A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We propose an SDP relaxation for the Gromov-Wasserstein distance, providing globally optimal solutions.
GAIL with neural networks converges to global optima and has a known rate.
Study optimal transport on globally hyperbolic spacetimes, focusing on weak Kantorovich potentials' regularity.
Paper solves globally optimal k-means for low dimensional data.
We solve the optimization of two-layer ReLU networks using convex math.
Paper proves global optimality of a simple optimization scheme for learning DAG models.
In this paper is proposed a new heuristic approach belonging to the field of evolutionary Estimation of Distribution Algorithms (EDAs). EDAs builds a probability model and a set of solutions is sampled from the model which characterizes the distribution of such solutions. The main framework of the proposed method is an…
Combines global and local search for efficient global optimization with Gaussian processes.
FOSC-X: An extended framework for extracting multiple optimal flat clusterings from hierarchical cluster trees
Graph cuts find global optima for Potts models in slight perturbations.
Solving statistical learning problems often involves nonconvex optimization. Despite the empirical success of nonconvex statistical optimization methods, their global dynamics, especially convergence to the desirable local minima, remain less well understood in theory. In this paper, we propose a new analytic paradigm …
Elman-type RNNs converge to globally optimal solutions in the mean-field regime.
Paper develops exact convex optimization for neural networks with polynomial activations.
In recent years, the nuclear norm minimization (NNM) problem has been attracting much attention in computer vision and machine learning. The NNM problem is capitalized on its convexity and it can be solved efficiently. The standard nuclear norm regularizes all singular values equally, which is however not flexible enou…
In this study we introduce a new technique for symbolic regression that guarantees global optimality. This is achieved by formulating a mixed integer non-linear program (MINLP) whose solution is a symbolic mathematical expression of minimum complexity that explains the observations. We demonstrate our approach by redis…
New algorithm solves optimization problems without submodularity.
Bayesian optimization is a sample-efficient method for finding a global optimum of an expensive-to-evaluate black-box function. A global solution is found by accumulating a pair of query point and its function value, repeating these two procedures: (i) modeling a surrogate function; (ii) maximizing an acquisition funct…
Radial Basis Functions Neural Networks (RBFNNs) are tools widely used in regression problems. One of their principal drawbacks is that the formulation corresponding to the training with the supervision of both the centers and the weights is a highly non-convex optimization problem, which leads to some fundamentally dif…
Global routing has been a historically challenging problem in electronic circuit design, where the challenge is to connect a large and arbitrary number of circuit components with wires without violating the design rules for the printed circuit boards or integrated circuits. Similar routing problems also exist in the de…
An Euler discretization of the Langevin diffusion is known to converge to the global minimizers of certain convex and non-convex optimization problems. We show that this property holds for any suitably smooth diffusion and that different diffusions are suitable for optimizing different classes of convex and non-convex …
Generative adversarial networks (GANs) are a widely used framework for learning generative models. Wasserstein GANs (WGANs), one of the most successful variants of GANs, require solving a minmax optimization problem to global optimality, but are in practice successfully trained using stochastic gradient descent-ascent.…
New framework for DNN training guarantees convergence to global minimum.
New method tackles inexact bilevel optimization for faster parameter learning.
The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local optimization heuristics without global optimality guarantees or with guarantees valid only…
SGD converges to global minimum for certain non-convex functions.
New geometric metrics improve Bayesian optimization performance evaluation.
We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality and small sample size . More specifically, we consider a function defined by local sparse models, one at each data point. We introduce sample-wis…
This work justifies neural collapse under MSE loss and analyzes the optimization landscape.
Local adaptive methods in FL can accelerate convergence but introduce bias, which is corrected.
The study examines when MAML's objective has a benign landscape.
A new framework for bilevel optimization tackles stochastic and global variance reduction.
Stability of singularity formation in Yang-Mills fields in higher dimensions.
Symmetric nonnegative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection and image segmentation. In this paper, we propose a novel nonconvex variable splitting method for solving SymNMF. The proposed algorithm is guaranteed to converge to…
Paper characterizes optimization landscape of Tucker decomposition.
In this paper, a new theory is developed for first-order stochastic convex optimization, showing that the global convergence rate is sufficiently quantified by a local growth rate of the objective function in a neighborhood of the optimal solutions. In particular, if the objective function in the -sub…
DEQs converge to optimal solutions with mild over-parameterization.
In this paper, we investigate the capability of the universal Kriging (UK) model for single-objective global optimization applied within an efficient global optimization (EGO) framework. We implemented this combined UK-EGO framework and studied four variants of the UK methods, that is, a UK with a first-order polynomia…
To integrate strategic, tactical and operational decisions, the two-stage optimization has been widely used to guide dynamic decision making. In this paper, we study the two-stage stochastic programming for complex systems with unknown response estimated by simulation. We introduce the global-local metamodel assisted t…
We present a global optimization approach for solving the maximum a-posteriori (MAP) clustering problem under the Gaussian mixture model.Our approach can accommodate side constraints and it preserves the combinatorial structure of the MAP clustering problem by formulating it asa mixed-integer nonlinear optimization pro…
In this paper, we study how to solve resource allocation problems in ultra-reliable and low-latency communications by unsupervised deep learning, which often yield functional optimization problems with quality-of-service (QoS) constraints. We take a joint power and bandwidth allocation problem as an example, which mini…
New algorithm solves large cardinality-constrained clustering problems.
We study nonconvex optimization landscapes for learning overcomplete representations, including learning (i) sparsely used overcomplete dictionaries and (ii) convolutional dictionaries, where these unsupervised learning problems find many applications in high-dimensional data analysis. Despite the empirical success of …
SBS uses SVGD to optimize continuous functions globally.
We propose a novel high-dimensional linear regression estimator: the Discrete Dantzig Selector, which minimizes the number of nonzero regression coefficients subject to a budget on the maximal absolute correlation between the features and residuals. Motivated by the significant advances in integer optimization over the…
Many mathematical imaging problems are posed as non-convex optimization problems. When numerically tractable global optimization procedures are not available, one is often interested in testing ex post facto whether or not a locally convergent algorithm has found the globally optimal solution. When the problem is formu…
New algorithm improves convergence for non-convex problems with boundaries.
ProGO optimizes non-convex functions without gradients, outperforming existing methods.
From minimal surfaces such as Simons' cone and catenoids, using refined Lyapunov-Schmidt reduction method, we construct new solutions for a free boundary problem whose free boundary has two components. In dimension , using variational arguments, we also obtain solutions which are global minimizers of the correspondi…