This paper is concerned with robustness analysis of decision making under uncertainty. We consider a class of iterative stochastic policy optimization problems and analyze the resulting expected performance for each newly updated policy at each iteration. In particular, we employ concentration-of-measure inequalities to compute future expected cost and probability of constraint violation using empirical runs. A novel inequality bound is derived that accounts for the possibly unbounded change-of-measure likelihood ratio resulting from iterative policy adaptation. The bound serves as a high-confidence certificate for providing future performance or safety guarantees. The approach is illustrated with a simple robot control scenario and initial steps towards applications to challenging aerial vehicle navigation problems are presented.

The success of machine learning in a broad range of applications has led to an ever-growing demand for machine learning systems that can be used off the shelf by non-experts. To be effective in practice, such systems need to automatically choose a good algorithm and feature preprocessing steps for a new dataset at hand, and also set their respective hyperparameters. Recent work has started to tackle this automated machine learning (AutoML) problem with the help of efficient Bayesian optimization methods. Building on this, we introduce a robust new AutoML system based on scikit-learn (using 15 classifiers, 14 feature preprocessing methods, and 4 data preprocessing methods, giving rise to a structured hypothesis space with 110 hyperparameters). This system, which we dub AUTO-SKLEARN, improves on existing AutoML methods by automatically taking into account past performance on similar datasets, and by constructing ensembles from the models evaluated during the optimization. Our system won the first phase of the ongoing ChaLearn AutoML challenge, and our comprehensive analysis on over 100 diverse datasets shows that it substantially outperforms the previous state of the art in AutoML. We also demonstrate the performance gains due to each of our contributions and derive insights into the effectiveness of the individual components of AUTO-SKLEARN.

Bandit convex optimization is one of the fundamental problems in the field of online learning. The best algorithm for the general bandit convex optimization problem guarantees a regret of $\widetilde{O}(T^{5/6})$, while the best known lower bound is $\Omega(T^{1/2})$. Many attemptshave been made to bridge the huge gap between these bounds. A particularly interesting special case of this problem assumes that the loss functions are smooth. In this case, the best known algorithm guarantees a regret of $\widetilde{O}(T^{2/3})$. We present an efficient algorithm for the banditsmooth convex optimization problem that guarantees a regret of $\widetilde{O}(T^{5/8})$. Our result rules out an $\Omega(T^{2/3})$ lower bound and takes a significant step towards the resolution of this open problem.

How can one find a subset, ideally as small as possible, that well represents a massive dataset? I.e., its corresponding utility, measured according to a suitable utility function, should be comparable to that of the whole dataset. In this paper, we formalize this challenge as a submodular cover problem. Here, the utility is assumed to exhibit submodularity, a natural diminishing returns condition preva- lent in many data summarization applications. The classical greedy algorithm is known to provide solutions with logarithmic approximation guarantees compared to the optimum solution. However, this sequential, centralized approach is imprac- tical for truly large-scale problems. In this work, we develop the first distributed algorithm – DISCOVER – for submodular set cover that is easily implementable using MapReduce-style computations. We theoretically analyze our approach, and present approximation guarantees for the solutions returned by DISCOVER. We also study a natural trade-off between the communication cost and the num- ber of rounds required to obtain such a solution. In our extensive experiments, we demonstrate the effectiveness of our approach on several applications, includ- ing active set selection, exemplar based clustering, and vertex cover on tens of millions of data points using Spark.

We study accelerated mirror descent dynamics in continuous and discrete time. Combining the original continuous-time motivation of mirror descent with a recent ODE interpretation of Nesterov's accelerated method, we propose a family of continuous-time descent dynamics for convex functions with Lipschitz gradients, such that the solution trajectories are guaranteed to converge to the optimum at a $O(1/t^2)$ rate. We then show that a large family of first-order accelerated methods can be obtained as a discretization of the ODE, and these methods converge at a $O(1/k^2)$ rate. This connection between accelerated mirror descent and the ODE provides an intuitive approach to the design and analysis of accelerated first-order algorithms.

This paper presents a Bayesian optimization method with exponential convergence without the need of auxiliary optimization and without the delta-cover sampling. Most Bayesian optimization methods require auxiliary optimization: an additional non-convex global optimization problem, which can be time-consuming and hard to implement in practice. Also, the existing Bayesian optimization method with exponential convergence requires access to the delta-cover sampling, which was considered to be impractical. Our approach eliminates both requirements and achieves an exponential convergence rate.

Multivariate loss functions are used to assess performance in many modern prediction tasks, including information retrieval and ranking applications. Convex approximations are typically optimized in their place to avoid NP-hard empirical risk minimization problems. We propose to approximate the training data instead of the loss function by posing multivariate prediction as an adversarial game between a loss-minimizing prediction player and a loss-maximizing evaluation player constrained to match specified properties of training data. This avoids the non-convexity of empirical risk minimization, but game sizes are exponential in the number of predicted variables. We overcome this intractability using the double oracle constraint generation method. We demonstrate the efficiency and predictive performance of our approach on tasks evaluated using the precision at k, the F-score and the discounted cumulative gain.

We study optimization algorithms based on variance reduction for stochastic gradientdescent (SGD). Remarkable recent progress has been made in this directionthrough development of algorithms like SAG, SVRG, SAGA. These algorithmshave been shown to outperform SGD, both theoretically and empirically. However,asynchronous versions of these algorithms—a crucial requirement for modernlarge-scale applications—have not been studied. We bridge this gap by presentinga unifying framework that captures many variance reduction techniques.Subsequently, we propose an asynchronous algorithm grounded in our framework,with fast convergence rates. An important consequence of our general approachis that it yields asynchronous versions of variance reduction algorithms such asSVRG, SAGA as a byproduct. Our method achieves near linear speedup in sparsesettings common to machine learning. We demonstrate the empirical performanceof our method through a concrete realization of asynchronous SVRG.

Over the past decades, Linear Programming (LP) has been widely used in different areas and considered as one of the mature technologies in numerical optimization. However, the complexity offered by state-of-the-art algorithms (i.e. interior-point method and primal, dual simplex methods) is still unsatisfactory for problems in machine learning with huge number of variables and constraints. In this paper, we investigate a general LP algorithm based on the combination of Augmented Lagrangian and Coordinate Descent (AL-CD), giving an iteration complexity of $O((\log(1/\epsilon))^2)$ with $O(nnz(A))$ cost per iteration, where $nnz(A)$ is the number of non-zeros in the $m\times n$ constraint matrix $A$, and in practice, one can further reduce cost per iteration to the order of non-zeros in columns (rows) corresponding to the active primal (dual) variables through an active-set strategy. The algorithm thus yields a tractable alternative to standard LP methods for large-scale problems of sparse solutions and $nnz(A)\ll mn$. We conduct experiments on large-scale LP instances from $\ell_1$-regularized multi-class SVM, Sparse Inverse Covariance Estimation, and Nonnegative Matrix Factorization, where the proposed approach finds solutions of $10^{-3}$ precision orders of magnitude faster than state-of-the-art implementations of interior-point and simplex methods.

We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a vector of random numbers u, in such a way that the outcome, knowing u, is deterministic. For each instantiation of u we run an optimization procedure to minimize the distance between summary statistics of the simulator and the data. After reweighing these samples using the prior and the Jacobian (accounting for the change of volume in transforming from the space of summary statistics to the space of parameters) we show that this weighted ensemble represents a Monte Carlo estimate of the posterior distribution. The procedure can be run embarrassingly parallel (each node handling one sample) and anytime (by allocating resources to the worst performing sample). The procedure is validated on six experiments.