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.

On the effectiveness of reward functions in reinforcement learning for confidence calibration of large language models

In this paper, we consider the setting where large language models (LLMs) are trained using reinforcement learning (RL) to simultaneously improve reasoning accuracy and verbalize its confidence. Our reward scheme uses two functions for rewarding confidence verbalized by the LLM: one when the LLM is correct and a different one when the LLM is incorrect. With a poorly designed reward scheme, the LLM may be incentivized to answer incorrectly so that it can be confident that its answer is indeed incorrect, a phenomenon that we call confidence reward hacking. We propose the concept of non-hackable confidence reward schemes and define a spectrum of such reward schemes for RL confidence calibration training in LLMs. We demonstrate that selective confidence reward hacking can occur in practical datasets with reward schemes that are not designed to be non-hackable. We also demonstrate that the reward scheme with the best calibration to accuracy tradeoff depends on the dataset and the application, and propose using the reward scheme as a hyperparameter to optimize the tradeoffs in accordance to what is important for the application. The code of our experiments is available in https://anonymous.4open.science/r/rl-confidence-calibration-9ED4/README.md.

Scaling with Confidence: Calibrating Confidence of LLMs for Adaptive Test Time Scaling

Training large language models (LLMs) with reinforcement learning (RL) has significantly advanced their performance on reasoning and question-answering tasks. However, prevailing RL reward designs typically prioritize response correctness, neglecting to incentivize models to express their confidence accurately. This leads to a critical problem: performance gains are often accompanied by poor calibration between confidence and accuracy, misleading models to overconfidently hallucinate when uncertain. To address this limitation, we propose $\textbf{C}$orrectness and $\textbf{C}$onfidence $\textbf{C}$alibration $\textbf{R}$einforcement $\textbf{L}$earning ($\textbf{C3RL}$), a novel RL algorithm integrating correctness, calibration and dataset-informed reference accuracy rewards together. Comprehensive evaluation across 8 text and multimodal datasets demonstrates that C3RL enhances calibration without sacrificing accuracy, outperforming the current state-of-the-art method in both performance and calibration metrics. Utilizing the well-calibrated verbalized confidence from C3RL, we further introduce $\textbf{C}$onfidence-based $\textbf{A}$daptive Test Time $\textbf{S}$caling ($\textbf{CAS}$), an adjustable inference-time strategy that allocates computational resources based on response confidence. Experiments show that CAS surpasses majority voting on both in-domain and out-of-domain datasets while reducing the inference budget by up to 12.33 times. We believe the synergy of C3RL and CAS paves the way for deploying more reliable and resource-efficient LLMs. The code, data and models will be released.