As machine learning powered decision making is playing an increasingly important role in our daily lives, it is imperative to strive for fairness of the underlying data processing and algorithms. We propose a pre-processing algorithm for fair data representation via which L2- objective supervised learning algorithms result in an estimation of the Pareto frontier between prediction error and statistical disparity. In particular, the present work applies the optimal positive definite affine transport maps to approach the post-processing Wasserstein barycenter characterization of the optimal fair L2-objective supervised learning via a pre-processing data deformation. We call the resulting data Wasserstein pseudo-barycenter. Furthermore, we show that the Wasserstein geodesics from the learning outcome marginals to the barycenter characterizes the Pareto frontier between L2-loss and total Wasserstein distance among learning outcome marginals. Thereby, an application of McCann interpolation generalizes the pseudo-barycenter to a family of data representations via which L2-objective supervised learning algorithms result in the Pareto frontier. Numerical simulations underscore the advantages of the proposed data representation: (1) the pre-processing step is compositive with arbitrary L2-objective supervised learning methods and unseen data; (2) the fair representation protects data privacy by preventing the training machine from direct or indirect access to the sensitive information of the data; (3) the optimal affine map results in efficient computation of fair supervised learning on high-dimensional data; (4) experimental results shed light on the fairness of L2-objective unsupervised learning via the proposed fair data representation.

We analyze the optimized adaptive importance sampler (OAIS) for performing Monte Carlo integration with general proposals. We leverage a classical result which shows that the bias and the mean-squared error (MSE) of the importance sampling scales with the $\chi^2$-divergence between the target and the proposal and develop a scheme which performs global optimization of $\chi^2$-divergence. While it is known that this quantity is convex for exponential family proposals, the case of the general proposals has been an open problem. We close this gap by utilizing stochastic gradient Langevin dynamics (SGLD) and its underdamped counterpart for the global optimization of $\chi^2$-divergence and derive nonasymptotic bounds for the MSE by leveraging recent results from non-convex optimization literature. The resulting AIS schemes have explicit theoretical guarantees uniform in the number of iterations.

The Internet of Things (IoT) is a paradigm characterized by a network of embedded sensors and services. These sensors are incorporated to collect various information, track physical conditions, e.g., waste bins' status, and exchange data with different centralized platforms. The need for such sensors is increasing; however, proliferation of technologies comes with various challenges. For example, how can IoT and its associated data be used to enhance waste management? In smart cities, an efficient waste management system is crucial. Artificial Intelligence (AI) and IoT-enabled approaches can empower cities to manage the waste collection. This work proposes an intelligent approach to route recommendation in an IoT-enabled waste management system given spatial constraints. It performs a thorough analysis based on AI-based methods and compares their corresponding results. Our solution is based on a multiple-level decision-making process in which bins' status and coordinates are taken into account to address the routing problem. Such AI-based models can help engineers design a sustainable infrastructure system.

Bayesian optimization (BO) is a framework for global optimization of expensive-to-evaluate objective functions. Classical BO methods assume that the objective function is a black box. However, internal information about objective function computation is often available. For example, when optimizing a manufacturing line's throughput with simulation, we observe the number of parts waiting at each workstation, in addition to the overall throughput. Recent BO methods leverage such internal information to dramatically improve performance. We call these "grey-box" BO methods because they treat objective computation as partially observable and even modifiable, blending the black-box approach with so-called "white-box" first-principles knowledge of objective function computation. This tutorial describes these methods, focusing on BO of composite objective functions, where one can observe and selectively evaluate individual constituents that feed into the overall objective; and multi-fidelity BO, where one can evaluate cheaper approximations of the objective function by varying parameters of the evaluation oracle.

The most common approaches for solving multistage stochastic programming problems in the research literature have been to either use value functions ("dynamic programming") or scenario trees ("stochastic programming") to approximate the impact of a decision now on the future. By contrast, common industry practice is to use a deterministic approximation of the future which is easier to understand and solve, but which is criticized for ignoring uncertainty. We show that a parameterized version of a deterministic optimization model can be an effective way of handling uncertainty without the complexity of either stochastic programming or dynamic programming. We present the idea of a parameterized deterministic optimization model, and in particular a deterministic lookahead model, as a powerful strategy for many complex stochastic decision problems. This approach can handle complex, high-dimensional state variables, and avoids the usual approximations associated with scenario trees or value function approximations. Instead, it introduces the offline challenge of designing and tuning the parameterization. We illustrate the idea by using a series of application settings, and demonstrate its use in a nonstationary energy storage problem with rolling forecasts.

Machine learning-based methods have shown potential for optimizing existing molecules with more desirable properties, a critical step towards accelerating new chemical discovery. Here we propose QMO, a generic query-based molecule optimization framework that exploits latent embeddings from a molecule autoencoder. QMO improves the desired properties of an input molecule based on efficient queries, guided by a set of molecular property predictions and evaluation metrics. We show that QMO outperforms existing methods in the benchmark tasks of optimizing small organic molecules for drug-likeness and solubility under similarity constraints. We also demonstrate substantial property improvement using QMO on two new and challenging tasks that are also important in real-world discovery problems: (1) optimizing existing potential SARS-CoV-2 main protease inhibitors towards higher binding affinity and (2) improving known antimicrobial peptides towards lower toxicity. Results from QMO show high consistency with external validations, suggesting an effective means to facilitate material optimization problems with design constraints. Zeroth-order optimization is used on problems where no explicit gradient function is accessible, but single points can be queried. Hoffman et al. present here a molecular design method that uses zeroth-order optimization to deal with the discreteness of molecule sequences and to incorporate external guidance from property evaluations and design constraints.

Stochastic and soft optimal policies resulting from entropy-regularized Markov decision processes (ER-MDP) are desirable for exploration and imitation learning applications. Motivated by the fact that such policies are sensitive with respect to the state transition probabilities, and the estimation of these probabilities may be inaccurate, we study a robust version of the ER-MDP model, where the stochastic optimal policies are required to be robust with respect to the ambiguity in the underlying transition probabilities. Our work is at the crossroads of two important schemes in reinforcement learning (RL), namely, robust MDP and entropy regularized MDP. We show that essential properties that hold for the non-robust ER-MDP and robust unregularized MDP models also hold in our settings, making the robust ER-MDP problem tractable. We show how our framework and results can be integrated into different algorithmic schemes including value or (modified) policy iteration, which would lead to new robust RL and inverse RL algorithms to handle uncertainties. Analyses on computational complexity and error propagation under conventional uncertainty settings are also provided.

This thesis reviews numerical optimization methods with machine learning problems in mind. Since machine learning models are highly parametrized, we focus on methods suited for high dimensional optimization. We build intuition on quadratic models to figure out which methods are suited for non-convex optimization, and develop convergence proofs on convex functions for this selection of methods. With this theoretical foundation for stochastic gradient descent and momentum methods, we try to explain why the methods used commonly in the machine learning field are so successful. Besides explaining successful heuristics, the last chapter also provides a less extensive review of more theoretical methods, which are not quite as popular in practice. So in some sense this work attempts to answer the question: Why are the default Tensorflow optimizers included in the defaults?

In this paper, we present a novel algorithm to address the Network Alignment problem. It is inspired from a previous message passing framework of Bayati et al. [2] and includes several modifications designed to significantly speed up the message updates as well as to enforce their convergence. Experiments show that our proposed model outperforms other state-of-the-art solvers. Finally, we propose an application of our method in order to address the Binary Diffing problem. We show that our solution provides better assignment than the reference differs in almost all submitted instances and outline the importance of leveraging the graphical structure of binary programs.

We consider Bayesian optimization of the output of a network of functions, where each function takes as input the output of its parent nodes, and where the network takes significant time to evaluate. Such problems arise, for example, in reinforcement learning, engineering design, and manufacturing. While the standard Bayesian optimization approach observes only the final output, our approach delivers greater query efficiency by leveraging information that the former ignores: intermediate output within the network. This is achieved by modeling the nodes of the network using Gaussian processes and choosing the points to evaluate using, as our acquisition function, the expected improvement computed with respect to the implied posterior on the objective. Although the non-Gaussian nature of this posterior prevents computing our acquisition function in closed form, we show that it can be efficiently maximized via sample average approximation. In addition, we prove that our method is asymptotically consistent, meaning that it finds a globally optimal solution as the number of evaluations grows to infinity, thus generalizing previously known convergence results for the expected improvement. Notably, this holds even though our method might not evaluate the domain densely, instead leveraging problem structure to leave regions unexplored. Finally, we show that our approach dramatically outperforms standard Bayesian optimization methods in several synthetic and real-world problems.