Quantum hardware and quantum-inspired algorithms are becoming increasingly popular for combinatorial optimization. However, these algorithms may require careful hyperparameter tuning for each problem instance. We use a reinforcement learning agent in conjunction with a quantum-inspired algorithm to solve the Ising energy minimization problem, which is equivalent to the Maximum Cut problem. The agent controls the algorithm by tuning one of its parameters with the goal of improving recently seen solutions. We propose a new Rescaled Ranked Reward (R3) method that enables stable single-player version of self-play training that helps the agent to escape local optima. The training on any problem instance can be accelerated by applying transfer learning from an agent trained on randomly generated problems. Our approach allows sampling high-quality solutions to the Ising problem with high probability and outperforms both baseline heuristics and a black-box hyperparameter optimization approach.

We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph structure or adding hard constraints to feature-space algorithms. Following a different path, we define a metric regression scheme where we train metric-constrained linear combinations of dissimilarity matrices. The idea is that the input matrices can be pre-computed dissimilarity measures obtained from any kind of available data (e.g. node attributes or edge structure). As the model inputs are distance measures, we do not need to assume the existence of any underlying feature space. Main challenge is that metric constraints (especially positive-definiteness and sub-additivity), are not automatically respected if, for example, the coefficients of the linear combination are allowed to be negative. Both positive and sub-additive constraints are linear inequalities, but the computational complexity of imposing them scales as O(D3), where D is the size of the input matrices (i.e. the size of the data set). This becomes quickly prohibitive, even when D is relatively small. We propose a new graph-based technique for optimizing under such constraints and show that, in some cases, our approach may reduce the original computational complexity of the optimization process by one order of magnitude. Contrarily to existing methods, our scheme applies to any (possibly non-convex) metric-constrained objective function.

The Gaussian process (GP) model, which has been extensively applied as priors of functions, has demonstrated excellent performance. The specification of a large number of parameters affects the computational efficiency and the feasibility of implementation of a control strategy. We propose a linear model to approximate GPs; this model expands the GP model by a series of basis functions. Several examples and simulation studies are presented to demonstrate the advantages of the proposed method. A control strategy is provided with the proposed linear model. Keywords: Data mining, forecasting, stochastic processes, control strategies INTRODUCTION The Gaussian process (GP) is a powerful modeling tool that has many applications in research and practice. It provides a practical and probabilistic approach to learning in kernel machines. The GP is extensively applied as a prior of a true function.

In this paper, we study the assortment optimization problem faced by many online retailers such as Amazon. We develop a \emph{cascade multinomial logit model}, based on the classic multinomial logit model, to capture the consumers' purchasing behavior across multiple stages. Different from existing studies, our model allows for repeated exposures of a product, i.e., the same product can be displayed multiple times across different stages. In addition, each consumer has a \emph{patience budget} that is sampled from a known distribution and each product is associated with a \emph{patience cost}, which captures the cognitive efforts spent on browsing that product. Given an assortment of products, a consumer sequentially browses them stage by stage. After browsing all products in one stage, if the utility of a product exceeds the utility of the outside option, the consumer proceeds to purchase the product and leave the platform. Otherwise, if the patience cost of all products browsed up to that point is no larger than her patience budget, she continues to view the next stage. We propose an approximation solution to this problem.

Stochastic Gradient Descent (SGD) is a popular tool in large scale optimization of machine learning objective functions. However, the performance is greatly variable, depending on the choice of the step sizes. In this paper, we introduce the exponential step sizes for stochastic optimization of smooth non-convex functions which satisfy the Polyak-\L{}ojasiewicz (PL) condition. We show that, without any information on the level of noise over the stochastic gradients, these step sizes guarantee a convergence rate for the last iterate that automatically interpolates between a linear rate (in the noisy-free case) and a $O(\frac{1}{T})$ rate (in the noisy case), up to poly-logarithmic factors. Moreover, if without the PL condition, the exponential step sizes still guarantee optimal convergence to a critical point, up to logarithmic factors. We also validate our theoretical results with empirical experiments on real-world datasets with deep learning architectures.

Smarter applications are making better use of the insights gleaned from data, having an impact on every industry and research discipline. At the core of this revolution lies the tools and the methods that are driving it, from processing the massive piles of data generated each day to learning from and taking useful action. Deep neural networks, along with advancements in classical ML and scalable general-purpose GPU computing, have become critical components of artificial intelligence, enabling many of these astounding breakthroughs and lowering the barrier to adoption. Python continues to be the most preferred language for scientific computing, data science, and machine learning, boosting both performance and productivity by enabling the use of low-level libraries and clean high-level APIs. This survey offers insight into the field of machine learning with Python, taking a tour through important topics to identify some of the core hardware and software paradigms that have enabled it. We cover widely-used libraries and concepts, collected together for holistic comparison, with the goal of educating the reader and driving the field of Python machine learning forward.

A variant of the classical knapsack problem is considered in which each item is associated with an integer weight and a qualitative level. We define a dominance relation over the feasible subsets of the given item set and show that this relation defines a preorder. We propose a dynamic programming algorithm to compute the entire set of non-dominated rank cardinality vectors and we state two greedy algorithms, which efficiently compute a single efficient solution.

Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based computation that generalizes a recent approach called "kernel-based dynamic mode decomposition". This new algorithm is characterized by a gain in approximation accuracy, as evidenced by numerical simulations, and in computational complexity.

In multi-task learning, difficulty levels of different tasks are varying. There are many works to handle this situation and we classify them into five categories, including the direct sum approach, the weighted sum approach, the maximum approach, the curriculum learning approach, and the multi-objective optimization approach. Those approaches have their own limitations, for example, using manually designed rules to update task weights, non-smooth objective function, and failing to incorporate other functions than training losses. In this paper, to alleviate those limitations, we propose a Balanced Multi-Task Learning (BMTL) framework. Different from existing studies which rely on task weighting, the BMTL framework proposes to transform the training loss of each task to balance difficulty levels among tasks based on an intuitive idea that tasks with larger training losses will receive more attention during the optimization procedure. We analyze the transformation function and derive necessary conditions. The proposed BMTL framework is very simple and it can be combined with most multi-task learning models. Empirical studies show the state-of-the-art performance of the proposed BMTL framework.

We study the fixed-support Wasserstein barycenter problem (FS-WBP), which consists in computing the Wasserstein barycenter of $m$ discrete probability measures supported on a finite metric space of size $n$. We show first that the constraint matrix arising from the linear programming (LP) representation of the FS-WBP is totally unimodular when $m \geq 3$ and $n = 2$, but not totally unimodular when $m \geq 3$ and $n \geq 3$. This result answers an open problem, since it shows that the FS-WBP is not a minimum-cost flow problem and therefore cannot be solved efficiently using linear programming. Building on this negative result, we propose and analyze a simple and efficient variant of the iterative Bregman projection (IBP) algorithm, currently the most widely adopted algorithm to solve the FS-WBP. The algorithm is an accelerated IBP algorithm which achieves the complexity bound of $\widetilde{\mathcal{O}}(mn^{7/3}/\varepsilon)$. This bound is better than that obtained for the standard IBP algorithm---$\widetilde{\mathcal{O}}(mn^{2}/\varepsilon^2)$---in terms of $\varepsilon$, and that of accelerated primal-dual gradient algorithm---$\widetilde{\mathcal{O}}(mn^{5/2}/\varepsilon)$---in terms of $n$. Empirical studies on simulated datasets demonstrate that the acceleration promised by the theory is real in practice.