arXiv research

First-order method solves stochastic bilevel optimization with linear constraints.

New methods reduce constraint violations to certainty in stochastic optimization.

A new method speeds up quantum state estimation.

New methods solve optimization problems with heavy-tailed noise, improving upon existing complexity bounds.

Unified approach for first-order methods with Markovian noise in stochastic optimization and variational inequalities.

First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored due to the high cost of computing the second-order information. In this paper we …

In this paper, we propose a new technique named \textit{Stochastic Path-Integrated Differential EstimatoR} (SPIDER), which can be used to track many deterministic quantities of interest with significantly reduced computational cost. We apply SPIDER to two tasks, namely the stochastic first-order and zeroth-order method…

Paper improves stochastic bilevel optimization methods for highly-smooth problems.

Simple stochastic Newton and cubic Newton methods with fast convergence.

Optimized method tackles convex optimization with heavy-tailed noise.

Novel BSG method for efficient stochastic optimization.

This is the first in a series of papers in which we study an efficient approximation scheme for solving the Hamilton-Jacobi-Bellman equation for multi-dimensional problems in stochastic control theory. The method is a combination of a WKB style asymptotic expansion of the value function, which reduces the second order …

Paper develops a TR-SSQP method for noisy optimization with heavy-tailed noise.

Two classes of methods have been proposed for escaping from saddle points with one using the second-order information carried by the Hessian and the other adding the noise into the first-order information. The existing analysis for algorithms using noise in the first-order information is quite involved and hides the es…

SVRN accelerates Newton methods by reducing variance and improving performance.

SFLS method finds feasible solutions faster with less data.

Method solves complex optimization problems with high probability bounds.

TRSVR combines SVRG with trust-region for faster optimization.

New adaptive methods solve weakly convex stochastic optimization problems.

New method solves stochastic optimization problems with random models.

Exact second-order optimization for deep learning reduces computational cost and improves performance.

Paper proposes a second-order method for faster SVI convergence.

New algorithm finds approximate stationary points in non-convex optimization.

Proposes a new stochastic quasi-Newton method with Nesterov's acceleration.

Proposes a new method for optimizing large-scale models using Nyström approximation of the Hessian.

First order discretizations of Langevin diffusion can achieve better generalization error with additional smoothness assumptions.

AdaSub optimizes with second-order info in low-dims subspace.

A new optimization method improves deep learning accuracy without hyper-parameter tuning.

A framework for decentralized optimization using first-order methods.

New algorithm tackles risk-aware learning problems efficiently.

We present novel minibatch stochastic optimization methods for empirical risk minimization problems, the methods efficiently leverage variance reduced first-order and sub-sampled higher-order information to accelerate the convergence speed. For quadratic objectives, we prove improved iteration complexity over state-of-…

New method reduces ensemble size for linear bandits, achieving near optimal regret.

We study distributed optimization algorithms for minimizing the average of convex functions. The applications include empirical risk minimization problems in statistical machine learning where the datasets are large and have to be stored on different machines. We design a distributed stochastic variance reduced gradien…

In this paper, we propose and analyze zeroth-order stochastic approximation algorithms for nonconvex and convex optimization, with a focus on addressing constrained optimization, high-dimensional setting and saddle-point avoiding. To handle constrained optimization, we first propose generalizations of the conditional g…

Optimal algorithms for Riemannian optimization with reduced complexity.

Consider the stochastic composition optimization problem where the objective is a composition of two expected-value functions. We propose a new stochastic first-order method, namely the accelerated stochastic compositional proximal gradient (ASC-PG) method, which updates based on queries to the sampling oracle using tw…

Unified framework for analyzing batch updating methods with noisy gradients.

Using agent-based modelling, empirical evidence and physical ideas, such as the energy function and the fact that the phase space must have twice the dimension of the configuration space, we argue that the stochastic differential equations which describe the motion of financial prices with respect to real world probabi…

New methods solve complex optimization problems without strong convexity assumptions.

In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems. We establish the complexity of this method for computing an approximate stationar…

Logistic regression is one of the most popular methods in binary classification, wherein estimation of model parameters is carried out by solving the maximum likelihood (ML) optimization problem, and the ML estimator is defined to be the optimal solution of this problem. It is well known that the ML estimator exists wh…

A new method helps escape saddle points in non-convex optimization.

New method for zeroth-order stochastic gradient algorithms provides confidence intervals.

In this paper, we consider multi-stage stochastic optimization problems with convex objectives and conic constraints at each stage. We present a new stochastic first-order method, namely the dynamic stochastic approximation (DSA) algorithm, for solving these types of stochastic optimization problems. We show that DSA c…

Develops first-order methods for average-reward MDPs with strong guarantees.

SSRGD finds local minima in nonconvex problems with simple gradient updates.

New algorithms optimize without knowing problem parameters.

New method solves optimization problems faster than existing methods.