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The Bellman equation and its continuous-time counterpart, the Hamilton-Jacobi-Bellman (HJB) equation, serve as necessary conditions for optimality in reinforcement learning and optimal control. While the value function is known to be the…

Machine Learning · Computer Science 2025-03-07 Haoxiang You , Lekan Molu , Ian Abraham

Offline reinforcement learning (RL) enables data-efficient and safe policy learning without online exploration, but its performance often degrades under distribution shift. The learned policy may visit out-of-distribution state-action pairs…

Artificial Intelligence · Computer Science 2026-03-17 Hongqiang Lin , Zhenghui Fu , Weihao Tang , Pengfei Wang , Yiding Sun , Qixian Huang , Dongxu Zhang

Proper scoring rules evaluate the quality of probabilistic predictions, playing an essential role in the pursuit of accurate and well-calibrated models. Every proper score decomposes into two fundamental components -- proper calibration…

Machine Learning · Computer Science 2023-12-15 Teodora Popordanoska , Sebastian G. Gruber , Aleksei Tiulpin , Florian Buettner , Matthew B. Blaschko

We propose a refinement of temporal-difference learning that enforces first-order Bellman consistency: the learned value function is trained to match not only the Bellman targets in value but also their derivatives with respect to states…

Machine Learning · Computer Science 2025-11-25 Fabian Schramm , Nicolas Perrin-Gilbert , Justin Carpentier

In this paper, we consider the uncertainty quantification problem for regression models. Specifically, we consider an individual calibration objective for characterizing the quantiles of the prediction model. While such an objective is…

Machine Learning · Computer Science 2023-10-27 Shang Liu , Zhongze Cai , Xiaocheng Li

Prediction error is critical to assessing the performance of statistical methods and selecting statistical models. We propose the cross-validation and approximated cross-validation methods for estimating prediction error under a broad…

Statistics Theory · Mathematics 2007-06-13 Jianqing Fan , Chunming Zhang

Calibrating blackbox machine learning models to achieve risk control is crucial to ensure reliable decision-making. A rich line of literature has been studying how to calibrate a model so that its predictions satisfy explicit finite-sample…

Machine Learning · Statistics 2025-06-02 Victor Li , Baiting Chen , Yuzhen Mao , Qi Lei , Zhun Deng

Offline reinforcement learning (RL) learns effective policies from pre-collected datasets, offering a practical solution for applications where online interactions are risky or costly. Model-based approaches are particularly advantageous…

Machine Learning · Computer Science 2026-05-14 Xuyang Chen , Keyu Yan , Guojian Wang , Lin Zhao

We present a distributional approach to theoretical analyses of reinforcement learning algorithms for constant step-sizes. We demonstrate its effectiveness by presenting simple and unified proofs of convergence for a variety of…

Machine Learning · Computer Science 2020-03-30 Philip Amortila , Doina Precup , Prakash Panangaden , Marc G. Bellemare

Sample-efficient offline reinforcement learning (RL) with linear function approximation has recently been studied extensively. Much of prior work has yielded the minimax-optimal bound of $\tilde{\mathcal{O}}(\frac{1}{\sqrt{K}})$, with $K$…

Machine Learning · Computer Science 2023-01-30 Thanh Nguyen-Tang , Ming Yin , Sunil Gupta , Svetha Venkatesh , Raman Arora

Policy evaluation is a fundamental component of the development and deployment pipeline for robotic policies. In modern manipulation systems, this problem is particularly challenging: rewards are often sparse, task progression of evaluation…

Robotics · Computer Science 2026-05-13 Hao Wang , Joshua Bowden , Colton Crosby , Somil Bansal

Calibrated predictions are useful because their numerical values can be interpreted as probabilities. Calibration errors are therefore widely used to evaluate, compare, and tune probabilistic predictors. Recently, Haghtalab et al. (2024)…

Machine Learning · Computer Science 2026-05-19 Yuxuan Lu , Yifan Wu , Jason Hartline , Lunjia Hu

The adoption of deep learning across various fields has been extensive, yet there is a lack of focus on evaluating the performance of deep learning pipelines. Typically, with the increased use of large datasets and complex models, the…

Machine Learning · Computer Science 2024-05-21 Yewen Fan , Nian Si , Xiangchen Song , Kun Zhang

Accurate uncertainty quantification is critical for reliable predictive modeling. Existing methods typically address either aleatoric uncertainty due to measurement noise or epistemic uncertainty resulting from limited data, but not both in…

Machine Learning · Statistics 2026-03-04 Ilia Azizi , Juraj Bodik , Jakob Heiss , Bin Yu

We study a sequential binary prediction setting where the forecaster is evaluated in terms of the calibration distance, which is defined as the $L_1$ distance between the predicted values and the set of predictions that are perfectly…

Machine Learning · Computer Science 2024-05-28 Mingda Qiao , Letian Zheng

While reinforcement learning (RL) promises to revolutionize the control of complex nonlinear robotic systems, a profound gap persists between the heuristic success of model-free off-policy deep RL and the underlying theory, which remains…

Machine Learning · Computer Science 2026-05-08 Manuel Haussmann , Mustafa Mert Çelikok , Melih Kandemir

Mainstream approximate action-value iteration reinforcement learning (RL) algorithms suffer from overestimation bias, leading to suboptimal policies in high-variance stochastic environments. Quantile-based action-value iteration methods…

Machine Learning · Computer Science 2025-12-09 Clinton Enwerem , Aniruddh G. Puranic , John S. Baras , Calin Belta

While pre-trained language models (PLMs) have become a de-facto standard promoting the accuracy of text classification tasks, recent studies find that PLMs often predict over-confidently. Although various calibration methods have been…

Computation and Language · Computer Science 2023-02-15 Jaeyoung Kim , Dongbin Na , Sungchul Choi , Sungbin Lim

Large Language Models (LLMs) have recently improved mathematical reasoning through Reinforcement Learning with Verifiable Reward (RLVR). However, existing RLVR algorithms require large query budgets, making annotation costly. We investigate…

Artificial Intelligence · Computer Science 2026-02-02 Hao Yi , Yulan Hu , Xin Li , Sheng Ouyang , Lizhong Ding , Yong Liu

We introduce and study the problem of calibrating conditional risk, which involves estimating the expected loss of a prediction model conditional on input features. We analyze this problem in both classification and regression settings and…

Machine Learning · Computer Science 2026-04-23 Andrey Vasilyev , Yikai Wang , Xiaocheng Li , Guanting Chen