7 papers
Monarch-Muon: Structure-Aware Muon for Fast and Memory-Efficient Pretraining
Alexander Miasnikov, Ruslan Kabirov, Gleb Molodtsov +7
Training large language models is constrained by both wall-clock time and memory footprint, and recent matrix-aware optimizers sharpen this tradeoff: Muon can improve optimization…
Lower Bounds For Gradient-Free Convex Optimization And Convex-Concave Saddle-Point Problems
Yuriy Dorn, Darina Dvinskikh, Timofei Loginov +4
We study the query complexity of optimization with exact scalar-value information. For globally -smooth convex functions on with a minimizer in a Euclidean ball of…
The Complexity of Convex Optimization with Mismatched Geometry
Timofei Loginov, Alexander Gasnikov, Yuriy Dorn +4
Optimal first-order methods on non-Euclidean domains such as the ball pair the prox-function with the norm in which smoothness…
Why SGD is not Brownian Motion: A New Perspective on Stochastic Dynamics
Igor Ignashin, Anna Radovskaya, Andrew Semenov +7
Stochastic Gradient Descent (SGD) is commonly modeled as a Langevin process, assuming that minibatch noise acts as Brownian motion. However, this approximation relies on a continuo…
Adaptive Regularized Newton Method with Inexact Hessian
Aleksandr Shestakov, Nail Bashirov, Andrei Semenov +4
Newton's method is the most widespread high-order method, demanding the gradient and the Hessian of the objective function. However, one of the main disadvantages of Newtons method…
Unified Theory of Adaptive Variance Reduction
Aleksandr Shestakov, Valery Parfenov, Aleksandr Beznosikov
Variance reduction is a family of powerful mechanisms for stochastic optimization that appears to be helpful in many machine learning tasks. It is based on estimating the exact gra…
Stochastic Frank-Wolfe: Unified Analysis and Zoo of Special Cases
Ruslan Nazykov, Aleksandr Shestakov, Vladimir Solodkin +3
The Conditional Gradient (or Frank-Wolfe) method is one of the most well-known methods for solving constrained optimization problems appearing in various machine learning tasks. Th…