Newton-Raphson Solver

Creates a solver that uses Newton-Raphson (second-order) optimization. Uses the Fisher information matrix to scale the gradient for faster convergence near the optimum.

Usage

newton_raphson(
  line_search = TRUE,
  max_iter = 50L,
  tol = 1e-08,
  backtrack_ratio = 0.5,
  min_step = 1e-12
)

Arguments

line_search

Use backtracking line search for stability

max_iter

Maximum number of iterations

tol

Convergence tolerance (on parameter change)

backtrack_ratio

Step size reduction factor for line search

min_step

Minimum step size before giving up

Value

A solver function with signature (problem, theta0, trace) -> mle_result

Details

Newton-Raphson computes the search direction as \(I(\theta)^{-1} s(\theta)\) where \(I\) is the Fisher information and \(s\) is the score. This accounts for parameter scaling and typically converges faster than gradient ascent when near the optimum.

Requires the problem to have a Fisher information function (either analytic or computed numerically).

Examples

if (FALSE) { # \dontrun{
# Basic usage
solver <- newton_raphson()
result <- solver(problem, c(0, 1))

# Often used after gradient ascent for refinement
strategy <- gradient_ascent(max_iter = 50) %>>% newton_raphson(max_iter = 20)
} # }