Calibrating LLMs with Semantic-level Reward

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.

Calibration measures whether a model's predicted confidence aligns with its empirical accuracy, and is central to the reliable deployment of large language models (LLMs) in high-stakes domains such as medicine and law. While much recent work focuses on improving LLM calibration, the equally important question of how to evaluate it in realistic settings remains underdeveloped. Open-ended question answering (QA), the most common deployment setting for modern LLMs, is where existing evaluation methods fall short: logit-based metrics need restricted output formats and internal probabilities; verbalized confidence is self-reported and often overconfident; and sampling-based methods rely on task-specific extraction rules without a clear finite-sample target. We introduce Sem-ECE (Semantic-Sampling Expected Calibration Error), a calibration evaluation framework for open-ended QA that samples answers from the model, groups them into semantic classes, and uses the resulting frequencies as confidence. We study two estimators within this framework: Sem$_1$-ECE, the same-sample self-consistency score, and Sem$_2$-ECE, a held-out variant that separates answer selection from confidence evaluation. We prove both are asymptotically unbiased, and further show that they agree on easy questions but diverge on hard ones with Sem$_2$ achieving strictly smaller calibration error, so their gap also serves as a diagnostic for question difficulty. Experiments on three open-ended QA benchmarks across five leading commercial LLMs match our theoretical predictions and show that Sem-ECE outperforms verbalized confidence and existing sampling-based methods, while complementing logit-based evaluation when internal probabilities are unavailable.