Log In Sign Up

A Stable High-order Tuner for General Convex Functions

by   José M. Moreu, et al.

Iterative gradient-based algorithms have been increasingly applied for the training of a broad variety of machine learning models including large neural-nets. In particular, momentum-based methods, with accelerated learning guarantees, have received a lot of attention due to their provable guarantees of fast learning in certain classes of problems and multiple algorithms have been derived. However, properties for these methods hold true only for constant regressors. When time-varying regressors occur, which is commonplace in dynamic systems, many of these momentum-based methods cannot guarantee stability. Recently, a new High-order Tuner (HT) was developed and shown to have 1) stability and asymptotic convergence for time-varying regressors and 2) non-asymptotic accelerated learning guarantees for constant regressors. These results were derived for a linear regression framework producing a quadratic loss function. In this paper, we extend and discuss the results of this same HT for general convex loss functions. Through the exploitation of convexity and smoothness definitions, we establish similar stability and asymptotic convergence guarantees. Additionally we conjecture that the HT has an accelerated convergence rate. Finally, we provide numerical simulations supporting the satisfactory behavior of the HT algorithm as well as the conjecture of accelerated learning.


page 1

page 2

page 3

page 4


Accelerated Learning with Robustness to Adversarial Regressors

High order iterative momentum-based parameter update algorithms have see...

A High-order Tuner for Accelerated Learning and Control

Gradient-descent based iterative algorithms pervade a variety of problem...

Shuffling Gradient-Based Methods with Momentum

We combine two advanced ideas widely used in optimization for machine le...

The Instability of Accelerated Gradient Descent

We study the algorithmic stability of Nesterov's accelerated gradient me...

Generalized AdaGrad (G-AdaGrad) and Adam: A State-Space Perspective

Accelerated gradient-based methods are being extensively used for solvin...

Accelerated Target Updates for Q-learning

This paper studies accelerations in Q-learning algorithms. We propose an...