Repair allocations left infeasible by plateaus in the objective

The objective has flat stretches wherever a predictive distribution has a point mass – always, for the degenerate distributions used by oracle_allocate() – so bisection on lambda can stall at an allocation that does not exhaust the budget. This finds bracketing vectors x_L and x_U and interpolates between them to hit the budget exactly.

Usage

post_process(x, K, lam, w, Lambda, eps_lam, point_mass_window)

Arguments

x

final allocation from the lambda search.

K

budget.

lam

final lambda iterate.

w

weights.

Lambda

list of marginal expected benefit functions.

eps_lam

relative tolerance for terminating the bisection on lambda.

point_mass_window

distance by which search intervals are widened in order to catch point masses in the Fs, intended or otherwise.

Value

An allocation vector exhausting the budget.

Examples

# a pair of targets whose marginal benefit declines linearly
Lambda <- list(function(x) 1 - x / 10, function(x) 1 - x / 10)
# the allocation c(8, 8) costs 16, over a budget of 12
post_process(
  x = c(8, 8), K = 12, lam = 0.5, w = c(1, 1),
  Lambda = Lambda, eps_lam = 1e-4, point_mass_window = 1e-3
)
#> [1] 6 6