We explore the connection between outlier-robust high-dimensional statistics and non-convex optimization in the presence of sparsity constraints, with a focus on the fundamental tasks of robust sparse mean estimation and robust sparse PCA. We develop novel and simple optimization formulations for these problems such that any approximate stationary point of the associated optimization problem yields a near-optimal solution for the underlying robust estimation task. As a corollary, we obtain that any first-order method that efficiently converges to stationarity yields an efficient algorithm for these tasks. The obtained algorithms are simple, practical, and succeed under broader distributional assumptions compared to prior work.

Metric Multidimensional scaling (MDS) is a classical method for generating meaningful (non-linear) low-dimensional embeddings of high-dimensional data. MDS has a long history in the statistics, machine learning, and graph drawing communities. In particular, the Kamada-Kawai force-directed graph drawing method is equivalent to MDS and is one of the most popular ways in practice to embed graphs into low dimensions. Despite its ubiquity, our theoretical understanding of MDS remains limited as its objective function is highly non-convex. In this paper, we prove that minimizing the Kamada-Kawai objective is NP-hard and give a provable approximation algorithm for optimizing it, which in particular is a PTAS on low-diameter graphs.

We study nonlinear optimization problems with stochastic objective and deterministic equality and inequality constraints, which emerge in numerous applications including finance, manufacturing, power systems and, recently, deep neural networks. We propose an active-set stochastic sequential quadratic programming algorithm, using a differentiable exact augmented Lagrangian as the merit function. The algorithm adaptively selects the penalty parameters of augmented Lagrangian and performs stochastic line search to decide the stepsize. The global convergence is established: for any initialization, the "liminf" of the KKT residuals converges to zero almost surely. Our algorithm and analysis further develop the prior work \cite{Na2021Adaptive} by allowing nonlinear inequality constraints. We demonstrate the performance of the algorithm on a subset of nonlinear problems collected in the CUTEst test set.

Pool-based active learning (AL) aims to optimize the annotation process (i.e., labeling) as the acquisition of annotations is often time-consuming and therefore expensive. For this purpose, an AL strategy queries annotations intelligently from annotators to train a high-performance classification model at a low annotation cost. Traditional AL strategies operate in an idealized framework. They assume a single, omniscient annotator who never gets tired and charges uniformly regardless of query difficulty. However, in real-world applications, we often face human annotators, e.g., crowd or in-house workers, who make annotation mistakes and can be reluctant to respond if tired or faced with complex queries. Recently, a wide range of novel AL strategies has been proposed to address these issues. They differ in at least one of the following three central aspects from traditional AL: (1) They explicitly consider (multiple) human annotators whose performances can be affected by various factors, such as missing expertise. (2) They generalize the interaction with human annotators by considering different query and annotation types, such as asking an annotator for feedback on an inferred classification rule. (3) They take more complex cost schemes regarding annotations and misclassifications into account. This survey provides an overview of these AL strategies and refers to them as real-world AL. Therefore, we introduce a general real-world AL strategy as part of a learning cycle and use its elements, e.g., the query and annotator selection algorithm, to categorize about 60 real-world AL strategies. Finally, we outline possible directions for future research in the field of AL.

This paper considers binary and multilabel classification problems in a setting where labels are missing independently and with a known rate. Missing labels are a ubiquitous phenomenon in extreme multi-label classification (XMC) tasks, such as matching Wikipedia articles to a small subset out of the hundreds of thousands of possible tags, where no human annotator can possibly check the validity of all the negative samples. For this reason, propensity-scored precision -- an unbiased estimate for precision-at-k under a known noise model -- has become one of the standard metrics in XMC. Few methods take this problem into account already during the training phase, and all are limited to loss functions that can be decomposed into a sum of contributions from each individual label. A typical approach to training is to reduce the multilabel problem into a series of binary or multiclass problems, and it has been shown that if the surrogate task should be consistent for optimizing recall, the resulting loss function is not decomposable over labels. Therefore, this paper derives the unique unbiased estimators for the different multilabel reductions, including the non-decomposable ones. These estimators suffer from increased variance and may lead to ill-posed optimization problems, which we address by switching to convex upper-bounds. The theoretical considerations are further supplemented by an experimental study showing that the switch to unbiased estimators significantly alters the bias-variance trade-off and may thus require stronger regularization, which in some cases can negate the benefits of unbiased estimation.

Dense disparities among multiple views is essential for estimating the 3D architecture of a scene based on the geometrical relationship among the scene and the views or cameras. Scenes with larger extents of heterogeneous textures, differing scene illumination among the multiple views and with occluding objects affect the accuracy of the estimated disparities. Markov random fields (MRF) based methods for disparity estimation address these limitations using spatial dependencies among the observations and among the disparity estimates. These methods, however, are limited by spatially fixed and smaller neighborhood systems or cliques. In this work, we present a new factor graph-based probabilistic graphical model for disparity estimation that allows a larger and a spatially variable neighborhood structure determined based on the local scene characteristics. We evaluated our method using the Middlebury benchmark stereo datasets and the Middlebury evaluation dataset version 3.0 and compared its performance with recent state-of-the-art disparity estimation algorithms. The new factor graph-based method provided disparity estimates with higher accuracy when compared to the recent non-learning- and learning-based disparity estimation algorithms. In addition to disparity estimation, our factor graph formulation can be useful for obtaining maximum a posteriori solution to optimization problems with complex and variable dependency structures as well as for other dense estimation problems such as optical flow estimation.

Many approaches have been proposed for early classification of time series in light of itssignificance in a wide range of applications including healthcare, transportation and fi-nance. Until now, the early classification problem has been dealt with by considering onlyirrevocable decisions. This paper introduces a new problem calledearly and revocabletimeseries classification, where the decision maker can revoke its earlier decisions based on thenew available measurements. In order to formalize and tackle this problem, we propose anew cost-based framework and derive two new approaches from it. The first approach doesnot consider explicitly the cost of changing decision, while the second one does. Exten-sive experiments are conducted to evaluate these approaches on a large benchmark of realdatasets. The empirical results obtained convincingly show (i) that the ability of revok-ing decisions significantly improves performance over the irrevocable regime, and (ii) thattaking into account the cost of changing decision brings even better results in general.Keywords:revocable decisions, cost estimation, online decision making

The ability to optimize multiple competing objective functions with high sample efficiency is imperative in many applied problems across science and industry. Multi-objective Bayesian optimization (BO) achieves strong empirical performance on such problems, but even with recent methodological advances, it has been restricted to simple, low-dimensional domains. Most existing BO methods exhibit poor performance on search spaces with more than a few dozen parameters. In this work we propose MORBO, a method for multi-objective Bayesian optimization over high-dimensional search spaces. MORBO performs local Bayesian optimization within multiple trust regions simultaneously, allowing it to explore and identify diverse solutions even when the objective functions are difficult to model globally. We show that MORBO significantly advances the state-of-the-art in sample-efficiency for several high-dimensional synthetic and real-world multi-objective problems, including a vehicle design problem with 222 parameters, demonstrating that MORBO is a practical approach for challenging and important problems that were previously out of reach for BO methods.

Interest in applying Artificial Intelligence (AI) techniques to compiler optimizations is increasing rapidly, but compiler research has a high entry barrier. Unlike in other domains, compiler and AI researchers do not have access to the datasets and frameworks that enable fast iteration and development of ideas, and getting started requires a significant engineering investment. What is needed is an easy, reusable experimental infrastructure for real world compiler optimization tasks that can serve as a common benchmark for comparing techniques, and as a platform to accelerate progress in the field. We introduce CompilerGym, a set of environments for real world compiler optimization tasks, and a toolkit for exposing new optimization tasks to compiler researchers. CompilerGym enables anyone to experiment on production compiler optimization problems through an easy-to-use package, regardless of their experience with compilers.

Algorithmic recommendations and decisions have become ubiquitous in today's society. Many of these and other data-driven policies are based on known, deterministic rules to ensure their transparency and interpretability. This is especially true when such policies are used for public policy decision-making. For example, algorithmic pre-trial risk assessments, which serve as our motivating application, provide relatively simple, deterministic classification scores and recommendations to help judges make release decisions. Unfortunately, existing methods for policy learning are not applicable because they require existing policies to be stochastic rather than deterministic. We develop a robust optimization approach that partially identifies the expected utility of a policy, and then finds an optimal policy by minimizing the worst-case regret. The resulting policy is conservative but has a statistical safety guarantee, allowing the policy-maker to limit the probability of producing a worse outcome than the existing policy. We extend this approach to common and important settings where humans make decisions with the aid of algorithmic recommendations. Lastly, we apply the proposed methodology to a unique field experiment on pre-trial risk assessments. We derive new classification and recommendation rules that retain the transparency and interpretability of the existing risk assessment instrument while potentially leading to better overall outcomes at a lower cost.