Mathematical optimization

The package also supports optimization of functions using RcppEnsmallen. Find out more at ensmallen.org. All code is compiled to C++. During the optimization there is no context switch back to R.

Arbitrary function

Here we minimize 2 * norm(x)^2 using simulated annealing.

# taken from the docs of ensmallen.org
optimize <- compile_optimization_problem(
  data = list(),
  evaluate = function(x) {
    return(2 * norm(x)^2)
  },
  optimizer = optimizer_SA()
)

# should be roughly 0
optimize(matrix(c(1, -1, 1), ncol = 1))
#>              [,1]
#> [1,] 0.0005135967
#> [2,] 0.0004418168
#> [3,] 0.0002552780

Optimizers:

  • Simulated Annealing through optimizer_SA
  • Conventional Neural Evolution optimizer_CNE
  • …

Differentiable functions

Here solve a linear regression problem using L-BFGS.

optimize_lbfgs <- compile_optimization_problem(
  data = list(design_matrix = type_matrix(), response = type_colvec()),
  evaluate = function(beta) {
    return(norm(response - design_matrix %*% beta)^2)
  },
  gradient = function(beta) {
    return(-2 %*% t(design_matrix) %*% (response - design_matrix %*% beta))
  },
  optimizer = optimizer_L_BFGS()
)

# this example is taken from the RcppEnsmallen package
# https://github.com/coatless/rcppensmallen/blob/master/src/example-linear-regression-lbfgs.cpp
n <- 1e6
beta <- c(-2, 1.5, 3, 8.2, 6.6)
p <- length(beta)
X <- cbind(1, matrix(rnorm(n), ncol = p - 1))
y <- X %*% beta + rnorm(n / (p - 1))

# Run optimization with lbfgs fullly in C++
optimize_lbfgs(
  design_matrix = X,
  response = y,
  beta = matrix(runif(p), ncol = 1)
)
#>           [,1]
#> [1,] -2.003886
#> [2,]  1.501473
#> [3,]  2.998593
#> [4,]  8.198516
#> [5,]  6.599749

Optimizers:

  • L-BFGS through optimizer_L_BFGS
  • Gradient Descent through optimizer_GradientDescent
  • …