We introduce an asymmetric distance in the space of learning tasks, and a framework to compute their complexity. These concepts are foundational to the practice of transfer learning, ubiquitous in Deep Learning, whereby a parametric model is pre-trained for a task, and then used for another after fine-tuning. The framework we develop is intrinsically non-asymptotic, capturing the finite nature of the training dataset, yet it allows distinguishing learning from memorization. It encompasses, as special cases, classical notions from Kolmogorov complexity, Shannon, and Fisher Information. However, unlike some of those frameworks, it can be applied easily to large-scale models and real-world datasets. It is the first framework to explicitly account for the optimization scheme, which plays a crucial role in Deep Learning, in measuring complexity and information.

A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The stochastic optimization problems arising in these machine learning problems is solved using algorithms such as stochastic gradient descent (SGD). A method based on estimates of the change in the minimizers and properties of the optimization algorithm is introduced for adaptively selecting the number of samples at each time step to ensure that the excess risk, i.e., the expected gap between the loss achieved by the approximate minimizer produced by the optimization algorithm and the exact minimizer, does not exceed a target level. A bound is developed to show that the estimate of the change in the minimizers is non-trivial provided that the excess risk is small enough. Extensions relevant to the machine learning setting are considered, including a cost-based approach to select the number of samples with a cost budget over a fixed horizon, and an approach to applying cross-validation for model selection. Finally, experiments with synthetic and real data are used to validate the algorithms.

This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and mathematical programming for decision-making under uncertainty, and identifies potential research opportunities. A brief review of classical mathematical programming techniques for hedging against uncertainty is first presented, along with their wide spectrum of applications in Process Systems Engineering. A comprehensive review and classification of the relevant publications on data-driven distributionally robust optimization, data-driven chance constrained program, data-driven robust optimization, and data-driven scenario-based optimization is then presented. This paper also identifies fertile avenues for future research that focuses on a closed-loop data-driven optimization framework, which allows the feedback from mathematical programming to machine learning, as well as scenario-based optimization leveraging the power of deep learning techniques. Perspectives on online learning-based data-driven multistage optimization with a learning-while-optimizing scheme is presented.

We propose a new topic modeling procedure that takes advantage of the fact that the There are many extensions of LDA, including a nonparametric Latent Dirichlet Allocation (LDA) log likelihood extension based on the Dirichlet process function is asymptotically equivalent called Hierarchical Dirichlet Process (Teh et al., to the logarithm of the volume of the topic 2005), a correlated topic extension based on the logistic simplex. This allows topic modeling to be normal prior on the topic proportions (Lafferty reformulated as finding the probability simplex and Blei, 2006), and a time-varying topic modeling that minimizes its volume and encloses extension (Blei and Lafferty, 2006). There are the documents that are represented as distributions two main approaches for estimation of the parameters over words. A convex relaxation of probabilistic topic models: the variational of the minimum volume topic model optimization approximation popularized by Blei et al. (2003) and is proposed, and it is shown that the sampling based approach studied by Pritchard the relaxed problem has the same global et al. (2000).

As algorithms are increasingly used to make important decisions pertaining to individuals, algorithmic discrimination is becoming a prominent concern. The seminal work of Dwork et al. [ITCS 2012] introduced the notion of individual fairness (IF): given a task-specific similarity metric, every pair of similar individuals should receive similar outcomes. In this work, we study fairness when individuals have diverse preferences over the possible outcomes. We show that in such settings, individual fairness can be too restrictive: requiring individual fairness can lead to less-preferred outcomes for the very individuals that IF aims to protect (e.g. a protected minority group). We introduce and study a new notion of preference-informed individual fairness (PIIF), a relaxation of individual fairness that allows for outcomes that deviate from IF, provided the deviations are in line with individuals' preferences. We show that PIIF can allow for solutions that are considerably more beneficial to individuals than the best IF solution. We further show how to efficiently optimize any convex objective over the outcomes subject to PIIF, for a rich class of individual preferences. Motivated by fairness concerns in targeted advertising, we apply this new fairness notion to the multiple-task setting introduced by Dwork and Ilvento [ITCS 2019]. We show that, in this setting too, PIIF can allow for considerably more beneficial solutions, and we extend our efficient optimization algorithm to this setting.

An energy based approach for stabilizing a mechanical system has offered a simple yet powerful control scheme. However, since it does not impose such strong constraints on parameter space of the controller, finding appropriate parameter values for an optimal controller is known to be hard. This paper intends to generate an optimal energy-based controller for swinging up a rotary inverted pendulum, also known as the Furuta pendulum, by applying the Bayesian optimization called Entropy Search. Simulations and experiments show that the optimal controller has an improved performance compared to a nominal controller for various initial conditions.

Air taxis are poised to be an additional mode of transportation in major cities suffering from ground transportation congestion. Among several potential applications of air taxis, we focus on their use within a city to transport passengers to nearby airports. Specifically, we consider the problem of determining optimal locations for skyports (enabling pick-up of passengers to airport) within a city. Our approach is inspired from hub location problems, and our proposed method optimizes for aggregate travel time to multiple airports while satisfying the demand (trips to airports) either via (i) ground transportation to skyport followed by an air taxi to the airport, or (ii) direct ground transportation to the airport. The number of skyports is a constraint, and the decision to go via the skyport versus direct ground transportation is a variable in the optimization problem. Extensive experiments on publicly available airport trips data from New York City (NYC) show the efficacy of our optimization method implemented using Gurobi. In addition, we share insightful results based on the NYC data set on how ground transportation congestion can impact the demand and service efficiency in such skyports; this emerges as yet another factor in deciding the optimal number of skyports and their locations for a given city.

Metaheuristics are general methods that guide application of concrete heuristic(s) to problems that are too hard to solve using exact algorithms. However, even though a growing body of literature has been devoted to their statistical evaluation, the approaches proposed so far are able to assess only coupled effects of metaheuristics and heuristics. They do not reveal us anything about how efficient the examined metaheuristic is at guiding its subordinate heuristic(s), nor do they provide us information about how much the heuristic component of the combined algorithm contributes to the overall performance. In this paper, we propose a simple yet effective methodology of doing so by deriving a naive, placebo metaheuristic from the one being studied and comparing the distributions of chosen performance metrics for the two methods. We propose three measures of difference between the two distributions. Those measures, which we call BER values (benefit, equivalence, risk) are based on a preselected threshold of practical significance which represents the minimal difference between two performance scores required for them to be considered practically different. We illustrate usefulness of our methodology on the example of Simulated Annealing, Boolean Satisfiability Problem, and the Flip heuristic.

For sampling from a log-concave density, we study implicit integrators resulting from $\theta$-method discretization of the overdamped Langevin diffusion stochastic differential equation. Theoretical and algorithmic properties of the resulting sampling methods for $ \theta \in [0,1] $ and a range of step sizes are established. Our results generalize and extend prior works in several directions. In particular, for $\theta\ge1/2$, we prove geometric ergodicity and stability of the resulting methods for all step sizes. We show that obtaining subsequent samples amounts to solving a strongly-convex optimization problem, which is readily achievable using one of numerous existing methods. Numerical examples supporting our theoretical analysis are also presented.

Optical scatterometry is a method to measure the size and shape of periodic micro- or nanostructures on surfaces. For this purpose the geometry parameters of the structures are obtained by reproducing experimental measurement results through numerical simulations. We compare the performance of Bayesian optimization to different local minimization algorithms for this numerical optimization problem. Bayesian optimization uses Gaussian-process regression to find promising parameter values. We examine how pre-computed simulation results can be used to train the Gaussian process and to accelerate the optimization.