arXiv research

We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping. We show that the resulting proximal Newton-type methods inherit the desirable convergence behavior of Newton-type methods for minimizing s…

We study the smooth structure of convex functions by generalizing a powerful concept so-called self-concordance introduced by Nesterov and Nemirovskii in the early 1990s to a broader class of convex functions, which we call generalized self-concordant functions. This notion allows us to develop a unified framework for …

New algorithms solve nonconvex-nonconcave minimax optimization problems.

We present a novel Newton-type method for distributed optimization, which is particularly well suited for stochastic optimization and learning problems. For quadratic objectives, the method enjoys a linear rate of convergence which provably \emph{improves} with the data size, requiring an essentially constant number of…

For distributed computing environment, we consider the empirical risk minimization problem and propose a distributed and communication-efficient Newton-type optimization method. At every iteration, each worker locally finds an Approximate NewTon (ANT) direction, which is sent to the main driver. The main driver, then, …

We study two types of preconditioners and preconditioned stochastic gradient descent (SGD) methods in a unified framework. We call the first one the Newton type due to its close relationship to the Newton method, and the second one the Fisher type as its preconditioner is closely related to the inverse of Fisher inform…

We propose a fast proximal Newton-type algorithm for minimizing regularized finite sums that returns an $ε$-suboptimal point in $\tilde{\mathcal{O}}(d(n + \sqrt{κd})\log(\frac{1}ε))$ FLOPS, where $n$ is number of samples, $d$ is feature dimension, and $κ$ is the condition number. As long as $n > d$, the proposed method…

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…

The paper optimizes policies constrained to Schur stabilizing controllers using a Newton-type algorithm.

While first-order optimization methods such as stochastic gradient descent (SGD) are popular in machine learning (ML), they come with well-known deficiencies, including relatively-slow convergence, sensitivity to the settings of hyper-parameters such as learning rate, stagnation at high training errors, and difficulty …

FedNew improves federated learning efficiency and privacy.

It has recently been shown that many of the existing quasi-Newton algorithms can be formulated as learning algorithms, capable of learning local models of the cost functions. Importantly, this understanding allows us to safely start assembling probabilistic Newton-type algorithms, applicable in situations where we only…

This paper studies distributed estimation and inference for a general statistical problem with a convex loss that could be non-differentiable. For the purpose of efficient computation, we restrict ourselves to stochastic first-order optimization, which enjoys low per-iteration complexity. To motivate the proposed metho…

Improved robustness in optimization methods using second-order information.

We study a time reparametrisation of the Newton type equations on Riemannian manifolds slightly modifying the Chaplygin multiplier method, allowing us to consider the Chaplygin method and the Maupertuis principle within a unified framework. As an example, the reduced nonholonomic problem of rolling without slipping and…

In this paper we present nonparametric estimators for coefficients in stochastic differential equation if the data are described by independent, identically distributed random variables. The problem is formulated as a nonlinear ill-posed operator equation with a deterministic forward operator described by the Fokker-Pl…

FedDANE adapts DANE for federated learning, but underperforms compared to existing methods.

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 $ε$-approximate seco…

In many learning tasks, structural models usually lead to better interpretability and higher generalization performance. In recent years, however, the simple structural models such as lasso are frequently proved to be insufficient. Accordingly, there has been a lot of work on "superposition-structured" models where mul…

During recent years there has been an increased interest in stochastic adaptations of limited memory quasi-Newton methods, which compared to pure gradient-based routines can improve the convergence by incorporating second order information. In this work we propose a direct least-squares approach conceptually similar to…

Regularizes 3D inverse scattering with tangent-point energy for better solutions.

We apply both distance-based (Jin and Matteson, 2017) and kernel-based (Pfister et al., 2016) mutual dependence measures to independent component analysis (ICA), and generalize dCovICA (Matteson and Tsay, 2017) to MDMICA, minimizing empirical dependence measures as an objective function in both deflation and parallel m…

Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape, researchers in practice areas such as marketing and social sciences also frequen…

This paper provides a block coordinate descent algorithm to solve unconstrained optimization problems. In our algorithm, computation of function values or gradients is not required. Instead, pairwise comparison of function values is used. Our algorithm consists of two steps; one is the direction estimate step and the o…

A new method for faster optimization on statistical manifolds.

Paper tackles distributed quantile regression with improved efficiency and support recovery.

WSFN overcomes saddle points for non-convex functionals in Wasserstein space.

SVRN accelerates Newton methods by reducing variance and improving performance.

We propose a new algorithm for finite sum optimization which we call the curvature-aided incremental aggregated gradient (CIAG) method. Motivated by the problem of training a classifier for a d-dimensional problem, where the number of training data is $m$ and $m \gg d \gg 1$, the CIAG method seeks to accelerate increme…

Mixtures-of-Experts (MoE) are conditional mixture models that have shown their performance in modeling heterogeneity in data in many statistical learning approaches for prediction, including regression and classification, as well as for clustering. Their estimation in high-dimensional problems is still however challeng…

New method solves convex optimization faster than NAG.

Study uses FEM for HJB in option pricing with borrowing fees, improving accuracy and efficiency.

Paper proposes differentially private quantile regression for high-dimensional data.

Paper presents a new training method for overparametrized neural networks that reduces time per iteration.

We consider the problem of finding the minimizer of a convex function $F: \mathbb R^d \rightarrow \mathbb R$ of the form $F(w) := \sum_{i=1}^n f_i(w) + R(w)$ where a low-rank factorization of $\nabla^2 f_i(w)$ is readily available. We consider the regime where $n \gg d$. As second-order methods prove to be effective in…

We study distributed algorithms for expected loss minimization where the datasets are large and have to be stored on different machines. Often we deal with minimizing the average of a set of convex functions where each function is the empirical risk of the corresponding part of the data. In the distributed setting wher…

SNS accelerates Sinkhorn algorithm with sparse Newton iterations.

New findings on optimization landscape of Toeplitz covariance estimation.

There is growing interest in large-scale machine learning and optimization over decentralized networks, e.g. in the context of multi-agent learning and federated learning. Due to the imminent need to alleviate the communication burden, the investigation of communication-efficient distributed optimization algorithms - p…

Improved iterative methods for risk parity portfolio weights.

We describe a novel optimization method for finite sums (such as empirical risk minimization problems) building on the recently introduced SAGA method. Our method achieves an accelerated convergence rate on strongly convex smooth problems. Our method has only one parameter (a step size), and is radically simpler than o…

A new method combines Laplace and Variational Bayes for scalable inference.

Unified framework for model explanation methods based on feature removal.

This work reviews and evaluates methods for predicting prediction intervals in regression problems.

Derives kernel PCA with Nyström method for scalability.

In this paper, the author considers the numerical computation of CVA for large systems by Mote Carlo methods. He introduces two types of stochastic mesh methods for the computations of CVA. In the first method, stochastic mesh method is used to obtain the future value of the derivative contracts. In the second method, …

New method combines spectral and sparse methods for Gaussian processes.

Simple stochastic Newton and cubic Newton methods with fast convergence.