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Check Gradient Consistency

Source: R/gradient_check.R
check_mize_gradient.Rd

Compares an analytic gradient with a finite-difference approximation of the objective function at a parameter vector.

Usage

check_mize_gradient(
  fg,
  par,
  method = c("central", "forward"),
  rel_eps = NULL,
  abs_eps = 0,
  ...
)

Arguments

fg

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

par

Parameter vector where the gradient should be checked.

method

Finite-difference method: either "central" or "forward".

rel_eps

Relative finite-difference step. If NULL, a method-specific default is used.

abs_eps

Non-negative scalar added to each finite-difference step.

...

Additional arguments passed to fg$fn, fg$gr, and fg$fg when present.

Value

A list with components:

  • par: Parameter vector checked.

  • method: Finite-difference method used.

  • step: Per-coordinate finite-difference steps.

  • fn: Function value at par.

  • gr: Gradient returned by fg$gr(par).

  • gr_fd: Finite-difference gradient approximation.

  • error: Difference gr - gr_fd.

  • abs_error: Absolute coordinate-wise errors.

  • rel_error: Relative coordinate-wise errors, scaled by the larger coordinate magnitude of gr and gr_fd.

  • max_abs_error: Maximum absolute error.

  • max_rel_error: Maximum relative error.

  • worst_abs: One-row data frame for the coordinate with the largest absolute error.

  • worst_rel: One-row data frame for the coordinate with the largest relative error.

  • by_coord: Data frame with per-coordinate gradient comparisons.

  • fg_consistency: List describing whether fg$fg() was checked and, when available, its function and gradient consistency with fg$fn() and fg$gr().

Details

The fg argument uses the same list shape as mize(): it must contain fn and gr functions. If it also contains an fg function, the combined function-and-gradient result is checked for consistency with the separate fn and gr functions at par.

The finite-difference step for each coordinate is abs_eps + rel_eps * pmax(abs(par), 1). Central differences are usually more accurate and use twice as many function evaluations as forward differences.

See also

mize()

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])
    )
  }
)

check <- check_mize_gradient(rb_fg, c(-1.2, 1))
check$max_abs_error
#> [1] 2.208253e-08