Artificial intelligence has the potential to greatly simplify our lives – but not everyone is a data scientist and not all data scientists are experts in machine learning. Enter AutoAI – a novel approach of designing, training and optimizing machine learning models automatically. With AutoAI, anyone could soon build machine learning pipelines from raw data directly, without writing complex code and performing tedious tuning and optimization, to then automate complicated, labor-intensive tasks. Several IBM papers selected for the AAAI-20 conference in New York demonstrate the value of AutoAI and different approaches to it in great detail. Most AutoAI research currently focuses on three areas: automatically determining the best models for each step of the desired machine learning and data science pipeline (model selection), automatically finding the best architecture of a deep learning-based AI model, and automatically finding the best hyperparameters (parameters for the model training process) for AI models and algorithms.

Recent works in high-dimensional model-predictive control and model-based reinforcement learning with learned dynamics and reward models have resorted to population-based optimization methods, such as the Cross-Entropy Method (CEM), for planning a sequence of actions. To decide on an action to take, CEM conducts a search for the action sequence with the highest return according to the dynamics model and reward. Action sequences are typically randomly sampled from an unconditional Gaussian distribution and evaluated on the environment. This distribution is iteratively updated towards action sequences with higher returns. However, this planning method can be very inefficient, especially for high-dimensional action spaces. An alternative line of approaches optimize action sequences directly via gradient descent, but are prone to local optima. We propose a method to solve this planning problem by interleaving CEM and gradient descent steps in optimizing the action sequence. Our experiments show faster convergence of the proposed hybrid approach, even for high-dimensional action spaces, avoidance of local minima, and better or equal performance to CEM. Code accompanying the paper is available here 1 .

The global sports betting market is worth an estimated $700 billion annually Flepp et al. (2017), and association football (also known as soccer or simply football), being the world's most popular spectator sport, constitutes around 70% of this ever-growing market Constantinou et al. (2012). The last decade has thus seen the emergence of numerous online and offline bookmakers, offering bettors the possibility to place wagers on the results of football matches in more than a hundred different leagues, worldwide. The sports betting industry offers a unique and very popular betting product known as an accumulator bet. In contrast with a single bet, which consists in betting on a single event for a payout equal to the stake (i.e. the sum wagered) multiplied by the odds set by the bookmaker for that event, an accumulator bet combines more than one (and generally less than seven) events into a single wager that pays out only when all individual events are correctly predicted. The payout for a correct accumulator bet is the stake multiplied by the product of the odds of all its constituting wagers. However, if one of these wagers is incorrect, the entire accumulator bet would lose. Thus, this product offers both significantly higher potential payouts and higher risks than single bets, and the large pool of online bookmakers, leagues and, matches that bettors can access nowadays has increased both the complexity of selecting a set of matches to place an accumulator bet on, and the number of opportunities to identify winning combinations. With the rise of sports analytics, a wide variety of statistical models for predicting the outcomes of football matches have been proposed, a good review of which can be found in Langseth (2013).

We introduce LiPopt, a polynomial optimization framework for computing increasingly tighter upper bounds on the Lipschitz constant of neural networks. The underlying optimization problems boil down to either linear (LP) or semidefinite (SDP) programming. We show how to use the sparse connectivity of a network, to significantly reduce the complexity of computation. This is specially useful for convolutional as well as pruned neural networks. We conduct experiments on networks with random weights as well as networks trained on MNIST, showing that in the particular case of the $\ell_\infty$-Lipschitz constant, our approach yields superior estimates, compared to baselines available in the literature.

We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization. This observation allows us to repose such problems via a suitable relaxation as convex optimization problems in the space of distributions over the training parameters. We derive some simple relationships between the distribution-space problem and the original problem, e.g. a distribution-space solution is at least as good as a solution in the original space. Moreover, we develop a numerical algorithm based on mixture distributions to perform approximate optimization directly in distribution space. Consistency of this approximation is established and the numerical efficacy of the proposed algorithm is illustrated on simple examples. In both theory and practice, this formulation provides an alternative approach to large-scale optimization in machine learning.

Ensemble-based methods are highly popular approaches that increase the accuracy of a decision by aggregating the opinions of individual voters. The common point is to maximize accuracy; however, a natural limitation occurs if incremental costs are also assigned to the individual voters. Consequently, we investigate creating ensembles under an additional constraint on the total cost of the members. This task can be formulated as a knapsack problem, where the energy is the ensemble accuracy formed by some aggregation rules. However, the generally applied aggregation rules lead to a nonseparable energy function, which takes the common solution tools -- such as dynamic programming -- out of action. We introduce a novel stochastic approach that considers the energy as the joint probability function of the member accuracies. This type of knowledge can be efficiently incorporated in a stochastic search process as a stopping rule, since we have the information on the expected accuracy or, alternatively, the probability of finding more accurate ensembles. Experimental analyses of the created ensembles of pattern classifiers and object detectors confirm the efficiency of our approach. Moreover, we propose a novel stochastic search strategy that better fits the energy, compared with general approaches such as simulated annealing.

We consider the maximum-a-posteriori inference problem in discrete graphical models and study solvers based on the dual block-coordinate ascent rule. We map all existing solvers in a single framework, allowing for a better understanding of their design principles. We theoretically show that some block-optimizing updates are sub-optimal and how to strictly improve them. On a wide range of problem instances of varying graph connectivity, we study the performance of existing solvers as well as new variants that can be obtained within the framework. As a result of this exploration we build a new state-of-the art solver, performing uniformly better on the whole range of test instances.

This paper intends to understand and to improve the working principle of decomposition-based multi-objective evolutionary algorithms. We review the design of the well-established Moea/d framework to support the smooth integration of different strategies for sub-problem selection, while emphasizing the role of the population size and of the number of offspring created at each generation. By conducting a comprehensive empirical analysis on a wide range of multi-and many-objective combinatorial NK landscapes, we provide new insights into the combined effect of those parameters on the anytime performance of the underlying search process. In particular, we show that even a simple random strategy selecting sub-problems at random outperforms existing sophisticated strategies. We also study the sensitivity of such strategies with respect to the ruggedness and the objective space dimension of the target problem.

We consider the least squares regression problem, penalized with a combination of the $\ell_{0}$ and $\ell_{2}$ norms (a.k.a. $\ell_0 \ell_2$ regularization). Recent work presents strong evidence that the resulting $\ell_0$-based estimators can outperform popular sparse learning methods, under many important high-dimensional settings. However, exact computation of $\ell_0$-based estimators remains a major challenge. Indeed, state-of-the-art mixed integer programming (MIP) methods for $\ell_0 \ell_2$-regularized regression face difficulties in solving many statistically interesting instances when the number of features $p \sim 10^4$. In this work, we present a new exact MIP framework for $\ell_0\ell_2$-regularized regression that can scale to $p \sim 10^7$, achieving over $3600$x speed-ups compared to the fastest exact methods. Unlike recent work, which relies on modern MIP solvers, we design a specialized nonlinear BnB framework, by critically exploiting the problem structure. A key distinguishing component in our algorithm lies in efficiently solving the node relaxations using specialized first-order methods, based on coordinate descent (CD). Our CD-based method effectively leverages information across the BnB nodes, through using warm starts, active sets, and gradient screening. In addition, we design a novel method for obtaining dual bounds from primal solutions, which certifiably works in high dimensions. Experiments on synthetic and real high-dimensional datasets demonstrate that our method is not only significantly faster than the state of the art, but can also deliver certifiably optimal solutions to statistically challenging instances that cannot be handled with existing methods. We open source the implementation through our toolkit L0BnB.

Information granules have been considered to be the fundamental constructs of Granular Computing (GrC). As a useful unsupervised learning technique, Fuzzy C-Means (FCM) is one of the most frequently used methods to construct information granules. The FCM-based granulation-degranulation mechanism plays a pivotal role in GrC. In this paper, to enhance the quality of the degranulation (reconstruction) process, we augment the FCM-based degranulation mechanism by introducing a vector of fuzzification factors (fuzzification factor vector) and setting up an adjustment mechanism to modify the prototypes and the partition matrix. The design is regarded as an optimization problem, which is guided by a reconstruction criterion. In the proposed scheme, the initial partition matrix and prototypes are generated by the FCM. Then a fuzzification factor vector is introduced to form an appropriate fuzzification factor for each cluster to build up an adjustment scheme of modifying the prototypes and the partition matrix. With the supervised learning mode of the granulation-degranulation process, we construct a composite objective function of the fuzzification factor vector, the prototypes and the partition matrix. Subsequently, the particle swarm optimization (PSO) is employed to optimize the fuzzification factor vector to refine the prototypes and develop the optimal partition matrix. Finally, the reconstruction performance of the FCM algorithm is enhanced. We offer a thorough analysis of the developed scheme. In particular, we show that the classical FCM algorithm forms a special case of the proposed scheme. Experiments completed for both synthetic and publicly available datasets show that the proposed approach outperforms the generic data reconstruction approach.