Optimization_Estimation: Iterative optimization procedure

In PLUCR: Policy Learning Under Constraint

Iterative optimization procedure

Description

This function performs an iterative optimization routine to correct and minimize the objective function. It iteratively finds a solution and corrects the objective function for such optimal solution, until two consecutive solutions do not change much.

Usage

Optimization_Estimation(
  mu0,
  nu0,
  prop_score,
  X,
  A,
  Y,
  Xi,
  lambda,
  alpha = 0.1,
  precision = 0.05,
  beta = 0.05,
  centered = FALSE,
  tol = 2.5 * 0.01,
  max_iter = 5
)

Arguments

mu0	A fold-specific function predicting primary outcome (Y) given treatment (A) and covariates (X).
nu0	A fold-specific function predicting adverse event outcome (Xi) given treatment (A) and covariates (X).
prop_score	A function that estimates the propensity score given treatment (A) and covariates (X).
X	A matrix of covariates of size n x d (input data in ⁠[0,1]⁠).
A	A binary vector or matrix of length n indicating treatment assignment (0 or 1).
Y	A numeric vector or matrix of length n representing primary outcomes (in ⁠[0,1]⁠).
Xi	A numeric vector or matrix of length n indicating adverse events (0 or 1).
lambda	A non-negative numeric scalar controlling the penalty for violating the constraint.
alpha	A numeric scalar representing the constraint tolerance (0.1 by default).
precision	A numeric scalar defining the desired convergence precision (0.05 by default). The number of Frank-Wolfe iterations (K) is inversely proportional to this value, calculated as 1/precision.
beta	A non-negative numeric scalar controlling the sharpness of the probability function (0.05 by default).
centered	A logical value indicating whether to apply centering in sigma_beta (FALSE by default).
tol	A numeric scalar used as an early stopping criterion based on the RMSE between consecutive solutions (0.025 by default).
max_iter	A numeric scalar specifying the maximum number of iterations (5 by default).

Details

This function saves intermediate results to files in order to recover progress or inspect iteration-level behavior. If the optimization converges or the maximum number of iterations is reached, the final parameter vector theta_init is saved.

Value

A list containing:

iter	The number of completed iterations.
offset_mu	Initial logit-transformed outcome predictions.
offset_nu	Initial logit-transformed auxiliary predictions.
psi_collection	Matrix of covariate projections across iterations.
sigma_psi_collection	Matrix of transformed projections across iterations.
epsilon1	GLM coefficients from the outcome model.
epsilon2	GLM coefficients from the auxiliary model.
theta_collection	List of parameter vectors from each iteration of the functional weight estimation.

PLUCR documentation built on March 30, 2026, 5:08 p.m.