IPS Weighting

Task

Implement ips_weighted_loss(losses: list[float], propensities: list[float], min_propensity: float) -> float. Compute mean inverse-propensity-score weighted loss with propensity clipping.

Requirements

• losses and propensities have equal length.
• Every propensity is in [0, 1], and min_propensity is in (0, 1].
• Clip each propensity from below with max(propensity, min_propensity).
• Divide each loss by its clipped propensity, then return the arithmetic mean of those corrected losses.
• Do not normalize by the sum of inverse-propensity weights.
• Return 0.0 when the inputs are empty.
• Do not mutate either input.

Example

ips_weighted_loss(
    [1.0, 2.0, 3.0],
    [0.5, 1.0, 0.25],
    0.1,
)
# 5.333333333333333