Dual-Anchor Loss Function

Computes the combined loss for K_J and first-weight targets used in the dual-anchor calibration framework (RN-06, Algorithm 2).

Usage

dual_anchor_loss(
  a,
  b,
  J,
  K_target,
  w1_target,
  lambda,
  M = .QUAD_NODES_DEFAULT,
  loss_type = c("relative", "adaptive", "absolute"),
  L_K_scale = NULL,
  L_w_scale = NULL
)

Arguments

a

Numeric; shape parameter of the Gamma prior (a > 0).

b

Numeric; rate parameter of the Gamma prior (b > 0).

J

Integer; sample size.

K_target

List with components mu_K and var_K.

w1_target

List specifying the first-weight target (quantile, prob, or mean).

lambda

Numeric value between 0 and 1; weight on K_J loss component.

M

Integer; number of Gauss-Laguerre quadrature nodes.

loss_type

Character; type of loss scaling:

"relative": (DEFAULT) Normalized squared errors - both losses dimensionless and comparable. RECOMMENDED for most cases.
"adaptive": Scaled by initial loss magnitudes - gives more aggressive weight reduction. Use when lambda=0.5 should truly mean "equal importance".
"absolute": Legacy behavior - NOT RECOMMENDED, causes optimizer to essentially ignore weight constraint.

L_K_scale, L_w_scale

Numeric; scaling factors for adaptive loss. Only used when loss_type = "adaptive". If NULL, computed internally.

Value

Numeric; the combined loss value.

Details

Loss Scaling Comparison

At typical K-only solution with \(P(w_1 > 0.5)\) approximately 0.48, target = 0.30:

ABSOLUTE: L_K approximately 0, L_w approximately 0.03. Any move causes L_K >> L_w. Optimizer stays at K-only. BROKEN.
RELATIVE: L_K_rel approximately 0, L_w approximately 0.03. Both dimensionless. lambda = 0.5 gives approximately 9 percent reduction in \(P(w_1 > 0.5)\).
ADAPTIVE: Losses normalized by initial magnitudes. lambda = 0.5 gives approximately 18 percent reduction in \(P(w_1 > 0.5)\).

Usage

Arguments

Value

Details

Loss Scaling Comparison

See also