16 accepted papers
Solving bilevel optimization (BLO) problems to global optimality is generally intractable. A common surrogate is to compute a hyper-stationary point—a stationary point of the hyper-objective function obtained by minimizing or maximizing the upper-level objective over the lower-level solution set. Ex…
In this paper, we propose a novel conceptual framework to detect outliers using optimal transport with a concave cost function. Conventional outlier detection approaches typically use a two-stage procedure: first, outliers are detected and removed, and then estimation is performed on the cleaned dat…
The performance of learning models often deteriorates when deployed in out-of-sample environments. To ensure reliable deployment, we propose a stability evaluation criterion based on distributional perturbations. Conceptually, our stability evaluation criterion is defined as the minimal perturbation…
In this work, we present the Bregman Alternating Projected Gradient (BAPG) method, a single-loop algorithm that offers an approximate solution to the Gromov-Wasserstein (GW) distance. We introduce a novel relaxation technique that balances accuracy and computational efficiency, albeit with some com…
Finding multiple solutions of non-convex optimization problems is a ubiquitous yet challenging task. Most past algorithms either apply single-solution optimization methods from multiple random initial guesses or search in the vicinity of found solutions using ad hoc heuristics. We present an end-to-…
Gromov-Wasserstein (GW) distance is a powerful tool for comparing and aligning probability distributions supported on different metric spaces. Recently, GW has become the main modeling technique for aligning heterogeneous data for a wide range of graph learning tasks. However, the GW distance is kno…
Nonconvex-nonconcave minimax optimization has received intense attention over the last decade due to its broad applications in machine learning. Most existing algorithms rely on one-sided information, such as the convexity (resp. concavity) of the primal (resp. dual) functions, or other specific str…
We focus on robust estimation of the unobserved state of a discrete-time stochastic system with linear dynamics. A standard analysis of this estimation problem assumes a baseline innovation model; with Gaussian innovations we recover the Kalman filter. However, in many settings, there is insufficien…
Graph Neural Networks (GNNs) are widely applied for graph anomaly detection. As one of the key components for GNN design is to select a tailored spectral filter, we take the first step towards analyzing anomalies via the lens of the graph spectrum. Our crucial observation is the existence of anomali…
Distributionally robust optimization (DRO) has been shown to offer a principled way to regularize learning models. In this paper, we find that Tikhonov regularization is distributionally robust in an optimal transport sense (i.e. if an adversary chooses distributions in a suitable optimal transport…
In this paper, we consider an inverse problem in graph learning domain -- "given the graph representations smoothed by Graph Convolutional Network (GCN), how can we reconstruct the input graph signal?" We propose Graph Deconvolutional Network (GDN) and motivate the design of GDN via a combination of…
We propose a novel Frank-Wolfe (FW) procedure for the optimization of infinite-dimensional functionals of probability measures - a task which arises naturally in a wide range of areas including statistical learning (e.g. variational inference) and artificial intelligence (e.g. generative adversarial…
Graph Neural Networks (GNN) and Variational Autoencoders (VAEs) have been widely used in modeling and generating graphs with latent factors. However there is no clear explanation of what these latent factors are and why they perform well. In this work, we present Dirichlet Graph Variational Autoenco…
Wasserstein \textbf{D}istributionally \textbf{R}obust \textbf{O}ptimization (DRO) is concerned with finding decisions that perform well on data that are drawn from the worst probability distribution within a Wasserstein ball centered at a certain nominal distribution. In recent years, it has been sh…
We analyze the Gambler's problem, a simple reinforcement learning problem where the gambler has the chance to double or lose their bets until the target is reached. This is an early example introduced in the reinforcement learning textbook by Sutton and Barto (2018), where they mention an interestin…
Wasserstein distance-based distributionally robust optimization (DRO) has received much attention lately due to its ability to provide a robustness interpretation of various learning models. Moreover, many of the DRO problems that arise in the learning context admits exact convex reformulations and…