Related papers: A New Lineserach for Accelerated Composite Minimiz…
This paper introduces a new method for minimizing matrix-smooth non-convex objectives through the use of novel Compressed Gradient Descent (CGD) algorithms enhanced with a matrix-valued stepsize. The proposed algorithms are theoretically…
We propose a new stochastic first-order algorithmic framework to solve stochastic composite nonconvex optimization problems that covers both finite-sum and expectation settings. Our algorithms rely on the SARAH estimator introduced in…
In this paper, we propose and analyse a family of generalised stochastic composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. Combined with an…
We study the iteration complexity of Lipschitz convex optimization problems satisfying a general error bound. We show that for this class of problems, subgradient descent with either Polyak stepsizes or decaying stepsizes achieves minimax…
We extend the convergence analysis of AdaSLS and AdaSPS in [Jiang and Stich, 2024] to the nonconvex setting, presenting a unified convergence analysis of stochastic gradient descent with adaptive Armijo line-search (AdaSLS) and Polyak…
We propose an adaptive step-size rule for decentralized optimization. Choosing a step-size that balances convergence and stability is challenging. This is amplified in the decentralized setting as agents observe only local (possibly…
We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients.…
Although ADAM is a very popular algorithm for optimizing the weights of neural networks, it has been recently shown that it can diverge even in simple convex optimization examples. Several variants of ADAM have been proposed to circumvent…
We derive several numerical methods for designing optimized first-order algorithms in unconstrained convex optimization settings. Our methods are based on the Performance Estimation Problem (PEP) framework, which casts the worst-case…
In stochastic convex optimization problems, most existing adaptive methods rely on prior knowledge about the diameter bound $D$ when the smoothness or the Lipschitz constant is unknown. This often significantly affects performance as only a…
Adaptive regularized framework using cubics has emerged as an alternative to line-search and trust-region algorithms for smooth nonconvex optimization, with an optimal complexity amongst second-order methods. In this paper, we propose and…
In this paper, we design and analyze a new family of adaptive subgradient methods for solving an important class of weakly convex (possibly nonsmooth) stochastic optimization problems. Adaptive methods that use exponential moving averages…
For deterministic optimization, line-search methods augment algorithms by providing stability and improved efficiency. We adapt a classical backtracking Armijo line-search to the stochastic optimization setting. While traditional…
We consider the problem of minimization of a convex function on a simple set with convex non-smooth inequality constraint and describe first-order methods to solve such problems in different situations: smooth or non-smooth objective…
We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order…
We propose an accelerated meta-algorithm, which allows to obtain accelerated methods for convex unconstrained minimization in different settings. As an application of the general scheme we propose nearly optimal methods for minimizing…
Using convex combination and linesearch techniques, we introduce a novel primal-dual algorithm for solving structured convex-concave saddle point problems with a generic smooth nonbilinear coupling term. Our adaptive linesearch strategy…
Majorization-minimization schemes are a broad class of iterative methods targeting general optimization problems, including nonconvex, nonsmooth and stochastic. These algorithms minimize successively a sequence of upper bounds of the…
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…
Although adaptive optimization algorithms have been successful in many applications, there are still some mysteries in terms of convergence analysis that have not been unraveled. This paper provides a novel non-convex analysis of adaptive…