For square-loss weighted ERM in the proportional asymptotic regime, the class weight that equalizes per-class errors is ρ̃ = π−/π+ + (π−/π+ − 1) δ/(2π+ − δ), exceeding the ratio of priors and growing with δ.
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Thumb on the Scale: Optimal Loss Weighting in Last Layer Retraining
For square-loss weighted ERM in the proportional asymptotic regime, the class weight that equalizes per-class errors is ρ̃ = π−/π+ + (π−/π+ − 1) δ/(2π+ − δ), exceeding the ratio of priors and growing with δ.