Learning a calibrated decision head from logged bandit feedback

Ye Yuan

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…