In this work, we attempt to solve the integer-weight knapsack problem using the D-Wave 2000Q adiabatic quantum computer. The knapsack problem is a well-known NP-complete problem in computer science, with applications in economics, business, finance, etc. We attempt to solve a number of small knapsack problems whose optimal solutions are known; we find that adiabatic quantum optimization fails to produce solutions corresponding to optimal filling of the knapsack in all problem instances. We compare results obtained on the quantum hardware to the classical simulated annealing algorithm and two solvers employing a hybrid branch-and-bound algorithm. The simulated annealing algorithm also fails to produce the optimal filling of the knapsack, though solutions obtained by simulated and quantum annealing are no more similar to each other than to the correct solution. We discuss potential causes for this observed failure of adiabatic quantum optimization.

Jigsaw puzzle solving, the problem of constructing a coherent whole from a set of non-overlapping unordered fragments, is fundamental to numerous applications, and yet most of the literature has focused thus far on less realistic puzzles whose pieces are identical squares. Here we formalize a new type of jigsaw puzzle where the pieces are general convex polygons generated by cutting through a global polygonal shape with an arbitrary number of straight cuts, a generation model inspired by the celebrated Lazy caterer's sequence. We analyze the theoretical properties of such puzzles, including the inherent challenges in solving them once pieces are contaminated with geometrical noise. To cope with such difficulties and obtain tractable solutions, we abstract the problem as a multi-body spring-mass dynamical system endowed with hierarchical loop constraints and a layered reconstruction process. We define evaluation metrics and present experimental results to indicate that such puzzles are solvable completely automatically.

In the power and energy systems area, a progressive increase of literature contributions containing applications of metaheuristic algorithms is occurring. In many cases, these applications are merely aimed at proposing the testing of an existing metaheuristic algorithm on a specific problem, claiming that the proposed method is better than other methods based on weak comparisons. This 'rush to heuristics' does not happen in the evolutionary computation domain, where the rules for setting up rigorous comparisons are stricter, but are typical of the domains of application of the metaheuristics. This paper considers the applications to power and energy systems, and aims at providing a comprehensive view of the main issues concerning the use of metaheuristics for global optimization problems. A set of underlying principles that characterize the metaheuristic algorithms is presented. The customization of metaheuristic algorithms to fit the constraints of specific problems is discussed. Some weaknesses and pitfalls found in literature contributions are identified, and specific guidelines are provided on how to prepare sound contributions on the application of metaheuristic algorithms to specific problems.

Grassmann manifold based sparse spectral clustering is a classification technique that  consists in learning a latent representation of data, formed by a subspace basis, which  is sparse. In order to learn a latent representation, spectral clustering is formulated in  terms of a loss minimization problem over a smooth manifold known as Grassmannian.  Such minimization problem cannot be tackled by one of traditional gradient-based learning  algorithms, which are only suitable to perform optimization in absence of constraints among  parameters. It is, therefore, necessary to develop specific optimization/learning algorithms  that are able to look for a local minimum of a loss function under smooth constraints in  an efficient way. Such need calls for manifold optimization methods. In this paper, we  extend classical gradient-based learning algorithms on   at parameter spaces (from classical  gradient descent to adaptive momentum) to curved spaces (smooth manifolds) by means  of tools from manifold calculus. We compare clustering performances of these methods  and known methods from the scientific literature. The obtained results confirm that the  proposed learning algorithms prove lighter in computational complexity than existing ones  without detriment in clustering efficacy.

Promotions and discounts have become key components of modern e-commerce platforms. For online travel platforms (OTPs), popular promotions include room upgrades, free meals and transportation services. By offering these promotions, customers can get more value for their money, while both the OTP and its travel partners may grow their loyal customer base. However, the promotions usually incur a cost that, if uncontrolled, can become unsustainable. Consequently, for a promotion to be viable, its associated costs must be balanced by incremental revenue within set financial constraints. Personalized treatment assignment can be used to satisfy such constraints. This paper introduces a novel uplift modeling technique, relying on the Knapsack Problem formulation, that dynamically optimizes the incremental treatment outcome subject to the required Return on Investment (ROI) constraints. The technique leverages Retrospective Estimation, a modeling approach that relies solely on data from positive outcome examples. The method also addresses training data bias, long term effects, and seasonality challenges via online-dynamic calibration. This approach was tested via offline experiments and online randomized controlled trials at Booking .com - a leading OTP with millions of customers worldwide, resulting in a significant increase in the target outcome while staying within the required financial constraints and outperforming other approaches.

We design layerwise objectives as functionals whose analytic minimizers sufficiently express the exact ground-truth network in terms of its parameters and nonlinearities. Following this objective landscape, learning a preReLU-TLRN from finite samples can be formulated as convex programming with nonparametric function estimation: For each layer, we first formulate the corresponding empirical risk minimization (ERM) as convex quadratic programming (QP), then we show the solution space of the QP can be equivalently determined by a set of linear inequalities, which can then be efficiently solved by linear programming (LP). Experiments show the robustness and sample efficiency of our methods.

When solving an equation, using the result to encode a message, transmitting the coded message to another device, decoding the message at the other end, saving the message onto a hard drive, or using it to create a visual rendering; inaccuracies are often the system's enemy and have to be fought against. Furthermore, if and when any of these computational operations is repeated, we expect the results to be unchanged. We view an unrepeatable result as a sign of a "bug" that either has to be fixed, tamed, or at least well understood and tolerated. Reduced precision and reliability is often considered as a price in the tradeoff with computational efficiency. The central thesis of this perspective article is that for machine learning (ML) specifically, and artificial intelligence (AI) more generally, probabilistic operations are fundamentally important building blocks, which the field is growing to rely on. We anticipate that stochasticity will therefore feature more prominently, and as a fundamental principle, in the future of machine intelligence.

Simulation is increasingly being used for generating large labelled datasets in many machine learning problems. Recent methods have focused on adjusting simulator parameters with the goal of maximising accuracy on a validation task, usually relying on REINFORCE-like gradient estimators. However these approaches are very expensive as they treat the entire data generation, model training, and validation pipeline as a black-box and require multiple costly objective evaluations at each iteration. We propose an efficient alternative for optimal synthetic data generation, based on a novel differentiable approximation of the objective. This allows us to optimize the simulator, which may be non-differentiable, requiring only one objective evaluation at each iteration with a little overhead. We demonstrate on a state-of-the-art photorealistic renderer that the proposed method finds the optimal data distribution faster (up to $50\times$), with significantly reduced training data generation (up to $30\times$) and better accuracy ($+8.7\%$) on real-world test datasets than previous methods.

Gradient methods are a fundamental building block of modern machine learning. Their scalability and small memory footprint makes them exceptionally well suite d to the massive volumes of data used for present-day learning tasks. While such optimization methods perform very well in practi ce, one of their major limitations consists of their inability to converge faster by taking advantage of specific features of the input data. For example, the training data used for classification tasks may exhibit a few very informative features, while all the others have only marginal relevance. Having access t o this information a priori would enable practitioners to appropriately tune first-order optimizat ion methods, thus allowing them to train much faster. Lacking this knowledge, one may attempt to reach a si milar performance by very carefully tuning hyper-parameters, which are all specific to the learning mod el and input data. This limitation has motivated the development of adaptive m ethods, which in absence of prior knowledge concerning the importance of various features in the da ta, adapt their learning rates based on the information they acquired in previous iterations. The most notable example is AdaGrad [ 13 ], which adaptively modifies the learning rate corresponding to each coordinate in the vector of weights. Following its success, a host of new adaptive methods appeared, inc luding Adam [ 17 ], AmsGrad [ 27 ], and Shampoo [ 14 ], which attained optimal rates for generic online learning tasks.

We consider off-policy evaluation (OPE), which evaluates the performance of a new policy from observed data collected from previous experiments, without requiring the execution of the new policy. This finds important applications in areas with high execution cost or safety concerns, such as medical diagnosis, recommendation systems and robotics. In practice, due to the limited information from off-policy data, it is highly desirable to construct rigorous confidence intervals, not just point estimation, for the policy performance. In this work, we propose a new variational framework which reduces the problem of calculating tight confidence bounds in OPE into an optimization problem on a feasible set that catches the true state-action value function with high probability. The feasible set is constructed by leveraging statistical properties of a recently proposed kernel Bellman loss (Feng et al., 2019). We design an efficient computational approach for calculating our bounds, and extend it to perform post-hoc diagnosis and correction for existing estimators. Empirical results show that our method yields tight confidence intervals in different settings.