# Bellman Calibration for V-Learning in Offline Reinforcement Learning

arXiv: https://arxiv.org/abs/2512.23694 · HTML: https://mlsanity.com/paper/2512.23694/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Offline RL algorithms, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 54 of its 108 references that are in the map.
- First posted on arXiv 29 Dec 2025.

## Placed in

- Offline RL and imitation learning from data / [Offline RL algorithms](https://mlsanity.com/offlinerl/offline-rl-algorithms/)

## Builds on (most cited first, 30 of 54)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Off-Policy Deep Reinforcement Learning without Exploration](https://mlsanity.com/paper/1812.02900/) (2018)
- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [AWAC: Accelerating Online Reinforcement Learning with Offline Datasets](https://mlsanity.com/paper/2006.09359/) (2020)
- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [Uncertainty-Based Offline Reinforcement Learning with Diversified Q-Ensemble](https://mlsanity.com/paper/2110.01548/) (2021)
- [Information-Theoretic Considerations in Batch Reinforcement Learning](https://mlsanity.com/paper/1905.00360/) (2019)
- [DualDICE: Behavior-Agnostic Estimation of Discounted Stationary Distribution Corrections](https://mlsanity.com/paper/1906.04733/) (2019)
- [Bellman Eluder Dimension: New Rich Classes of RL Problems, and Sample-Efficient Algorithms](https://mlsanity.com/paper/2102.00815/) (2021)
- [A Theoretical Analysis of Deep Q-Learning](https://mlsanity.com/paper/1901.00137/) (2019)
- [Offline-to-Online Reinforcement Learning via Balanced Replay and Pessimistic Q-Ensemble](https://mlsanity.com/paper/2107.00591/) (2021)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Minimax Weight and Q-Function Learning for Off-Policy Evaluation](https://mlsanity.com/paper/1910.12809/) (2019)
- [Safe Policy Improvement with Baseline Bootstrapping](https://mlsanity.com/paper/1712.06924/) (2017)
- [GenDICE: Generalized Offline Estimation of Stationary Values](https://mlsanity.com/paper/2002.09072/) (2020)
- [OptiDICE: Offline Policy Optimization via Stationary Distribution Correction Estimation](https://mlsanity.com/paper/2106.10783/) (2021)
- [Double Reinforcement Learning for Efficient Off-Policy Evaluation in Markov Decision Processes](https://mlsanity.com/paper/1908.08526/) (2019)
- [Batch Value-function Approximation with Only Realizability](https://mlsanity.com/paper/2008.04990/) (2020)
- [The Role of Coverage in Online Reinforcement Learning](https://mlsanity.com/paper/2210.04157/) (2022)
- [Distribution-free binary classification: prediction sets, confidence intervals and calibration](https://mlsanity.com/paper/2006.10564/) (2020)
- [Efficiently Breaking the Curse of Horizon in Off-Policy Evaluation with Double Reinforcement Learning](https://mlsanity.com/paper/1909.05850/) (2019)
- [Offline Reinforcement Learning: Fundamental Barriers for Value Function Approximation](https://mlsanity.com/paper/2111.10919/) (2021)
- [Finite Sample Analysis of Minimax Offline Reinforcement Learning: Completeness, Fast Rates and First-Order Efficiency](https://mlsanity.com/paper/2102.02981/) (2021)
- [Distribution-free calibration guarantees for histogram binning without sample splitting](https://mlsanity.com/paper/2105.04656/) (2021)
- [An Exponential Lower Bound for Linearly-Realizable MDPs with Constant Suboptimality Gap](https://mlsanity.com/paper/2103.12690/) (2021)
- [Calibrated Model-Based Deep Reinforcement Learning](https://mlsanity.com/paper/1906.08312/) (2019)

## Built on by (most cited first, 3 of 3)

- [Calibeating Prediction-Powered Inference](https://mlsanity.com/paper/2604.21260/) (2026)
- [Temporal Difference Calibration in Sequential Tasks: Application to Vision-Language-Action Models](https://mlsanity.com/paper/2604.20472/) (2026)
- [Bellman Calibration for Marginalized Importance Weighting in Offline Reinforcement Learning](https://mlsanity.com/paper/2608.24858/) (2026)

## Abstract (arXiv)

Reliable long-horizon value prediction is difficult in offline reinforcement learning because fitted value methods combine bootstrapping, function approximation, and distribution shift, while standard guarantees often require Bellman completeness or realizability. We introduce Bellman calibration, a weak reliability criterion requiring that states assigned similar predicted values have average Bellman targets that agree with those predictions. This criterion yields a scalar calibration error for diagnosing systematic numerical miscalibration, which we estimate from off-policy data using doubly robust Bellman target estimates. We then propose Iterated Bellman Calibration, a model-agnostic post-hoc procedure that recalibrates any learned value predictor by fitting a one-dimensional map of its original prediction, with histogram and isotonic variants. We prove finite-sample guarantees showing that Bellman calibration error is controlled at one-dimensional nonparametric rates without Bellman completeness or value-function realizability. Our value-error bounds separate statistical estimation, finite-iteration, and approximation errors, clarifying when calibration improves value prediction and when its gains are limited by the information in the original predictor or insufficient coverage.