'MADGRAD' Method for Stochastic Optimization

A Momentumized, Adaptive, Dual Averaged Gradient Method for Stochastic Optimization algorithm. MADGRAD is a 'best-of-both-worlds' optimizer with the generalization performance of stochastic gradient descent and at least as fast convergence as that of Adam, often faster. A drop-in optim_madgrad() implementation is provided based on Defazio et al (2020) .

madgrad

The Madgrad package is an R port of the original madgrad by Aaron Defazio and Samy Jelassi. See the Arxiv paper for details on the method.

Installation

You can install madgrad from CRAN using:

install.packages("madgrad")

The development version from GitHub can be installed with:

# install.packages("devtools")
devtools::install_github("mlverse/madgrad")

Example

This is a small example showing how to use madgrad with torch to minimize a function, of course, madgrad is not the best algorithm for this task and should work better for neural network training.

library(madgrad)
library(torch)

torch_manual_seed(1)

f <- function(x, y) {
  log((1.5 - x + x*y)^2 + (2.25 - x - x*(y^2))^2 + (2.625 - x + x*(y^3))^2)
}

x <- torch_tensor(-5, requires_grad = TRUE)
y <- torch_tensor(-2, requires_grad = TRUE)

opt <- optim_madgrad(params = list(x, y), lr = 0.1)

for (i in 1:100) {
  opt$zero_grad()
  z <- f(x, y)
  z$backward()
  opt$step()
}
x
#> torch_tensor
#>  2.2882
#> [ CPUFloatType{1} ]
y
#> torch_tensor
#>  0.2412
#> [ CPUFloatType{1} ]