Real-world optimization problems often require black-box optimization with observation failure, where we can obtain the objective function value if we succeed, otherwise, we can only obtain a fact of failure. Moreover, this failure region can be complex by several latent constraints, whose number is also unknown. For this problem, we propose a failure-aware Gaussian process upper confidence bound (F-GP-UCB), which only requires a mild assumption for the observation failure that an optimal solution lies on an interior of a feasible region. Furthermore, we show that the number of successful observations grows linearly, by which we provide the first regret upper bounds and the convergence of F-GP-UCB. We demonstrate the effectiveness of F-GP-UCB in several benchmark functions, including the simulation function motivated by material synthesis experiments.

To regulate a social system comprised of self-interested agents, economic incentives are often required to induce a desirable outcome. This incentive design problem naturally possesses a bilevel structure, in which a designer modifies the payoffs of the agents with incentives while anticipating the response of the agents, who play a non-cooperative game that converges to an equilibrium. The existing bilevel optimization algorithms raise a dilemma when applied to this problem: anticipating how incentives affect the agents at equilibrium requires solving the equilibrium problem repeatedly, which is computationally inefficient; bypassing the time-consuming step of equilibrium-finding can reduce the computational cost, but may lead the designer to a sub-optimal solution. To address such a dilemma, we propose a method that tackles the designer's and agents' problems simultaneously in a single loop. Specifically, at each iteration, both the designer and the agents only move one step. Nevertheless, we allow the designer to gradually learn the overall influence of the incentives on the agents, which guarantees optimality after convergence. The convergence rate of the proposed scheme is also established for a broad class of games.

Bilevel optimization has been recently used in many machine learning problems such as hyperparameter optimization, policy optimization, and meta learning. Although many bilevel optimization methods have been proposed, they still suffer from the high computational complexities and do not consider the more general bilevel problems with nonsmooth regularization. In the paper, thus, we propose a class of enhanced bilevel optimization methods with using Bregman distance to solve bilevel optimization problems, where the outer subproblem is nonconvex and possibly nonsmooth, and the inner subproblem is strongly convex. Specifically, we propose a bilevel optimization method based on Bregman distance (BiO-BreD) to solve deterministic bilevel problems, which achieves a lower computational complexity than the best known results. Meanwhile, we also propose a stochastic bilevel optimization method (SBiO-BreD) to solve stochastic bilevel problems based on stochastic approximated gradients and Bregman distance. Moreover, we further propose an accelerated version of SBiO-BreD method (ASBiO-BreD) using the variance-reduced technique, which can achieve a lower computational complexity than the best known computational complexities with respect to condition number $\kappa$ and target accuracy $\epsilon$ for finding an $\epsilon$-stationary point. We conduct data hyper-cleaning task and hyper-representation learning task to demonstrate that our new algorithms outperform related bilevel optimization approaches.

Developing deep generative models has been an emerging field due to the ability to model and generate complex data for various purposes, such as image synthesis and molecular design. However, the advance of deep generative models is limited by the challenges to generate objects that possess multiple desired properties because: 1) the existence of complex correlation among real-world properties is common but hard to identify; 2) controlling individual property enforces an implicit partially control of its correlated properties, which is difficult to model; 3) controlling multiple properties under variour manners simultaneously is hard and underexplored. We address these challenges by proposing a novel deep generative framework that recovers semantics and correlation of properties through disentangled latent vectors. The correlation is handled via an explainable mask pooling layer, and properties are precisely retained by the generated objects via the mutual dependence between latent vectors and properties. Our generative model preserves properties of interest while handles correlation and conflicts of properties under a multi-objective optimization framework. The experiments demonstrate our model's superior performance in generating objects with desired properties.

We can compress a rectifier network while exactly preserving its underlying functionality with respect to a given input domain if some of its neurons are stable. However, current approaches to determine the stability of neurons with Rectified Linear Unit (ReLU) activations require solving or finding a good approximation to multiple discrete optimization problems. In this work, we introduce an algorithm based on solving a single optimization problem to identify all stable neurons. Our approach is on median 183 times faster than the state-of-art method on CIFAR-10, which allows us to explore exact compression on deeper (5 x 100) and wider (2 x 800) networks within minutes. For classifiers trained under an amount of L1 regularization that does not worsen accuracy, we can remove up to 56% of the connections on the CIFAR-10 dataset.

In this work, we consider one challenging training time attack by modifying training data with bounded perturbation, hoping to manipulate the behavior (both targeted or non-targeted) of any corresponding trained classifier during test time when facing clean samples. To achieve this, we proposed to use an auto-encoder-like network to generate such adversarial perturbations on the training data together with one imaginary victim differentiable classifier. The perturbation generator will learn to update its weights so as to produce the most harmful noise, aiming to cause the lowest performance for the victim classifier during test time. This can be formulated into a non-linear equality constrained optimization problem. Unlike GANs, solving such problem is computationally challenging, we then proposed a simple yet effective procedure to decouple the alternating updates for the two networks for stability. By teaching the perturbation generator to hijacking the training trajectory of the victim classifier, the generator can thus learn to move against the victim classifier step by step. The method proposed in this paper can be easily extended to the label specific setting where the attacker can manipulate the predictions of the victim classifier according to some predefined rules rather than only making wrong predictions. Experiments on various datasets including CIFAR-10 and a reduced version of ImageNet confirmed the effectiveness of the proposed method and empirical results showed that, such bounded perturbations have good transferability across different types of victim classifiers.

An emerging problem in trustworthy machine learning is to train models that produce robust interpretations for their predictions. We take a step towards solving this problem through the lens of axiomatic attribution of neural networks. Our theory is grounded in the recent work, Integrated Gradients (IG) [STY17], in axiomatically attributing a neural network's output change to its input change. We propose training objectives in classic robust optimization models to achieve robust IG attributions. Our objectives give principled generalizations of previous objectives designed for robust predictions, and they naturally degenerate to classic soft-margin training for one-layer neural networks. We also generalize previous theory and prove that the objectives for different robust optimization models are closely related. Experiments demonstrate the effectiveness of our method, and also point to intriguing problems which hint at the need for better optimization techniques or better neural network architectures for robust attribution training.

Thompson sampling (TS) has attracted a lot of interest in the bandit area. It was introduced in the 1930s but has not been theoretically proven until recent years. All of its analysis in the combinatorial multi-armed bandit (CMAB) setting requires an exact oracle to provide optimal solutions with any input. However, such an oracle is usually not feasible since many combinatorial optimization problems are NP-hard and only approximation oracles are available. An example \cite{WangC18} has shown the failure of TS to learn with an approximation oracle. However, this oracle is uncommon and is designed only for a specific problem instance.

Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i) empirical convergence rates; (ii) robustness to data contamination; and (iii) efficient computational methods. For empirical convergence, we derive fast rates with explicit dependence of constants on dimension, subject to log-concavity of the population distributions. For robustness, we characterize minimax optimal, dimension-free robust estimation risks, and show an equivalence between robust sliced 1-Wasserstein estimation and robust mean estimation. This enables lifting statistical and algorithmic guarantees available for the latter to the sliced 1-Wasserstein setting. Moving on to computational aspects, we analyze the Monte Carlo estimator for the average-sliced distance, demonstrating that larger dimension can result in faster convergence of the numerical integration error. For the max-sliced distance, we focus on a subgradient-based local optimization algorithm that is frequently used in practice, albeit without formal guarantees, and establish an $O(\epsilon^{-4})$ computational complexity bound for it. Our theory is validated by numerical experiments, which altogether provide a comprehensive quantitative account of the scalability question.

Low-rank and nonsmooth matrix optimization problems capture many fundamental tasks in statistics and machine learning. While significant progress has been made in recent years in developing efficient methods for \textit{smooth} low-rank optimization problems that avoid maintaining high-rank matrices and computing expensive high-rank SVDs, advances for nonsmooth problems have been slow paced. In this paper we consider standard convex relaxations for such problems. Mainly, we prove that under a natural \textit{generalized strict complementarity} condition and under the relatively mild assumption that the nonsmooth objective can be written as a maximum of smooth functions, the \textit{extragradient method}, when initialized with a warm-start'' point, converges to an optimal solution with rate $O(1/t)$ while requiring only two \textit{low-rank} SVDs per iteration. We give a precise trade-off between the rank of the SVDs required and the radius of the ball in which we need to initialize the method. We support our theoretical results with empirical experiments on several nonsmooth low-rank matrix recovery tasks, demonstrating that using simple initializations, the extragradient method produces exactly the same iterates when full-rank SVDs are replaced with SVDs of rank that matches the rank of the (low-rank) ground-truth matrix to be recovered.