Related papers: NCVX: A User-Friendly and Scalable Package for Non…
The yaglm package aims to make the broader ecosystem of modern generalized linear models accessible to data analysts and researchers. This ecosystem encompasses a range of loss functions (e.g. linear, logistic, quantile regression),…
In recent years, nonconvex minimax problems have attracted significant attention due to their broad applications in machine learning, including generative adversarial networks, robust optimization and adversarial training. Most existing…
Recently, message-passing graph neural networks (MPNNs) have shown potential for solving combinatorial and continuous optimization problems due to their ability to capture variable-constraint interactions. While existing approaches leverage…
Decentralized optimization is a promising parallel computation paradigm for large-scale data analytics and machine learning problems defined over a network of nodes. This paper is concerned with decentralized non-convex composite problems…
Support vector machines (SVMs) are invaluable tools for many practical applications in artificial intelligence, e.g., classification and event recognition. However, popular SVM solvers are not sufficiently efficient for applications with a…
Learning the underlying equation from data is a fundamental problem in many disciplines. Recent advances rely on Neural Networks (NNs) but do not provide theoretical guarantees in obtaining the exact equations owing to the non-convexity of…
Solving non-convex regularized inverse problems is challenging due to their complex optimization landscapes and multiple local minima. However, these models remain widely studied as they often yield high-quality, task-oriented solutions,…
Trajectory optimization offers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to…
In additive models with many nonparametric components, a number of regularized estimators have been proposed and proven to attain various error bounds under different combinations of sparsity and fixed smoothness conditions. Some of these…
In this paper, we consider the problem of stochastic optimization, where the objective function is in terms of the expectation of a (possibly non-convex) cost function that is parametrized by a random variable. While the convergence speed…
We consider optimization problems in which the goal is find a $k$-dimensional subspace of $\mathbb{R}^n$, $k<<n$, which minimizes a convex and smooth loss. Such problems generalize the fundamental task of principal component analysis (PCA)…
The problem of minimizing the sum of nonsmooth, convex objective functions defined on a real Hilbert space over the intersection of fixed point sets of nonexpansive mappings, onto which the projections cannot be efficiently computed, is…
An emerging new paradigm for solving inverse problems is via the use of deep learning to learn a regularizer from data. This leads to high-quality results, but often at the cost of provable guarantees. In this work, we show how…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…
As surrogate functions of $L_0$-norm, many nonconvex penalty functions have been proposed to enhance the sparse vector recovery. It is easy to extend these nonconvex penalty functions on singular values of a matrix to enhance low-rank…
Robust optimization is a common framework in optimization under uncertainty when the problem parameters are not known, but it is rather known that the parameters belong to some given uncertainty set. In the robust optimization framework the…
We present new large-scale algorithms for fitting a subgradient regularized multivariate convex regression function to $n$ samples in $d$ dimensions -- a key problem in shape constrained nonparametric regression with applications in…
Recently, convex nested stochastic composite optimization (NSCO) has received considerable attention for its applications in reinforcement learning and risk-averse optimization. The current NSCO algorithms have worse stochastic oracle…
Gradient clipping is commonly used in training deep neural networks partly due to its practicability in relieving the exploding gradient problem. Recently, \citet{zhang2019gradient} show that clipped (stochastic) Gradient Descent (GD)…