We consider the problem of black-box multi-objective optimization (MOO) using expensive function evaluations (also referred to as experiments), where the goal is to approximate the true Pareto set of solutions by minimizing the total resource cost of experiments. For example, in hardware design optimization, we need to find the designs that trade-off performance, energy, and area overhead using expensive computational simulations. The key challenge is to select the sequence of experiments to uncover high-quality solutions using minimal resources. In this paper, we propose a general framework for solving MOO problems based on the principle of output space entropy (OSE) search: select the experiment that maximizes the information gained per unit resource cost about the true Pareto front. We appropriately instantiate the principle of OSE search to derive efficient algorithms for the following four MOO problem settings: 1) The most basic single-fidelity setting, where experiments are expensive and accurate; 2) Handling black-box constraints which cannot be evaluated without performing experiments; 3) The discrete multi-fidelity setting, where experiments can vary in the amount of resources consumed and their evaluation accuracy; and 4) The continuous-fidelity setting, where continuous function approximations result in a huge space of experiments. Experiments on diverse synthetic and real-world benchmarks show that our OSE search based algorithms improve over state-of-the-art methods in terms of both computational-efficiency and accuracy of MOO solutions.

Generative Adversarial Networks are a popular method for learning distributions from data by modeling the target distribution as a function of a known distribution. The function, often referred to as the generator, is optimized to minimize a chosen distance measure between the generated and target distributions. One commonly used measure for this purpose is the Wasserstein distance. However, Wasserstein distance is hard to compute and optimize, and in practice entropic regularization techniques are used to improve numerical convergence. The influence of regularization on the learned solution, however, remains not well-understood. In this paper, we study how several popular entropic regularizations of Wasserstein distance impact the solution in a simple benchmark setting where the generator is linear and the target distribution is high-dimensional Gaussian. We show that entropy regularization promotes the solution sparsification, while replacing the Wasserstein distance with the Sinkhorn divergence recovers the unregularized solution. Both regularization techniques remove the curse of dimensionality suffered by Wasserstein distance. We show that the optimal generator can be learned to accuracy $\epsilon$ with $O(1/\epsilon^2)$ samples from the target distribution. We thus conclude that these regularization techniques can improve the quality of the generator learned from empirical data for a large class of distributions.

Recent advances in Federated Learning (FL) have brought large-scale machine learning opportunities for massive distributed clients with performance and data privacy guarantees. However, most current works only focus on the interest of the central controller in FL, and ignore the interests of clients. This may result in unfairness which discourages clients from actively participating in the learning process and damages the sustainability of the whole FL system. Therefore, the topic of ensuring fairness in an FL is attracting a great deal of research interest. In recent years, diverse Fairness-Aware FL (FAFL) approaches have been proposed in an effort to achieve fairness in FL from different viewpoints. However, there is no comprehensive survey which helps readers gain insight into this interdisciplinary field. This paper aims to provide such a survey. By examining the fundamental and simplifying assumptions, as well as the notions of fairness adopted by existing literature in this field, we propose a taxonomy of FAFL approaches covering major steps in FL, including client selection, optimization, contribution evaluation and incentive distribution. In addition, we discuss the main metrics for experimentally evaluating the performance of FAFL approaches, and suggest some promising future research directions.

The problem of identifying algorithmic recourse for people affected by machine learning model decisions has received much attention recently. Some recent works model user-incurred cost, which is directly linked to user satisfaction. But they assume a single global cost function that is shared across all users. This is an unrealistic assumption when users have dissimilar preferences about their willingness to act upon a feature and different costs associated with changing that feature. In this work, we formalize the notion of user-specific cost functions and introduce a new method for identifying actionable recourses for users. By default, we assume that users' cost functions are hidden from the recourse method, though our framework allows users to partially or completely specify their preferences or cost function. We propose an objective function, Expected Minimum Cost (EMC), based on two key ideas: (1) when presenting a set of options to a user, it is vital that there is at least one low-cost solution the user could adopt; (2) when we do not know the user's true cost function, we can approximately optimize for user satisfaction by first sampling plausible cost functions, then finding a set that achieves a good cost for the user in expectation. We optimize EMC with a novel discrete optimization algorithm, Cost-Optimized Local Search (COLS), which is guaranteed to improve the recourse set quality over iterations. Experimental evaluation on popular real-world datasets with simulated user costs demonstrates that our method satisfies up to 25.89 percentage points more users compared to strong baseline methods. Using standard fairness metrics, we also show that our method can provide more fair solutions across demographic groups than comparable methods, and we verify that our method is robust to misspecification of the cost function distribution.

We consider the problem of optimizing combinatorial spaces (e.g., sequences, trees, and graphs) using expensive black-box function evaluations. For example, optimizing molecules for drug design using physical lab experiments. Bayesian optimization (BO) is an efficient framework for solving such problems by intelligently selecting the inputs with high utility guided by a learned surrogate model. A recent BO approach for combinatorial spaces is through a reduction to BO over continuous spaces by learning a latent representation of structures using deep generative models (DGMs). The selected input from the continuous space is decoded into a discrete structure for performing function evaluation. However, the surrogate model over the latent space only uses the information learned by the DGM, which may not have the desired inductive bias to approximate the target black-box function. To overcome this drawback, this paper proposes a principled approach referred as LADDER. The key idea is to define a novel structure-coupled kernel that explicitly integrates the structural information from decoded structures with the learned latent space representation for better surrogate modeling. Our experiments on real-world benchmarks show that LADDER significantly improves over the BO over latent space method, and performs better or similar to state-of-the-art methods.

We consider safety in simultaneous learning and control of discrete-time linear time-invariant systems. We provide rigorous confidence bounds on the learned model of the system based on the number of utilized state measurements. These bounds are used to modify control inputs to the system via an optimization problem with potentially time-varying safety constraints. We prove that the state can only exit the safe set with small probability, provided a feasible solution to the safety-constrained optimization exists. This optimization problem is then reformulated in a more computationally-friendly format by tightening the safety constraints to account for model uncertainty during learning. The tightening decreases as the confidence in the learned model improves. We finally prove that, under persistence of excitation, the tightening becomes negligible as more measurements are gathered.

We address the issue of safety in reinforcement learning. We pose the problem in a discounted infinite-horizon constrained Markov decision process framework. Existing results have shown that gradient-based methods are able to achieve an $\mathcal{O}(1/\sqrt{T})$ global convergence rate both for the optimality gap and the constraint violation. We exhibit a natural policy gradient-based algorithm that has a faster convergence rate $\mathcal{O}(\log(T)/T)$ for both the optimality gap and the constraint violation. When Slater's condition is satisfied and known a priori, zero constraint violation can be further guaranteed for a sufficiently large $T$ while maintaining the same convergence rate.

Most real optimization problems are defined over a mixed search space where the variables are both discrete and continuous. In engineering applications, the objective function is typically calculated with a numerically costly black-box simulation.General mixed and costly optimization problems are therefore of a great practical interest, yet their resolution remains in a large part an open scientific question. In this article, costly mixed problems are approached through Gaussian processes where the discrete variables are relaxed into continuous latent variables. The continuous space is more easily harvested by classical Bayesian optimization techniques than a mixed space would. Discrete variables are recovered either subsequently to the continuous optimization, or simultaneously with an additional continuous-discrete compatibility constraint that is handled with augmented Lagrangians. Several possible implementations of such Bayesian mixed optimizers are compared. In particular, the reformulation of the problem with continuous latent variables is put in competition with searches working directly in the mixed space. Among the algorithms involving latent variables and an augmented Lagrangian, a particular attention is devoted to the Lagrange multipliers for which a local and a global estimation techniques are studied. The comparisons are based on the repeated optimization of three analytical functions and a beam design problem.

Despite strong performance in numerous applications, the fragility of deep learning to input perturbations has raised serious questions about its use in safety-critical domains. While adversarial training can mitigate this issue in practice, state-of-the-art methods are increasingly application-dependent, heuristic in nature, and suffer from fundamental trade-offs between nominal performance and robustness. Moreover, the problem of finding worst-case perturbations is non-convex and underparameterized, both of which engender a non-favorable optimization landscape. Thus, there is a gap between the theory and practice of adversarial training, particularly with respect to when and why adversarial training works. In this paper, we take a constrained learning approach to address these questions and to provide a theoretical foundation for robust learning. In particular, we leverage semi-infinite optimization and non-convex duality theory to show that adversarial training is equivalent to a statistical problem over perturbation distributions, which we characterize completely. Notably, we show that a myriad of previous robust training techniques can be recovered for particular, sub-optimal choices of these distributions. Using these insights, we then propose a hybrid Langevin Monte Carlo approach of which several common algorithms (e.g., PGD) are special cases. Finally, we show that our approach can mitigate the trade-off between nominal and robust performance, yielding state-of-the-art results on MNIST and CIFAR-10. Our code is available at: https://github.com/arobey1/advbench.

The field of machine learning for drug discovery is witnessing an explosion of novel methods. These methods are often benchmarked on simple physicochemical properties such as solubility or general druglikeness, which can be readily computed. However, these properties are poor representatives of objective functions in drug design, mainly because they do not depend on the candidate's interaction with the target. By contrast, molecular docking is a widely successful method in drug discovery to estimate binding affinities. However, docking simulations require a significant amount of domain knowledge to set up correctly which hampers adoption. To this end, we present DOCKSTRING, a bundle for meaningful and robust comparison of ML models consisting of three components: (1) an open-source Python package for straightforward computation of docking scores; (2) an extensive dataset of docking scores and poses of more than 260K ligands for 58 medically-relevant targets; and (3) a set of pharmaceutically-relevant benchmark tasks including regression, virtual screening, and de novo design. The Python package implements a robust ligand and target preparation protocol that allows non-experts to obtain meaningful docking scores. Our dataset is the first to include docking poses, as well as the first of its size that is a full matrix, thus facilitating experiments in multiobjective optimization and transfer learning. Overall, our results indicate that docking scores are a more appropriate evaluation objective than simple physicochemical properties, yielding more realistic benchmark tasks and molecular candidates.