TALC: Target-Aware Loss Comparison for Cost-Based Decisions

When learned costs feed a decision solver, a lower prediction loss can leave the decision unchanged. We introduce TALC (Target-Aware Loss Comparison), a framework that separates target choice, scoring rule, training procedure and decision cost. Our analysis decomposes squared threshold excess risk into decoded-mean error and a component invisible to the decoder. For arbitrary finite linear decision sets and finite cost alphabets, expected-cost regret bounds depend only on the decoded-mean component, by specializing existing squared-risk bounds. A cost-preserving projection can improve threshold Brier loss and binary cross-entropy while preserving the argmin set in exact arithmetic. We compare these two scores with decoded-mean MSE using a shared head, decoder and solver. On 300 saved models, projection reduces Brier scores with no observed change in true-cost error or regret; floating-point path identities can differ. Brier's extra residual constraint does not uniformly reduce cost error or regret. Across shortest-path tasks, corrected comparisons support threshold supervision in several settings. On fresh synthetic cost rules, specified learning-rate and duration changes significantly shift the BCE–Brier error difference, with observed mean orderings crossing. On Warcraft, most exact route errors add less than 0.1% stored cost, and their incidence depends on the cost precision used. A predicted training-duration reversal fails to transfer to battery scheduling. TALC connects what a loss constrains to what a decision actually costs.