From Critic to Confidence: PPO for Language-Based Quantitative Prediction with Confidence Estimation

LLMs can perform language-based quantitative prediction from unstructured inputs, but remain susceptible to hallucinations and overconfident errors, making it critical to know not only what a model predicts, but when its predictions can be trusted. We introduce CARE-PPO, a reinforcement learning framework that establishes a connection between loss prediction for uncertainty estimation and actor-critic PPO fine-tuning, enabling joint learning of accurate numerical estimates and reliable confidence signals in language-based quantitative prediction. CARE-PPO uses a Confidence-Aligned Reward for Estimation, defined as a function of prediction error, to provide dense error-aware feedback to the actor while inducing the critic to learn a value function aligned with prediction quality. During inference, we repurpose the critic as a confidence estimator. Across two real-world tasks in healthcare and finance and two Qwen-3 model scales (4B and 8B), CARE-PPO achieves strong quantitative prediction performance, while producing significantly better-aligned confidence estimates through the critic than logit-based and verbalized baselines. These gains persist under realistic out-of-distribution settings across domains, spanning linguistic and domain shifts. Finally, CARE-PPO reduces task-specific overfitting on general instruction-following prompts, consistent with the broader generalization advantages of RL fine-tuning over supervised approaches.