Despite all the benefits of automated hyperparameter optimization (HPO), most modern HPO algorithms are black-boxes themselves. This makes it difficult to understand the decision process which leads to the selected configuration, reduces trust in HPO, and thus hinders its broad adoption. Here, we study the combination of HPO with interpretable machine learning (IML) methods such as partial dependence plots. These techniques are more and more used to explain the marginal effect of hyperparameters on the black-box cost function or to quantify the importance of hyperparameters. However, if such methods are naively applied to the experimental data of the HPO process in a post-hoc manner, the underlying sampling bias of the optimizer can distort interpretations. We propose a modified HPO method which efficiently balances the search for the global optimum w.r.t. predictive performance \emph{and} the reliable estimation of IML explanations of an underlying black-box function by coupling Bayesian optimization and Bayesian Algorithm Execution. On benchmark cases of both synthetic objectives and HPO of a neural network, we demonstrate that our method returns more reliable explanations of the underlying black-box without a loss of optimization performance.

Cyber-physical systems (CPSs) are usually complex and safety-critical; hence, it is difficult and important to guarantee that the system's requirements, i.e., specifications, are fulfilled. Simulation-based falsification of CPSs is a practical testing method that can be used to raise confidence in the correctness of the system by only requiring that the system under test can be simulated. As each simulation is typically computationally intensive, an important step is to reduce the number of simulations needed to falsify a specification. We study Bayesian optimization (BO), a sample-efficient method that learns a surrogate model that describes the relationship between the parametrization of possible input signals and the evaluation of the specification. In this paper, we improve the falsification using BO by; first adopting two prominent BO methods, one fits local surrogate models, and the other exploits the user's prior knowledge. Secondly, the formulation of acquisition functions for falsification is addressed in this paper. Benchmark evaluation shows significant improvements in using local surrogate models of BO for falsifying benchmark examples that were previously hard to falsify. Using prior knowledge in the falsification process is shown to be particularly important when the simulation budget is limited. For some of the benchmark problems, the choice of acquisition function clearly affects the number of simulations needed for successful falsification.

Stochastic bilevel optimization, which captures the inherent nested structure of machine learning problems, is gaining popularity in many recent applications. Existing works on bilevel optimization mostly consider either unconstrained problems or constrained upper-level problems. This paper considers the stochastic bilevel optimization problems with equality constraints both in the upper and lower levels. By leveraging the special structure of the equality constraints problem, the paper first presents an alternating implicit projected SGD approach and establishes the $\tilde{\cal O}(\epsilon^{-2})$ sample complexity that matches the state-of-the-art complexity of ALSET \citep{chen2021closing} for unconstrained bilevel problems. To further save the cost of projection, the paper presents two alternating implicit projection-efficient SGD approaches, where one algorithm enjoys the $\tilde{\cal O}(\epsilon^{-2}/T)$ upper-level and $\tilde{\cal O}(\epsilon^{-1.5}/T^{\frac{3}{4}})$ lower-level projection complexity with ${\cal O}(T)$ lower-level batch size, and the other one enjoys $\tilde{\cal O}(\epsilon^{-1.5})$ upper-level and lower-level projection complexity with ${\cal O}(1)$ batch size. Application to federated bilevel optimization has been presented to showcase the empirical performance of our algorithms. Our results demonstrate that equality-constrained bilevel optimization with strongly-convex lower-level problems can be solved as efficiently as stochastic single-level optimization problems.

We propose a new \textit{quadratic programming-based} method of approximating a nonstandard density using a multivariate Gaussian density. Such nonstandard densities usually arise while developing posterior samplers for unobserved components models involving inequality constraints on the parameters. For instance, Chan et al. (2016) provided a new model of trend inflation with linear inequality constraints on the stochastic trend. We implemented the proposed quadratic programming-based method for this model and compared it to the existing approximation. We observed that the proposed method works as well as the existing approximation in terms of the final trend estimates while achieving gains in terms of sample efficiency.

Modern NLP systems exhibit a range of biases, which a growing literature on model debiasing attempts to correct. However current progress is hampered by a plurality of definitions of bias, means of quantification, and oftentimes vague relation between debiasing algorithms and theoretical measures of bias. This paper seeks to clarify the current situation and plot a course for meaningful progress in fair learning, with two key contributions: (1) making clear inter-relations among the current gamut of methods, and their relation to fairness theory; and (2) addressing the practical problem of model selection, which involves a trade-off between fairness and accuracy and has led to systemic issues in fairness research. Putting them together, we make several recommendations to help shape future work.

Human-in-the-loop optimization utilizes human expertise to guide machine optimizers iteratively and search for an optimal solution in a solution space. While prior empirical studies mainly investigated novices, we analyzed the impact of the levels of expertise on the outcome quality and corresponding subjective satisfaction. We conducted a study (N=60) in text, photo, and 3D mesh optimization contexts. We found that novices can achieve an expert level of quality performance, but participants with higher expertise led to more optimization iteration with more explicit preference while keeping satisfaction low. In contrast, novices were more easily satisfied and terminated faster. Therefore, we identified that experts seek more diverse outcomes while the machine reaches optimal results, and the observed behavior can be used as a performance indicator for human-in-the-loop system designers to improve underlying models. We inform future research to be cautious about the impact of user expertise when designing human-in-the-loop systems.

Financial experts and analysts seek to predict the variability of financial markets. In particular, the correct prediction of this variability ensures investors successful investments. However, there has been a big trend in finance in the last years, which are the ESG criteria. Concretely, ESG (Economic, Social and Governance) criteria have become more significant in finance due to the growing importance of investments being socially responsible, and because of the financial impact companies suffer when not complying with them. Consequently, creating a stock portfolio should not only take into account its performance but compliance with ESG criteria. Hence, this paper combines mathematical modelling, with ESG and finance. In more detail, we use Bayesian optimization (BO), a sequential state-of-the-art design strategy to optimize black-boxes with unknown analytical and costly-to compute expressions, to maximize the performance of a stock portfolio under the presence of ESG criteria soft constraints incorporated to the objective function. In an illustrative experiment, we use the Sharpe ratio, that takes into consideration the portfolio returns and its variance, in other words, it balances the trade-off between maximizing returns and minimizing risks. In the present work, ESG criteria have been divided into fourteen independent categories used in a linear combination to estimate a firm total ESG score. Most importantly, our presented approach would scale to alternative black-box methods of estimating the performance and ESG compliance of the stock portfolio. In particular, this research has opened the door to many new research lines, as it has proved that a portfolio can be optimized using a BO that takes into consideration financial performance and the accomplishment of ESG criteria.

Sampling from an unnormalized target distribution is an essential problem with many applications in probabilistic inference. Stein Variational Gradient Descent (SVGD) has been shown to be a powerful method that iteratively updates a set of particles to approximate the distribution of interest. Furthermore, when analysing its asymptotic properties, SVGD reduces exactly to a single-objective optimization problem and can be viewed as a probabilistic version of this single-objective optimization problem. A natural question then arises: "Can we derive a probabilistic version of the multi-objective optimization?". To answer this question, we propose Stochastic Multiple Target Sampling Gradient Descent (MT-SGD), enabling us to sample from multiple unnormalized target distributions. Specifically, our MT-SGD conducts a flow of intermediate distributions gradually orienting to multiple target distributions, which allows the sampled particles to move to the joint high-likelihood region of the target distributions. Interestingly, the asymptotic analysis shows that our approach reduces exactly to the multiple-gradient descent algorithm for multi-objective optimization, as expected. Finally, we conduct comprehensive experiments to demonstrate the merit of our approach to multi-task learning.

In this paper, we study nonparametric estimation of instrumental variable (IV) regressions. Recently, many flexible machine learning methods have been developed for instrumental variable estimation. However, these methods have at least one of the following limitations: (1) restricting the IV regression to be uniquely identified; (2) only obtaining estimation error rates in terms of pseudometrics (\emph{e.g.,} projected norm) rather than valid metrics (\emph{e.g.,} $L_2$ norm); or (3) imposing the so-called closedness condition that requires a certain conditional expectation operator to be sufficiently smooth. In this paper, we present the first method and analysis that can avoid all three limitations, while still permitting general function approximation. Specifically, we propose a new penalized minimax estimator that can converge to a fixed IV solution even when there are multiple solutions, and we derive a strong $L_2$ error rate for our estimator under lax conditions. Notably, this guarantee only needs a widely-used source condition and realizability assumptions, but not the so-called closedness condition. We argue that the source condition and the closedness condition are inherently conflicting, so relaxing the latter significantly improves upon the existing literature that requires both conditions. Our estimator can achieve this improvement because it builds on a novel formulation of the IV estimation problem as a constrained optimization problem.

Federated learning is a privacy-preserving training paradigm over distributed networks that are designed for edge computing (McMahan et al., 2017). In federated learning, multiple edge devices (or clients) work together to learn a global model under the coordination of a central server. Instead of transmitting user data directly to the central server, each client stores data and computes locally and only transmits the privacy-preserving information. This paradigm is increasingly attractive due to the growing computational power of edge devices and the increasing demand for privacy protection. Federated learning is facing more challenges than traditional distributed optimization due to the high communication cost, data and system heterogeneity, and privacy concerns. Recent years have witnessed great progress in the algorithmic design and system deployment to address such challenges (Wang & Joshi, 2021; Karimireddy et al., 2019; Stich & Karimireddy, 2020). Recently, federated bilevel learning has received increasing attention (Chen et al., 2018; Fallah et al., 2020; Zeng et al., 2021) because many modern machine learning problems naturally exhibit a bilevel optimization structure. For example, Chen et al. 2018; Fallah et al. 2020 studied the federated meta-learning problems, Khodak et al. 2021 proposed federated hyperparameter optimization approaches, and Zeng et al. 2021 improved the fairness in federated learning using a bilevel method. This motivates us to study the following federated bilevel optimization problem.