On the effectiveness of reward functions in reinforcement learning for confidence calibration of large language models
Authors: Chee Heng Tan, Zhuoyi Lin, Mehul Motani, Wee Sun Lee
Abstract
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 test-time computation with reinforcement learning (RL) has emerged as a reliable path to improve large language models (LLM) reasoning ability. Yet, outcome-based reward often incentivizes models to be overconfident, leading to hallucinations, unreliable confidence-based control, and unnecessary compute allocation. We introduce Reinforcement Learning with Confidence Margin (\textbf{RLCM}), a calibration-aware RL framework that jointly optimizes correctness and confidence reliability via a margin-enhanced process reward over intermediate-budget completions. Rather than aligning confidence to correctness likelihoods, RLCM encourages to widen the confidence margin between correct and incorrect steps within a single reasoning trajectory. Across mathematical, code, logic and science benchmarks, our method substantially improves calibration while maintaining or improving accuracy. We further show that, with calibrated confidence signals, the resulting models enable more efficient conformal risk control and effective confidence-weighted aggregation.
As large language models (LLMs) are deployed in consequential settings such as medical question answering and legal reasoning, the ability to estimate when their outputs are likely to be correct is essential for safe and reliable use, requiring well-calibrated uncertainty. Standard reinforcement learning with verifiable rewards (RLVR) trains models with a binary correctness reward that is indifferent to confidence, providing no penalty for confident but wrong predictions and thereby degrading calibration. Recent work addresses this by training models to produce verbalized confidence scores alongside answers and rewarding agreement with correctness. However, verbalized confidence is calibrated at the token level and thus exhibits inconsistency across textual variations with same semantic meaning. We propose \textbf{Calibration with Semantic Reward (CSR)}, a framework that calibrates language models directly in semantic space without a verbalized confidence interface. CSR combines the correctness reward with a novel semantic calibration reward that encourages exploitation among correct rollouts by promoting semantic agreement, and exploration among incorrect ones by discouraging spurious consistency. Experiments across three model families on HotpotQA (in-distribution) and TriviaQA, MSMARCO, and NQ-Open (out-of-distribution) show that CSR consistently achieves lower ECE and higher AUROC than verbalized-confidence baselines across nearly all settings, reducing ECE by up to 40% and improving AUROC by up to 31% over verbalized-confidence baselines, with calibration behavior generalizing robustly across all four evaluation settings.
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 Correctness and Confidence Calibration Reinforcement Learning (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 Confidence-based Adaptive Test Time Scaling (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.