Mize Step Summary

Produces a result summary for an optimization iteration. Information such as function value, gradient norm and step size may be returned.

Usage

mize_step_summary(opt, par, fg, par_old = NULL, calc_fn = NULL, calc_gr = NULL)

Arguments

opt

Optimizer to generate summary for, from return value of mize_step().

par

Vector of parameters at the end of the iteration, from return value of mize_step().

fg

Function and gradient list. See the documentation of mize().

par_old

(Optional). Vector of parameters at the end of the previous iteration. Used to calculate step size.

calc_fn

(Optional). If TRUE, force calculation of function if not already cached in opt, even if it would not be needed for convergence checking.

calc_gr

(Optional). If TRUE, force calculation of gradient if not already cached in opt, even if it would not be needed for convergence checking.

Value

A list with the following items:

• opt: Optimizer with updated state (e.g. function and gradient counts).

• iter: Iteration number.

• f: Function value at par.

• g2n: 2-norm of the gradient at par.

• ginfn: Infinity-norm of the gradient at par.

• nf: Number of function evaluations so far.

• ng: Number of gradient evaluations so far.

• step: Size of the step between par_old and par, if par_old is provided.

• alpha: Step length of the gradient descent part of the step.

• mu: Momentum coefficient for this iteration.

Details

By default, convergence tolerance parameters will be used to determine what function and gradient data is returned. The function value will be returned if it was already calculated and cached in the optimization iteration. Otherwise, it will be calculated only if a non-null absolute or relative tolerance value was asked for. A gradient norm will be returned only if a non-null gradient tolerance was specified, even if the gradient is available.

Note that if a function tolerance was specified, but was not calculated for the relevant value of par, they will be calculated here and the calculation does contribute to the total function count (and will be cached for potential use in the next iteration). The same applies for gradient tolerances and gradient calculation. Function and gradient calculation can also be forced here by setting the calc_fn and calc_gr (respectively) parameters to TRUE.

Examples

rb_fg <- list(
  fn = function(x) {
    100 * (x[2] - x[1] * x[1])^2 + (1 - x[1])^2
  },
  gr = function(x) {
    c(
      -400 * x[1] * (x[2] - x[1] * x[1]) - 2 * (1 - x[1]),
      200 * (x[2] - x[1] * x[1])
    )
  }
)
rb0 <- c(-1.2, 1)

opt <- make_mize(method = "BFGS", par = rb0, fg = rb_fg, max_iter = 30)
mize_res <- mize_step(opt = opt, par = rb0, fg = rb_fg)
# Get info about first step, use rb0 to compare new par with initial value
step_info <- mize_step_summary(mize_res$opt, mize_res$par, rb_fg, rb0)