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.
Optimizes solving complex min-max problems with stochastic and nonconvex elements.
Improved stochastic Halpern iteration for fixed-point approximation in normed spaces.
In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic subspace ascent. A common feature of these methods is that in their update rule a cert…
The paper relaxes assumptions for analyzing stochastic optimization algorithms.
New algorithms solve monotone inclusions and convex-concave minimax problems.
Inexact Riemannian optimization converges to stationary points efficiently.
Inexact acquisition solutions in BO lead to sublinear cumulative regret.
We propose novel first-order stochastic approximation algorithms for canonical correlation analysis (CCA). Algorithms presented are instances of inexact matrix stochastic gradient (MSG) and inexact matrix exponentiated gradient (MEG), and achieve -suboptimality in the population objective in $\operatorname{poly}(\fr…
In this paper, we consider the convergence of an abstract inexact nonconvex and nonsmooth algorithm. We promise a pseudo sufficient descent condition and a pseudo relative error condition, which are both related to an auxiliary sequence, for the algorithm; and a continuity condition is assumed to hold. In fact, a lot o…
The paper studies the solution of stochastic optimization problems in which approximations to the gradient and Hessian are obtained through subsampling. We first consider Newton-like methods that employ these approximations and discuss how to coordinate the accuracy in the gradient and Hessian to yield a superlinear ra…
In this paper we consider the problem of minimizing a convex function using a randomized block coordinate descent method. One of the key steps at each iteration of the algorithm is determining the update to a block of variables. Existing algorithms assume that in order to compute the update, a particular subproblem is …
Develops accelerated fixed-point methods with delayed oracles for scientific computing.
Inexact subgradient methods work well for semialgebraic functions with additive errors.
We consider variants of trust-region and cubic regularization methods for non-convex optimization, in which the Hessian matrix is approximated. Under mild conditions on the inexact Hessian, and using approximate solution of the corresponding sub-problems, we provide iteration complexity to achieve -approximate seco…
Paper proposes iLPA for solving DC composite optimization problems, with applications to matrix completion with outliers.
Develops methods for spectral estimation and rare-event prediction in complex systems.
Two accelerated extragradient methods converge at rate for co-hypomonotone inclusions.
Interpreting gradient methods as fixed-point iterations, we provide a detailed analysis of those methods for minimizing convex objective functions. Due to their conceptual and algorithmic simplicity, gradient methods are widely used in machine learning for massive data sets (big data). In particular, stochastic gradien…
This paper analyzes how errors accumulate in PCA's deflation method.
Trust region and cubic regularization methods have demonstrated good performance in small scale non-convex optimization, showing the ability to escape from saddle points. Each iteration of these methods involves computation of gradient, Hessian and function value in order to obtain the search direction and adjust the r…
Survey on extragradient methods for solving nonlinear equations and inclusions.
In kernel methods, the kernels are often required to be positive definite, which restricts the use of many indefinite kernels. To consider those non-positive definite kernels, in this paper, we aim to build an indefinite kernel learning framework for kernel logistic regression. The proposed indefinite kernel logistic r…
We propose a supervised anomaly detection method for data with inexact anomaly labels, where each label, which is assigned to a set of instances, indicates that at least one instance in the set is anomalous. Although many anomaly detection methods have been proposed, they cannot handle inexact anomaly labels. To measur…
New method solves constrained optimization problems efficiently.
In machine learning research, the proximal gradient methods are popular for solving various optimization problems with non-smooth regularization. Inexact proximal gradient methods are extremely important when exactly solving the proximal operator is time-consuming, or the proximal operator does not have an analytic sol…
We adopt data structure in the form of cover trees and iteratively apply approximate nearest neighbour (ANN) searches for fast compressed sensing reconstruction of signals living on discrete smooth manifolds. Levering on the recent stability results for the inexact Iterative Projected Gradient (IPG) algorithm and by us…
Paper shows how gradient concentration helps in learning from inexact data.
New characterization limits sampling with inexact scores.
We consider distributed convex optimization problems originated from sample average approximation of stochastic optimization, or empirical risk minimization in machine learning. We assume that each machine in the distributed computing system has access to a local empirical loss function, constructed with i.i.d. data sa…
Method solves complex optimization problems with high probability bounds.
New algorithm for computing Wasserstein barycenters with guarantees.
Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating over the remaining variables. Over the last 30 years, the technique has been widely used, with empirical and theoretical results demonstrating both greater efficacy and greater stability c…
First-order optimization methods, such as stochastic gradient descent (SGD) and its variants, are widely used in machine learning applications due to their simplicity and low per-iteration costs. However, they often require larger numbers of iterations, with associated communication costs in distributed environments. I…
New analysis of stochastic approximation with non-expansive mappings.
We present ErasureHead, a new approach for distributed gradient descent (GD) that mitigates system delays by employing approximate gradient coding. Gradient coded distributed GD uses redundancy to exactly recover the gradient at each iteration from a subset of compute nodes. ErasureHead instead uses approximate gradien…
This paper analyzes the bias of inexact MCMC methods in high dimensions.
Evolutionary forms, as well as exterior forms, are skew-symmetric differential forms. But in contrast to the exterior forms, the basis of evolutionary forms is deforming manifolds (with unclosed metric forms). Such forms possess a peculiarity, namely, the closed inexact exterior forms are obtained from that. The closur…
New methods solve complex optimization problems in machine learning.
New algorithm solves phase retrieval with adaptive stopping criteria.
A new method tackles nonconvex optimization with penalties and proximal terms.
New algorithm tackles complex optimization problems with inexact and stochastic methods.
Cubic regularization (CR) is an optimization method with emerging popularity due to its capability to escape saddle points and converge to second-order stationary solutions for nonconvex optimization. However, CR encounters a high sample complexity issue for finite-sum problems with a large data size. %Various inexact …
New methods optimize functions faster with less gradient accuracy needed.
VR-GHAL method solves stochastic fixed-point equations with high probability.
Riemannian Proximal Sampler improves sampling on manifold data.
Second order Sobolev metrics are a useful tool in the shape analysis of curves. In this paper we combine these metrics with varifold-based inexact matching to explore a new strategy of computing geodesics between unparametrized curves. We describe the numerical method used for solving the inexact matching problem, appl…
Paper solves DRO for continuous distributions with iterative algorithms.
The mirror descent algorithm (MDA) generalizes gradient descent by using a Bregman divergence to replace squared Euclidean distance. In this paper, we similarly generalize the alternating direction method of multipliers (ADMM) to Bregman ADMM (BADMM), which allows the choice of different Bregman divergences to exploit …