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.
First order methods can take extremely long to find global minima of non-convex functions.
Non-convex extremal length found in surface metrics.
We consider regret minimization in repeated games with non-convex loss functions. Minimizing the standard notion of regret is computationally intractable. Thus, we define a natural notion of regret which permits efficient optimization and generalizes offline guarantees for convergence to an approximate local optimum. W…
A meta-learning approach improves the performance of alternating minimization for non-convex optimization problems.
Unified analysis improves SAM for non-convex optimization.
In this paper, we study a family of non-convex and possibly non-smooth inf-projection minimization problems, where the target objective function is equal to minimization of a joint function over another variable. This problem include difference of convex (DC) functions and a family of bi-convex functions as special cas…
Non-convex optimization is ubiquitous in machine learning. Majorization-Minimization (MM) is a powerful iterative procedure for optimizing non-convex functions that works by optimizing a sequence of bounds on the function. In MM, the bound at each iteration is required to \emph{touch} the objective function at the opti…
New method improves efficiency of non-convex matrix reconstruction.
Optimal control in changing systems without strong convexity assumptions.
The min-max problem, also known as the saddle point problem, is a class of optimization problems which minimizes and maximizes two subsets of variables simultaneously. This class of problems can be used to formulate a wide range of signal processing and communication (SPCOM) problems. Despite its popularity, most exist…
Optimally shows the distance between perturbed convex functions and their Γ-regularizations.
The paper analyzes adaptive algorithms in non-convex optimization landscapes.
This paper improves convergence guarantees for SGD algorithms in non-convex smooth functions.
WSFN overcomes saddle points for non-convex functionals in Wasserstein space.
The problem of minimizing sum-of-nonconvex functions (i.e., convex functions that are average of non-convex ones) is becoming increasingly important in machine learning, and is the core machinery for PCA, SVD, regularized Newton's method, accelerated non-convex optimization, and more. We show how to provably obtain an …
We consider the problem of finding local minimizers in non-convex and non-smooth optimization. Under the assumption of strict saddle points, positive results have been derived for first-order methods. We present the first known results for the non-smooth case, which requires different analysis and a different algorithm…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective function downhill. Such a simple principle is widely applicable and has been very popu…
Rank minimization (RM) is a wildly investigated task of finding solutions by exploiting low-rank structure of parameter matrices. Recently, solving RM problem by leveraging non-convex relaxations has received significant attention. It has been demonstrated by some theoretical and experimental work that non-convex relax…
Stochastic Gradient Langevin Dynamics (SGLD) is a popular variant of Stochastic Gradient Descent, where properly scaled isotropic Gaussian noise is added to an unbiased estimate of the gradient at each iteration. This modest change allows SGLD to escape local minima and suffices to guarantee asymptotic convergence to g…
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 …
New framework for optimizing machine learning risks.
Paper extends SMM to weakly convex and multi-convex surrogates for non-convex optimization.
This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g. sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of…
Iterative Hard Thresholding (IHT) is a class of projected gradient descent methods for optimizing sparsity-constrained minimization models, with the best known efficiency and scalability in practice. As far as we know, the existing IHT-style methods are designed for sparse minimization in primal form. It remains open t…
We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order non-convex optimization remain to be full gradient descent that converges in $O(1/\varep…
Tensor completion and robust principal component analysis have been widely used in machine learning while the key problem relies on the minimization of a tensor rank that is very challenging. A common way to tackle this difficulty is to approximate the tensor rank with the norm of singular values based on its …
We target the problem of finding a local minimum in non-convex finite-sum minimization. Towards this goal, we first prove that the trust region method with inexact gradient and Hessian estimation can achieve a convergence rate of order as long as those differential estimations are sufficientl…
In this paper we investigate panel regression models with interactive fixed effects. We propose two new estimation methods that are based on minimizing convex objective functions. The first method minimizes the sum of squared residuals with a nuclear (trace) norm regularization. The second method minimizes the nuclear …
New algorithms help machines forget old data efficiently.
A fast method for decentralized non-convex optimization over networks.
Improved convergence analysis for decentralized non-convex optimization.
The paper generalizes offset Rademacher complexities to convex and non-convex problems.
Heavy Ball method speeds up finding global optima in non-convex problems.
New methods improve convergence in non-convex non-smooth learning problems.
Non-bilinear observations make optimal control harder, showing non-convex costs and non-affine optimal controllers.
Online algorithms for identifying river pollution sources.
NSGLD improves SGLD for non-convex optimization problems.
SGD and stochastic gradient descent converge at optimal rates for certain non-convex functions.
The TREX is a recently introduced method for performing sparse high-dimensional regression. Despite its statistical promise as an alternative to the lasso, square-root lasso, and scaled lasso, the TREX is computationally challenging in that it requires solving a non-convex optimization problem. This paper shows a remar…
Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal processing. In this paper, we intend to make this principle scalable. We introduc…
Improved DP algorithms for non-convex optimization with tighter generalization bounds.
Develops a new interior-point technique for non-convex optimization problems.
We consider the optimization of active extension portfolios. For this purpose, the optimization problem is rewritten as a stochastic programming model and solved using a clever multi-start local search heuristic, which turns out to provide stable solutions. The heuristic solutions are compared to optimization results o…
New bounds found for optimizing non-convex functions with noisy data.
SGD converges almost surely in non-convex problems, avoiding saddle points and accelerating convergence.
Paper tackles constrained learning with non-convex losses, overcoming challenges with new approach.
A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low rank are frequently imposed or else the objective itself is designed to be a non-c…
In this paper we focus on the problem of Online Principal Component Analysis in the regret minimization framework. For this problem, all existing regret minimization algorithms for the fully-adversarial setting are based on a positive semidefinite convex relaxation, and hence require quadratic memory and SVD computatio…