to show how portfolio allocation can benefit from the development of these large-scale optimization algorithms. Not all of these algorithms are useful in our case, but four of them are essential when solving complex portfolio optimization problems. These four algorithms are the coordinate descent, the alternating direction method of multipliers, the proximal gradient method and the Dykstra's algorithm.
Trimmed Constrained Mixed Effects Models: Formulations and Algorithms
Zheng, Peng, Aravkin, Aleksandr Y., Barber, Ryan, Sorensen, Reed J. D., Murray, Christopher J. L.
Mixed effects (ME) models inform a vast array of problems in the physical and social sciences, and are pervasive in meta-analysis. We consider ME models where the random effects component is linear. We then develop an efficient approach for a broad problem class that allows nonlinear measurements, priors, and constraints, and finds robust estimates in all of these cases using trimming in the associated marginal likelihood. We illustrate the efficacy of the approach on a range of applications for meta-analysis of global health data. Constraints and priors are used to impose monotonicity, convexity and other characteristics on dose-response relationships, while nonlinear observations enable new epidemiological analyses in place of approximations. Robust extensions ensure that spurious studies do not drive our understanding of between-study heterogeneity. The software accompanying this paper is disseminated as an open-source Python package called limeTR.