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Primal-dual algorithm (PDA) is a classic and popular scheme for convex-concave saddle point problems. It is universally acknowledged that the proximal terms in the subproblems about the primal and dual variables are crucial to the…
In this paper, we leverage an information-theoretic upper bound on the maximum admissible level of noise (MALN) in convex Lipschitz-continuous zeroth-order optimisation to establish corresponding upper bounds for classes of strongly convex…
This paper studies the complexity for finding approximate stationary points of nonconvex-strongly-concave (NC-SC) smooth minimax problems, in both general and averaged smooth finite-sum settings. We establish nontrivial lower complexity…
We study gradient-based optimization methods obtained by direct Runge-Kutta discretization of the ordinary differential equation (ODE) describing the movement of a heavy-ball under constant friction coefficient. When the function is high…
Many fundamental problems in machine learning can be formulated by the convex program \[ \min_{\theta\in R^d}\ \sum_{i=1}^{n}f_{i}(\theta), \] where each $f_i$ is a convex, Lipschitz function supported on a subset of $d_i$ coordinates of…
We present an optimal gradient method for smooth strongly convex optimization. The method is optimal in the sense that its worst-case bound on the distance to an optimal point exactly matches the lower bound on the oracle complexity for the…
First-order methods for minimization and saddle point (min-max) problems are widely used for solving large-scale problems, in particular arising in machine learning. The majority of works obtain favorable complexity guarantees of such…
In this paper, we develop new first-order method for composite non-convex minimization problems with simple constraints and inexact oracle. The objective function is given as a sum of "`hard"', possibly non-convex part, and "`simple"'…
This paper shows that the OSGA algorithm -- which uses first-order information to solve convex optimization problems with optimal complexity -- can be used to efficiently solve arbitrary bound-constrained convex optimization problems. This…
In this paper, we study nonconvex constrained optimization problems with both equality and inequality constraints, covering deterministic and stochastic settings. We propose a novel first-order algorithm framework that employs a…
In this paper, we propose a unifying framework incorporating several momentum-related search directions for solving strongly monotone variational inequalities. The specific combinations of the search directions in the framework are made to…
In this paper, we propose a unified two-phase scheme to accelerate any high-order regularized tensor approximation approach on the smooth part of a composite convex optimization model. The proposed scheme has the advantage of not needing to…
We consider non-smooth saddle point optimization problems. To solve these problems, we propose a zeroth-order method under bounded or Lipschitz continuous noise, possible adversarial. In contrast to the state-of-the-art algorithms, our…
We propose a new family of adaptive first-order methods for a class of convex minimization problems that may fail to be Lipschitz continuous or smooth in the standard sense. Specifically, motivated by a recent flurry of activity on…
In recent years, nonconvex minimax problems have attracted significant attention due to their broad applications in machine learning, including generative adversarial networks, robust optimization and adversarial training. Most existing…
The derivation of second-order ordinary differential equations (ODEs) as continuous-time limits of optimization algorithms has been shown to be an effective tool for the analysis of these algorithms. Additionally, discretizing…
In this paper, we consider non-smooth convex optimization with a zeroth-order oracle corrupted by symmetric stochastic noise. Unlike the existing high-probability results requiring the noise to have bounded $\kappa$-th moment with $\kappa…
We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [5] by taking a different…
It is well-known that the lower bound of iteration complexity for solving nonconvex unconstrained optimization problems is $\Omega(1/\epsilon^2)$, which can be achieved by standard gradient descent algorithm when the objective function is…
This work introduces a new cubic regularization method for nonconvex unconstrained multiobjective optimization problems. At each iteration of the method, a model associated with the cubic regularization of each component of the objective…