Efficient Low-Rank Semidefinite Programming with Robust Loss Functions

In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated as low-rank semi-definite programming (SDP) problems. Traditional formulations use square loss, which is notorious for being sensitive to outliers. We propose to replace this with more robust noise models, including the $\ell_1$-loss and other nonconvex losses. However, the resultant optimization problem becomes difficult as the objective is no longer convex or smooth. To alleviate this problem, we design an efficient algorithm based on majorization-minimization. The crux is on constructing a good optimization surrogate, and we show that this surrogate can be efficiently obtained by the alternating direction method of multipliers (ADMM). By properly monitoring ADMM's convergence, the proposed algorithm is empirically efficient and also theoretically guaranteed to converge to a critical point. Extensive experiments are performed on four machine learning applications using both synthetic and real-world data sets. Results show that the proposed algorithm is not only fast but also has better performance than the state-of-the-art.Comment: Preprint version. Final version is accepted to "IEEE Transactions on Pattern Analysis and Machine Intelligence

Addressing the Loss-Metric Mismatch with Adaptive Loss Alignment

In most machine learning training paradigms a fixed, often handcrafted, loss function is assumed to be a good proxy for an underlying evaluation metric. In this work we assess this assumption by meta-learning an adaptive loss function to directly optimize the evaluation metric. We propose a sample efficient reinforcement learning approach for adapting the loss dynamically during training. We empirically show how this formulation improves performance by simultaneously optimizing the evaluation metric and smoothing the loss landscape. We verify our method in metric learning and classification scenarios, showing considerable improvements over the state-of-the-art on a diverse set of tasks. Importantly, our method is applicable to a wide range of loss functions and evaluation metrics. Furthermore, the learned policies are transferable across tasks and data, demonstrating the versatility of the method.Comment: Accepted to ICML 201

Consistent Second-Order Conic Integer Programming for Learning Bayesian Networks

Bayesian Networks (BNs) represent conditional probability relations among a set of random variables (nodes) in the form of a directed acyclic graph (DAG), and have found diverse applications in knowledge discovery. We study the problem of learning the sparse DAG structure of a BN from continuous observational data. The central problem can be modeled as a mixed-integer program with an objective function composed of a convex quadratic loss function and a regularization penalty subject to linear constraints. The optimal solution to this mathematical program is known to have desirable statistical properties under certain conditions. However, the state-of-the-art optimization solvers are not able to obtain provably optimal solutions to the existing mathematical formulations for medium-size problems within reasonable computational times. To address this difficulty, we tackle the problem from both computational and statistical perspectives. On the one hand, we propose a concrete early stopping criterion to terminate the branch-and-bound process in order to obtain a near-optimal solution to the mixed-integer program, and establish the consistency of this approximate solution. On the other hand, we improve the existing formulations by replacing the linear "big-$M$" constraints that represent the relationship between the continuous and binary indicator variables with second-order conic constraints. Our numerical results demonstrate the effectiveness of the proposed approaches

A Survey on State Estimation Techniques and Challenges in Smart Distribution Systems

This paper presents a review of the literature on State Estimation (SE) in power systems. While covering some works related to SE in transmission systems, the main focus of this paper is Distribution System State Estimation (DSSE). The paper discusses a few critical topics of DSSE, including mathematical problem formulation, application of pseudo-measurements, metering instrument placement, network topology issues, impacts of renewable penetration, and cyber-security. Both conventional and modern data-driven and probabilistic techniques have been reviewed. This paper can provide researchers and utility engineers with insights into the technical achievements, barriers, and future research directions of DSSE

Hardware-Aware Machine Learning: Modeling and Optimization

Recent breakthroughs in Deep Learning (DL) applications have made DL models a key component in almost every modern computing system. The increased popularity of DL applications deployed on a wide-spectrum of platforms have resulted in a plethora of design challenges related to the constraints introduced by the hardware itself. What is the latency or energy cost for an inference made by a Deep Neural Network (DNN)? Is it possible to predict this latency or energy consumption before a model is trained? If yes, how can machine learners take advantage of these models to design the hardware-optimal DNN for deployment? From lengthening battery life of mobile devices to reducing the runtime requirements of DL models executing in the cloud, the answers to these questions have drawn significant attention. One cannot optimize what isn't properly modeled. Therefore, it is important to understand the hardware efficiency of DL models during serving for making an inference, before even training the model. This key observation has motivated the use of predictive models to capture the hardware performance or energy efficiency of DL applications. Furthermore, DL practitioners are challenged with the task of designing the DNN model, i.e., of tuning the hyper-parameters of the DNN architecture, while optimizing for both accuracy of the DL model and its hardware efficiency. Therefore, state-of-the-art methodologies have proposed hardware-aware hyper-parameter optimization techniques. In this paper, we provide a comprehensive assessment of state-of-the-art work and selected results on the hardware-aware modeling and optimization for DL applications. We also highlight several open questions that are poised to give rise to novel hardware-aware designs in the next few years, as DL applications continue to significantly impact associated hardware systems and platforms.Comment: ICCAD'18 Invited Pape

Machine learning for cognitive networks : technology assessment and research challenges

The field of machine learning has made major strides over the last 20 years. This document summarizes the major problem formulations that the discipline has studied, then reviews three tasks in cognitive networking and briefly discusses how aspects of those tasks fit these formulations. After this, it discusses challenges for machine learning research raised by Knowledge Plane applications and closes with proposals for the evaluation of learning systems developed for these problems

Cautious NMPC with Gaussian Process Dynamics for Autonomous Miniature Race Cars

This paper presents an adaptive high performance control method for autonomous miniature race cars. Racing dynamics are notoriously hard to model from first principles, which is addressed by means of a cautious nonlinear model predictive control (NMPC) approach that learns to improve its dynamics model from data and safely increases racing performance. The approach makes use of a Gaussian Process (GP) and takes residual model uncertainty into account through a chance constrained formulation. We present a sparse GP approximation with dynamically adjusting inducing inputs, enabling a real-time implementable controller. The formulation is demonstrated in simulations, which show significant improvement with respect to both lap time and constraint satisfaction compared to an NMPC without model learning

Learning Features for Offline Handwritten Signature Verification using Deep Convolutional Neural Networks

Verifying the identity of a person using handwritten signatures is challenging in the presence of skilled forgeries, where a forger has access to a person's signature and deliberately attempt to imitate it. In offline (static) signature verification, the dynamic information of the signature writing process is lost, and it is difficult to design good feature extractors that can distinguish genuine signatures and skilled forgeries. This reflects in a relatively poor performance, with verification errors around 7% in the best systems in the literature. To address both the difficulty of obtaining good features, as well as improve system performance, we propose learning the representations from signature images, in a Writer-Independent format, using Convolutional Neural Networks. In particular, we propose a novel formulation of the problem that includes knowledge of skilled forgeries from a subset of users in the feature learning process, that aims to capture visual cues that distinguish genuine signatures and forgeries regardless of the user. Extensive experiments were conducted on four datasets: GPDS, MCYT, CEDAR and Brazilian PUC-PR datasets. On GPDS-160, we obtained a large improvement in state-of-the-art performance, achieving 1.72% Equal Error Rate, compared to 6.97% in the literature. We also verified that the features generalize beyond the GPDS dataset, surpassing the state-of-the-art performance in the other datasets, without requiring the representation to be fine-tuned to each particular dataset

Feature-based tuning of simulated annealing applied to the curriculum-based course timetabling problem

We consider the university course timetabling problem, which is one of the most studied problems in educational timetabling. In particular, we focus our attention on the formulation known as the curriculum-based course timetabling problem, which has been tackled by many researchers and for which there are many available benchmarks. The contribution of this paper is twofold. First, we propose an effective and robust single-stage simulated annealing method for solving the problem. Secondly, we design and apply an extensive and statistically-principled methodology for the parameter tuning procedure. The outcome of this analysis is a methodology for modeling the relationship between search method parameters and instance features that allows us to set the parameters for unseen instances on the basis of a simple inspection of the instance itself. Using this methodology, our algorithm, despite its apparent simplicity, has been able to achieve high quality results on a set of popular benchmarks. A final contribution of the paper is a novel set of real-world instances, which could be used as a benchmark for future comparison

Optimistic Robust Optimization With Applications To Machine Learning

Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this paper, we explore an optimistic, or best-case view of uncertainty and show that it can be a fruitful approach. We show that these techniques can be used to address a wide variety of problems. First, we apply our methods in the context of robust linear programming, providing a method for reducing conservatism in intuitive ways that encode economically realistic modeling assumptions. Second, we look at problems in machine learning and find that this approach is strongly connected to the existing literature. Specifically, we provide a new interpretation for popular sparsity inducing non-convex regularization schemes. Additionally, we show that successful approaches for dealing with outliers and noise can be interpreted as optimistic robust optimization problems. Although many of the problems resulting from our approach are non-convex, we find that DCA or DCA-like optimization approaches can be intuitive and efficient