Learning a calibrated decision head from logged bandit feedback

A decision head reads a state and a list of options and returns a probability per option in one forward pass. Once deployed, it usually observes only whether the option it chose was right: logged bandit feedback. We adapt such a head, LoRA on Qwen3-0.6B-Base and 1.7B-Base, from that feedback and report three results. First, the Brier or log score of the sampled action's own probability is not a usable REINFORCE reward: every wrong action earns at least gold's reward, with a mean baseline the lowest-probability wrong action gets the largest advantage, and at two options the signal is zero; in one run it cut accuracy on ordered-scale questions from .636 to .111. Scoring the probability as a loss by the pathwise gradient avoids the collapse, as do the REINFORCE rewards r and r minus p. Second, with full labels, none of four tested bandit arms beat cross-entropy plus one temperature on mean expected calibration error (ECE) over four unseen label schemas. Third, from logged feedback alone, Chosen-Action Proper Scoring (CAPS), the direct method with a proper score on the chosen action's probability, beats fine-tuning on confirmed answers only, which discards negatives: on Banking77 by 2.6 accuracy points, .053 lower ECE and lower selective risk (three seeds against one baseline seed), and by 21.7 points on one seed on emotion data with an often-wrong logger. At N 5000, CAPS stays 1.5 points below full-label training at 0.6B and .6 points at 1.7B against one full-label seed, and propensity weights add nothing on this log. Under feedback flipped at a known rate, one seed per rate, CAPS's confidence tracks the noisy channel on average, backward correction recovers most of the clean calibration, and early stopping on held-out logged outcomes prevented memorising noisy draws in all three runs. Code, adapters, logs and per-record results are public.