ResearchResearch paperEfficiency & Inference · Reinforcement Learning · Training & Scaling1 source · Oct 15, 2026

Sharp and Stable Label-Free Calibration Certificates from Logical Coherence

Query-conditioned probabilistic predictors answer logically related questions one at a time, and labels to check their calibration are often missing.

For each restriction on what a bettor's stakes may use, a minimax theorem identifies, for finitely supported laws of the answers, the sharp label-free lower bound on the corresponding calibration residual.
The sharp marginal bound is discontinuous in the answers, and no label-free lower bound continuous in the Wasserstein distance stays within a constant factor of it.
Lipschitz stakes give a stable bound, sharp for a smooth calibration residual and, for every positive Lipschitz constant, positive exactly when the sharp marginal bound is.
On i.i.d. streams, projected online gradient ascent at fixed nodes gives fixed-horizon certificates whose shortfall is bounded by grid, learning and statistical terms, and predictable betting gives anytime-valid ones.

[1]Sharp and Stable Label-Free Calibration Certificates from Logical Coherence
arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 15, 09:23 AM
Query-conditioned probabilistic predictors answer logically related questions one at a time, and labels to check their calibration are often missing.
For each restriction on what a bettor's stakes may use, a minimax theorem identifies, for finitely supported laws of the answers, the sharp label-free lower bound on the corresponding calibration residual.

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