Reinforcement Learning over Predictive Distributions for LLM Regression

Large language models (LLMs) have emerged as flexible regressors capable of predicting real-valued quantities from heterogeneous inputs. Yet most LLM regression objectives optimize predictions independently, often yielding poor calibration. We introduce Distribution-Aware Reward (DAR), an on-policy reinforcement learning objective that instead jointly evaluates the empirical predictive distribution formed by multiple predictions for the same input. To translate this distribution-level objective into rollout-level rewards, we assign each prediction credit based on its leave-one-out contribution to the quality of the overall predictive distribution. This encourages predictions that are well-centered and appropriately dispersed around the target. We evaluate on three regression settings: a synthetic task probing interpolation and extrapolation, and two real-world scientific tasks involving code and molecular data. Across tasks, DAR produces better-calibrated uncertainty estimates while consistently reducing prediction error and improving ranking quality over supervised fine-tuning and pointwise reinforcement learning. Together, these results highlight the benefits of distribution-aware training for LLM regression.