Related papers: Using second-order information in gradient samplin…
We consider the problem of efficiently computing the maximum likelihood estimator in Generalized Linear Models (GLMs) when the number of observations is much larger than the number of coefficients ($n \gg p \gg 1$). In this regime,…
This paper contributes to the exploration of a recently introduced computational paradigm known as second-order flows, which are characterized by novel dissipative hyperbolic partial differential equations extending accelerated gradient…
We present a novel adaptive optimization algorithm for large-scale machine learning problems. Equipped with a low-cost estimate of local curvature and Lipschitz smoothness, our method dynamically adapts the search direction and step-size.…
This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and…
We propose a second-order (Hessian or Hessian-free) based optimization method for variational inference inspired by Gaussian backpropagation, and argue that quasi-Newton optimization can be developed as well. This is accomplished by…
Using double-smoothing technique and stochastic mirror descent with inexact oracle we built an optimal algorithm (up to a multiplicative factor) for two-points gradient-free non-smooth stochastic convex programming. We investigate how much…
We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…
We present a novel second-order trajectory optimization algorithm based on Stein Variational Newton's Method and Maximum Entropy Differential Dynamic Programming. The proposed algorithm, called Stein Variational Differential Dynamic…
We consider a distributionally robust second-order stochastic dominance constrained optimization problem. We require the dominance constraints hold with respect to all probability distributions in a Wasserstein ball centered at the…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
In a Hilbert setting we study the convergence properties of a second order in time dynamical system combining viscous and Hessian-driven damping with time scaling in relation with the minimization of a nonsmooth and convex function. The…
The value of second-order methods lies in the use of curvature information. Yet, this information is costly to extract and once obtained, valuable negative curvature information is often discarded so that the method is globally convergent.…
For the composite multi-objective optimization problem composed of two nonsmooth terms, a smoothing method is used to overcome the nonsmoothness of the objective function, making the objective function contain at most one nonsmooth term.…
Score-based diffusion models have emerged as powerful tools in generative modeling, yet their theoretical foundations remain underexplored. In this work, we focus on the Wasserstein convergence analysis of score-based diffusion models.…
This paper presents a special type of distributed optimization problems, where the summation of agents' local cost functions (i.e., global cost function) is convex, but each individual can be non-convex. Unlike most distributed optimization…
We study a class of zeroth-order distributed optimization problems, where each agent can control a partial vector and observe a local cost that depends on the joint vector of all agents, and the agents can communicate with each other with…
We propose a descent subgradient algorithm for minimizing a real function, assumed to be locally Lipschitz, but not necessarily smooth or convex. To find an effective descent direction, the Goldstein subdifferential is approximated through…
In this paper, we consider an unconstrained stochastic optimization problem where the objective function exhibits high-order smoothness. Specifically, we propose a new stochastic first-order method (SFOM) with multi-extrapolated momentum,…
This paper presents the first optimal-rate $p$-th order methods with $p\geq 1$ for finding first and second-order stationary points of non-convex smooth objective functions over Riemannian manifolds. In contrast to the geodesically convex…
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…