Uncertainty Estimation in RL

RL: Reinforcement Learning

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24 papers2 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

Oct 16, 2026

Alliance of Stochastic Routing and Reinforcement Fusion for Multi-Model Reasoning

This paper studies dynamic model routing under uncertainty in multimodal settings, where a system must select and potentially compose multiple models to answer a query. Standard reinforcement learning approaches for routing often suffer from premature convergence to suboptimal models due to noisy rewards and insufficient exploration. We propose a unified vision-language framework (VL-Scout) for efficient multimodal and multi-step reasoning with turn-based reinforcement fusion. First, VL-Scout combines Bayesian priors, policy gradient optimization, and sequential decision-making to enable structured exploration and adaptive inference. A context-dependent Dirichlet belief model allows for epistemic uncertainty over model quality and is updated online based on observed rewards and context-specific evidence, enabling Thompson-style exploration while serving as a prior for regularization. Second, a routing policy is trained via a KL-regularized REINFORCE objective by maximizing a reward-weighted evidence lower bound, where the policy acts as an amortized posterior, and the Dirichlet belief serves as a prior. Third, we introduce a fusion policy trained with Group Relative Policy Optimization (GRPO) or Reinforcement Learning with Verifiable Rewards (RLVR), which operates over intermediate model rationales and selects between two actions: CONTINUE or ANSWER, terminating with a generated output. We evaluate VL-Scout on four representative multi-modal benchmarks (MMMU, MMMU-Pro, OKVQA, and RealWorldQA), compared against 11 representative routing and policy optimization baselines. Our method provides consistent performance improvements while reducing premature policy collapse. These results highlight the importance of integrating uncertainty-aware priors with both amortized policy learning and sequential fusion for robust and efficient model selection in discrete action spaces

Selim Furkan Tekin, Ling Liu

Georgia Institute of Technology

Adaptive Model Routing LLM Routing RL for Language Model Reasoning Multimodal Reasoning Bayesian RL Uncertainty Estimation in RL

Sep 28, 2026

Deep Epistemic Value Functions for Optimistic Exploration

Principled exploration in reinforcement learning requires an agent to quantify its epistemic uncertainty and act to resolve it. Uncertainty over the value function provides a natural signal for exploration, yet existing deep approximations remain brittle and perform inconsistently. The central challenge is therefore to scale these ideas robustly. We conduct a systematic empirical study of how epistemic uncertainty is represented, propagated, and optimized in deep epistemic value functions, and uncover distinct failure modes along each of these axes. These findings motivate DEVOTE, a model-free reinforcement learning algorithm that controls how uncertainty generalizes beyond observed data, stabilizes its temporal propagation, and preserves adaptation to the resulting non-stationary exploration objective. Across reward-free exploration and challenging continuous-control tasks, DEVOTE reaches novel states more effectively and achieves higher task return than strong model-free and model-based exploration baselines. These results provide evidence that deep epistemic value functions are a promising path toward scalable, principled exploration.

Leander Diaz-Bone, Marco Bagatella, Jonas Hübotter +1

ETH Zürich, Switzerland · Max Planck Institute for Intelligent Systems, Germany

Value Function Estimation RL Exploration Model-Free RL Reward-Free RL Uncertainty-Aware Exploration Uncertainty Estimation in RL

Aug 31, 2026

BCPPO: Bachelier-Inspired Constrained Proximal Policy Optimization for Tail-Risk-Aware Safe Reinforcement Learning

Expected-cost constraints can still permit rare, high-cost events. Monte Carlo conditional value at risk (CVaR) gradients can be noisy at high confidence, whereas critics that model an outcome distribution add complexity. We propose BCPPO (Bachelier-Inspired Constrained Proximal Policy Optimization), a proximal policy optimization (PPO) method. Separately initialized cost-prediction networks (critics), trained with random sample masks, produce disagreement that marks predictions sensitive to which state-action regions occur in the training data and to critic training. A Bachelier formula for the expected amount above a reference level converts this disagreement into a smooth policy-update penalty. Gradients from this penalty do not alter the critics, so temporal-difference (TD) critic learning is unchanged. A saturation-aware controller adjusts the mean-cost penalty and stops accumulated error from growing while that penalty is clipped. Deployment retains only the policy network. The disagreement penalty is neither a tail-event probability nor a guaranteed error bound, and it provides no safety guarantee. Across 175 runs with shared tasks, costs, budgets, training steps, and evaluation seeds, no comparator attains both higher mean return and lower mean CVaR than BCPPO in any task. On Push1, BCPPO has no lower return and no higher CVaR than every comparator, with at least one strict gain. These results support a practical balance among reward, caution around cost predictions that vary across trained critics, and policy-only deployment.

Dongsheng Hou, Yanqiao Chen, Yuhan Rui

Southern University of Science and Technology

Reinforcement Learning Constrained RL Uncertainty Estimation in RL Proximal Policy Optimization Safe RL Conditional Value-at-Risk

Aug 30, 2026

Uncertainty-Driven Replay Memory for Reinforcement Learning

Uncertainty estimation provides promising capabilities for reinforcement learning (RL) agents. Notably, estimating uncertainty can reduce the training time and enable agents to obtain greater rewards over time by exploiting information related to whether an action would facilitate exploration of portions of an environment that are well-known versus those that are relatively unknown. In this work, we propose a novel formulation of the experience replay buffer commonly used in RL that we call uncertainty-driven replay memory (UDRM), which entails an update scheme for internally stored memories based on uncertainty estimates obtained by an RL model during training. In contrast to existing forms of RL, which typically use temporal difference error or the distribution of transitions to update the replay memory buffer and train RL controllers, our scheme biases the memory buffer to store more uncertain transitions that will improve an RL agent's generalization throughout training. Experimental results demonstrate that our proposed uncertainty-aware replay buffer enables an RL agent to obtain higher rewards during training compared to other existing uncertainty-aware RL frameworks.

Sheeraja Rajakrishnan, Alexander G. Ororbia, Travis Desell +1

Rochester Institute of Technology

Reinforcement Learning Uncertainty Estimation in RL Generalization in RL

Aug 5, 2026

Toward Integrating Adaptive Experience Replay and Online Uncertainty Estimation in Safe Actor-Critic Optimal Control

Safe actor-critic control often treats barrier filtering, uncertainty estimation, and experience replay as separate modules, even though each changes the data used for learning and control. We develop an integrated architecture in which the uncertainty estimate updates the obstacle geometry used by a control barrier function, filter interventions and estimation residuals determine replay priority, and the critic learns from the executed rather than nominal action. We instantiate the architecture on a two-dimensional robot-navigation task with corrupted obstacle measurements and compare six component-matched configurations under common training budgets, random seeds, sensor streams, exploration, and disturbances. Evaluation includes a moderate post-training test, an eleven-level perception-noise sweep, and an exploratory extreme-stress test at multiplier

6.0

. In the extreme test, the integrated configuration recorded no contacts and reached the goal in all five evaluation seeds. Its mean cost was

7.63\pm0.44

and its obstacle-belief root-mean-square error was

3.52\pm0.55

cm. The uncertainty-estimation ablation also recorded no contacts but reached the goal in four of five seeds, with mean cost

8.96\pm2.08

and belief error

11.08\pm1.23

cm. A finite-training bound clarifies replay exposure, and a robust barrier condition states the required estimation-error and feasibility assumptions. The results support coupling estimation, safety filtering, and replay on this benchmark; broader safety and convergence claims require further study.

Mahshad Rastegarmoghaddam, Davoud Nikkhouy, Shima Samadzadeh

Department of Mechanical Engineering, Politecnico di Milano, Milan, Italy

Control Barrier Functions Reinforcement Learning Robot Navigation RL Control Actor-Critic Methods Safe RL+1

Aug 3, 2026

Analytic Planning under Uncertainty with Moment Closure

Effective model-based reinforcement learning in stochastic environments requires planning that accounts for predictive uncertainty. Propagating full state distributions analytically offers a principled way to do this, but has traditionally required restrictive policy or reward structures to remain tractable. Consequently, modern deep reinforcement learning has largely retreated to either stochastic sampling, which introduces significant target variance, or deterministic point estimates that ignore predictive covariance entirely. We investigate whether distribution-aware planning is possible without these constraints. Using a quadratic action-value parameterization, we first reduce the Bellman backup to an expectation over the state-value function alone; the key idea is then a compatibility principle between the predictive transition distribution and the value function class, under which this expectation is analytic in the distribution's moments. We instantiate this principle with a Gaussian transition model paired with a radial-basis value function, yielding a closed-form backup that propagates both predictive mean and covariance. Empirically, our approach reduces target variance and yields well-calibrated predictive uncertainty under stochastic observations in continuous control, providing a principled framework for planning with learned distribution models.

Shishir Sharma, Doina Precup

1McGill University, Montreal, Canada · 2Mila – Quebec Artificial Intelligence Institute, Montreal, Canada

Decision-Making under Uncertainty Model-Based RL Uncertainty Estimation in RL

Jul 22, 2026

Generalized Kalman filter based temporal difference reinforcement learning

In this paper, we present a generalized temporal-difference (TD) reinforcement learning framework based on the theory of conditional expectations. The value and action-value (Q-value) functions are treated as uncertain quantities, and their estimation is formulated as a stochastic inference problem. Unlike classical Kalman-based temporal-difference learning, which relies on linear-Gaussian assumptions, the proposed formulation is derived directly from the conditional expectation framework and naturally extends to nonlinear models and non-Gaussian probability distributions. The proposed method recursively estimates not only the conditional expectation of the value function but also its second probabilistic moment, thereby quantifying the uncertainty associated with the learned value function throughout the learning process. To obtain a computationally tractable algorithm, the stochastic problem is discretized using either polynomial chaos expansions or ensemble-based approximations, providing efficient representations of the underlying random variables. The proposed framework is demonstrated on two optimal control problems: a linear mass--spring--damper system and a nonlinear heat conduction problem in a closed cavity. The numerical examples illustrate the capability of the proposed method to accurately estimate both the value function and its associated uncertainty, while extending classical Kalman-based temporal-difference learning to a broader class of stochastic systems.

Vasos Arnaoutis, Eric Lutters, Bojana Rosić

Applied Mechanics and Data Analysis, Faculty of Engineering Technology, University of Twente, Enschede, the Netherlands · Department of Design, Production and Management, Faculty of Engineering Technology, University of Twente, Enschede, the Netherlands · Digital Engineering research group, Faculty of Mechanical and Industrial Engineering, Vienna University of Technology, Vienna, Austria

RL Control Reinforcement Learning Value Function Estimation Temporal-Difference Learning Uncertainty Estimation in RL

Jul 21, 2026

Conservative Query and Adaptive Regularization for Offline RL Under Uncertainty Estimation

Offline reinforcement learning (RL) aims to learn an effective policy from a static dataset, but its performance is fundamentally limited by dataset coverage. Action preference queries leverage expert feedback without additional environment interaction, enabling policy improvement during offline training. However, existing methods still face two key challenges: selecting informative preference queries and effectively exploiting the collected feedback. Current approaches typically rely only on the distance between policy actions and dataset actions for query selection, while enforcing fixed constraints that keep the policy close to queried preferences. Such strategies often lead to unstable policy updates and integrate poorly with value regularization. To address these limitations, we propose Conservative Query and Adaptive Regularization under Uncertainty Estimation, a lightweight framework that jointly improves preference querying and preference exploitation. Specifically, we employ a Morse network to estimate the uncertainty of policy actions with respect to the offline dataset. Based on this uncertainty, we introduce a conservative query strategy that selectively queries actions near the dataset to preserve Bellman-update stability, together with an uncertainty-aware adaptive regularization scheme that dynamically adjusts data-level constraints during policy optimization. We integrate our framework with CQL and evaluate it extensively on the D4RL benchmark. Experimental results demonstrate superior or competitive performance across a wide range of tasks.

Li-Rong Zhou, Qin-Wen Luo, Sheng-Jun Huang

Nanjing University of Aeronautics and Astronautics, Nanjing, China

Reinforcement Learning Offline RL Uncertainty Estimation in RL Preference-Based RL

Jul 20, 2026

Information-Based Exploration via Random Features for Reinforcement Learning

Representation learning has enabled classical exploration strategies to be extended to deep Reinforcement Learning (RL), but often makes algorithms more complex and theoretical guarantees harder to establish. We introduce Random Feature Information Gain (RFIG), grounded in Bayesian kernel methods theory, which uses random Fourier features to approximate information gain and compute exploration bonuses in non-countable spaces. We provide error bounds on information gain approximation and avoid the black-box aspects of neural network-based uncertainty estimation, for optimism-based exploration. We present practical details that make RFIG scalable to deep RL scenarios, enabling smooth integration into standard deep RL algorithms. Experimental evaluation across diverse control and navigation tasks demonstrates that RFIG achieves competitive performance with well-established deep exploration methods while offering superior theoretical interpretation.

Waris Radji, Odalric-Ambrym Maillard

Univ. Lille, Inria, CNRS, Centrale Lille, UMR 9189-CRIStAL, F-59000 Lille, France

RL Exploration Uncertainty-Aware Exploration Uncertainty Estimation in RL

Jul 3, 2026

Trading Confidence: Comprehensive Uncertainty Estimation in Algorithmic Trading

Reinforcement Learning (RL) has emerged as a powerful approach in financial trading, enabling agents to learn optimal strategies through direct market interaction. However, financial markets are highly uncertain, with price fluctuations driven by stochastic volatility, model limitations, and regime shifts. Traditional RL models struggle in dynamic environments, often failing to adapt to sudden market disruptions, leading to suboptimal trading decisions. To address this challenge, we propose an uncertainty-aware RL framework that integrates distributional, epistemic, and aleatoric uncertainty estimations. Our approach enhances uncertainty estimation using SHAP-weighted reconstruction uncertainty, MC Dropout, and an LSTM-based technical indicator consensus mechanism. Experimental results on five major U.S. stock indices demonstrate that RL agents equipped with uncertainty estimation significantly outperform traditional models in return and risk management. This study advances uncertainty estimation in RL-based financial trading, with future research extending its application to other asset classes and alternative RL architectures for greater adaptability.

Lin Li, Li Rong Wang, Hsuan Fu +1

Nanyang Technological University 50 Nanyang Avenue, Singapore · Nanyang Technological University Centre for Frontier AI Research, A*STAR 50 Nanyang Avenue, Singapore · Laval University Quebec, Canada

Reinforcement Learning Uncertainty Quantification Uncertainty Estimation in RL Aleatoric Uncertainty Algorithmic Trading Epistemic Uncertainty

Jun 17, 2026

UBP2: Uncertainty-Balanced Preference Planning for Efficient Preference-based Reinforcement Learning

Preference-based RL provides an approach to learning reward models from pairwise comparisons of behaviors, bypassing the need for explicit reward design. However, existing methods typically rely on passive data collection and suffer from poor sample efficiency, especially during the early stages of learning. We introduce a model-based approach that actively directs exploration by jointly reasoning over uncertainties in the reward, dynamics, and value functions. Our method, Uncertainty-Balanced Preference Planning (UBP2), uses ensembles of reward, dynamics, and value function models to evaluate candidate trajectories according to a unified score that combines expected reward, terminal value, and epistemic uncertainty. Planning under this objective yields an explicit tradeoff between exploitation and information acquisition without requiring ad hoc exploration heuristics. Under standard regularity assumptions, we establish sublinear regret guarantees for both finite-horizon and infinite-horizon settings. Empirically, experiments on the Meta-World benchmark show UBP2 achieves substantially higher sample efficiency than model-free preference-based methods and non-optimistic model-based baselines.

Mohamed Nabail, Leo Kaixuan Cheng, Jingmin Wang +1

Learning, Embodied Autonomy, and Forecasting (LEAF) Lab, University of Toronto

Preference-Based RL Model-Based RL Pairwise Preference Evaluation RL Exploration Model-Based Planning Sample-Efficient RL+2

Jun 8, 2026

A Unifying Lens on Reward Uncertainty in RLHF

Reinforcement learning from human feedback (RLHF) is bottlenecked by reward hacking, where the policy exploits errors in a proxy reward model (RM) and produces high RM scores without genuine quality gains. A natural mitigation is pessimism: lowering rewards in regions where the RM is uncertain. However, standard scalar RMs provide no principled notion of uncertainty. We argue that the right object is a distributional reward model

p(r\mid x,y)

. Under either a Bayesian inference or a KL-distributionally robust optimization (KL-DRO) lens, the KL-regularized RLHF objective admits a closed-form effective reward

\tilde r(x,y) = \pmβ\log\mathbb{E}_p[e^{\pm r/β}]

. The pessimistic branch unifies the prior heuristics for RM ensemble aggregation: mean aggregation, worst-case optimization (WCO), and uncertainty-weighted optimization (UWO) all emerge as limits or truncations of this single expression. This also clarifies the implicit assumptions of each existing rule.

Ely Hahami, Yoel Zimmermann, Ray Zhou +1

Harvard College, Harvard University, Cambridge, MA, USA · John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

Reward Modeling KL-Regularized RL Distributionally Robust RL RL from Human Feedback Uncertainty Estimation in RL

Jun 5, 2026

Exploring Agentic Tool-Calling Decisions via Uncertainty-Aligned Reinforcement Learning

Large language model (LLM)-based agents often make suboptimal tool-use decisions, including unsupported tool invocation and hallucinated direct responses, which may accumulate errors throughout multi-step interactions. Existing approaches mainly improve these behaviors through inference-time correction or coarse-grained reward signals based on decision outcomes and structured checklists, leaving the uncertainty characteristics of agent decisions underexplored. We observe that decision-oriented reinforcement learning tends to weaken the uncertainty separation between correct and incorrect actions, resulting in overconfident mistakes and weaker exploration signals. Therefore, we propose TRUST, which incorporates uncertainty quantification into reward design as a repulsive force for maintaining uncertainty separation, and labels lightweight key-turn annotations for unified post-training of multi-turn trajectories. Experimental results across diverse tool-use benchmarks show that TRUST consistently enhances both decision quality and agent performance while maintaining more reliable uncertainty estimates during optimization.

Yijin Zhou, Linqian Zeng, Xiaoya Lu +4

Shanghai Jiao Tong University, China · Shanghai Artificial Intelligence Laboratory, China · Shanghai Innovation Institute, China

Reinforcement Learning LLM Uncertainty Estimation LLM Agent Reliability RL for Tool Use Uncertainty Estimation in RL

May 31, 2026

All Models are Wrong, Knowing Where is Useful: On Model Uncertainty in Reinforcement Learning

Model-based reinforcement learning (MBRL) infers information about the environment from a learned dynamics model and bears the potential to address open problems such as data efficient and safe learning in robotics. However, inaccuracies of the learned dynamics model are typically exploited by the agent, substantially hampering the capabilities of MBRL methods. We present a framework for dealing with inaccuracies of probabilistic models through targeted handling of uncertainty that effectively mitigates model exploitation. We present recent successes in learning directly on hardware and safe exploration, and discuss future directions for uncertainty-aware MBRL.

Bernd Frauenknecht, Devdutt Subhasish, Artur Eisele +2

Institute for Data Science in Mechanical Engineering, RWTH Aachen University, 52062 Aachen, Germany

Robotic RL Safe RL Model-Based RL Uncertainty Estimation in RL

May 29, 2026

Efficient and Uncertainty-Aware Diffusion Framework for Offline-to-Online Reinforcement Learning

Offline-to-Online Reinforcement Learning (O2O-RL) leverages an offline, pre-trained policy to minimize costly online interactions. Although data-efficient, O2O-RL is susceptible to shifts between offline and online distributions. Existing work aims to mitigate the harm of this shift by finetuning the policy on trajectory data sampled from a diffusion model. Inspired by this line of work, we propose DUAL: an efficient Diffusion Uncertainty-Aware framework for offline-to-online reinforcement Learning. DUAL utilizes the prior knowledge of the diffusion model to distill a fast-sampling diffusion actor policy and transition model in the offline phase. DUAL also employs a Laplace approximation and distance transition-state-shift detection, thereby using uncertainty quantification to improve exploration versus exploitation in the online phase. We formally show that our actor loss with the Laplace approximation provides a proxy for a principled estimate of epistemic uncertainty. Empirically, DUAL improves the online expected return over O2O-RL baselines across multiple settings and environments.

Ha Manh Bui, Metod Jazbec, Eric Nalisnick +1

Department of Computer Science, Johns Hopkins University, Baltimore, MD, U.S.A. · AMLab, University of Amsterdam, Amsterdam, Netherlands

Reinforcement Learning Diffusion Policy Uncertainty Estimation in RL Offline-To-Online RL Model-Based RL

May 28, 2026

UNIQ: Conformal Calibration for Adaptive Conservatism in Offline Reinforcement Learning

Offline reinforcement learning requires careful conservatism to mitigate distribution shift, yet most existing methods apply a fixed penalty uniformly across all states regardless of local data coverage. We present UNIQ (Uncertainty-Informed Quantile), an offline RL method that introduces state-adaptive conservatism through conformally calibrated uncertainty estimation. Built on the Implicit Q-Learning (IQL) backbone, UNIQ trains a multi-expectile value ensemble, computes distribution-free uncertainty estimates using split conformal prediction, and maps the resulting signal to a state-dependent expectile that relaxes conservatism in well-covered regions while strengthening it in uncertain regions near the data frontier. On D4RL MuJoCo benchmarks, UNIQ consistently improves over IQL, with the largest gains observed on Walker2d and replay-heavy tasks. At the same time, UNIQ operates at near-IQL memory cost (approximately 250 MB peak VRAM), providing roughly a 10x reduction compared to EDAC. Rather than pursuing overall state-of-the-art performance, we position UNIQ as a practical mechanism contribution that improves the performance-efficiency trade-off in offline reinforcement learning.

Aditya Upadhyay

IIIT Delhi

Conservative RL Offline RL Uncertainty Estimation in RL

Apr 29, 2026

Uncertainty-Aware Reward Discounting for Mitigating Reward Hacking

Reinforcement learning from human feedback (RLHF) systems face a compounding alignment challenge: not only are learned reward models uncertain about unseen state-action pairs, but the human preference annotations they are trained on are themselves inconsistent, context-dependent, and noisy. Existing approaches address these uncertainty sources in isolation - epistemic uncertainty is used to guide exploration, while preference uncertainty is absorbed during reward model training but discarded during policy optimization. We introduce Uncertainty-Aware Reward Discounting (UARD), a principled framework that jointly models epistemic uncertainty in value estimation via ensemble disagreement and aleatoric uncertainty in human preference annotations via annotator variability, combining these signals through a confidence-adjusted Reliability Filter that adaptively modulates reward weighting during policy optimization. We prove that this dynamic discounting preserves the contraction property of the Bellman operator, guaranteeing convergence to a unique fixed point, and provide an information-theoretic justification grounded in the Information Bottleneck principle. Empirically, UARD reduces reward hacking incidents by up to 93.6% across discrete decision-making and continuous control benchmarks (MuJoCo) compared to nine baselines including DQN, Ensemble-DQN, CQL, CPO, TRPO, SAC, EDAC, SUNRISE, and PPO, while maintaining competitive task performance on well-specified rewards. Under annotation noise ranging from 10% to 30% Gaussian perturbation, UARD retains near-zero safety violations compared to baselines' near-linear degradation. These results demonstrate that treating uncertainty as an active component of the optimization objective - rather than a passive diagnostic signal - provides a principled pathway toward more reliable and aligned RL systems.

Disha Singha

Reward Hacking Reinforcement Learning Uncertainty Estimation in RL Aleatoric Uncertainty Safe RL RL from Human Feedback

Apr 28, 2026

Biased Dreams: Limitations to Epistemic Uncertainty Quantification in Latent Space Models

Model-Based Reinforcement Learning distinguishes between physical dynamics models operating on proprioceptive inputs and latent dynamics models operating on high-dimensional image observations. A prominent latent approach is the Recurrent State Space Model used in the Dreamer family. While epistemic uncertainty quantification to inform exploration and mitigate model exploitation is well established for physical dynamics models, its transfer to latent dynamics models has received limited scrutiny. We empirically demonstrate that latent transitions are biased toward well-represented regions of latent space, exhibiting an attractor behavior that can deviate from true environment dynamics. As a result, discrepancies in environment dynamics may not manifest in latent space, undermining the reliability of epistemic uncertainty estimates. Because these attractors often lie in high-reward regions, latent rollouts systematically overestimate predicted rewards. Our findings highlight key limitations of epistemic uncertainty estimation in latent dynamics models and motivate more critical evaluation of this method.

Julia Berger, Bernd Frauenknecht, Sebastian Trimpe +1

1RWTH Aachen University

Uncertainty Quantification Latent Dynamics Modeling Latent World Models Model-Based RL Epistemic Uncertainty Uncertainty Estimation in RL

Apr 8, 2026

Epistemic Robust Offline Reinforcement Learning

Offline reinforcement learning learns policies from fixed datasets without further environment interaction. A key challenge in this setting is epistemic uncertainty, arising from limited or biased data coverage, particularly when the behavior policy systematically avoids certain actions. This can lead to inaccurate value estimates and unreliable generalization. Ensemble-based methods like SAC-N mitigate this by conservatively estimating Q-values using the ensemble minimum, but they require large ensembles and often conflate epistemic with aleatoric uncertainty. To address these limitations, we propose a unified and generalizable framework that replaces discrete ensembles with compact uncertainty sets over Q-values. %We further introduce an Epinet based model that directly shapes the uncertainty sets to optimize the cumulative reward under the robust Bellman objective without relying on ensembles. We also introduce a benchmark for evaluating offline RL algorithms under risk-sensitive behavior policies, and demonstrate that our method achieves improved robustness and generalization over ensemble-based baselines across both tabular and continuous state domains.

Abhilash Reddy Chenreddy, Erick Delage

GERAD, Department of Decision Sciences, HEC Montréal, Montréal, Québec H3T 2A7, Canada

Uncertainty Estimation in RL Offline RL Robust RL Epistemic Uncertainty Risk-Sensitive RL

Apr 2, 2026

When to ASK: Uncertainty-Gated Language Assistance for Reinforcement Learning

Reinforcement learning (RL) agents often struggle with out-of-distribution (OOD) scenarios, leading to high uncertainty and random behavior. While language models (LMs) contain valuable world knowledge, larger ones incur high computational costs, hindering real-time use, and exhibit limitations in autonomous planning. We introduce Adaptive Safety through Knowledge (ASK), which combines smaller LMs with trained RL policies to enhance OOD generalization without retraining. ASK employs Monte Carlo Dropout to assess uncertainty and queries the LM for action suggestions only when uncertainty exceeds a set threshold. This selective use preserves the efficiency of existing policies while leveraging the language model's reasoning in uncertain situations. In experiments on the FrozenLake environment, ASK shows no improvement in-domain, but demonstrates robust navigation in transfer tasks, achieving a reward of 0.95. Our findings indicate that effective neuro-symbolic integration requires careful orchestration rather than simple combination, highlighting the need for sufficient model scale and effective hybridization mechanisms for successful OOD generalization.

Juarez Monteiro, Nathan Gavenski, Gianlucca Zuin +1

Kunumi Institute Belo Horizonte, MG, Brazil · King’s College London London, England, UK

Uncertainty Estimation in RL Reinforcement Learning LLM-Guided RL Generalization in RL Robust RL

Mar 27, 2026

Online Statistical Inference of Constant Sample-averaged Q-Learning

Reinforcement learning algorithms have been widely used for decision-making tasks in various domains. However, the performance of these algorithms can be impacted by high variance and instability, particularly in environments with noise or sparse rewards. In this paper, we propose a framework to perform statistical online inference for a sample-averaged Q-learning approach. We adapt the functional central limit theorem (FCLT) for the modified algorithm under some general conditions and then construct confidence intervals for the Q-values via random scaling. We conduct experiments to perform inference on both the modified approach and its traditional counterpart, Q-learning using random scaling and report their coverage rates and confidence interval widths on two problems: a grid world problem as a simple toy example and a dynamic resource-matching problem as a real-world example for comparison between the two solution approaches.

Saunak Kumar Panda, Tong Li, Ruiqi Liu +1

Department of Industrial Engineering, University of Houston · Department of Mathematics and Statistics, Texas Tech University

Reinforcement Learning Q-Learning Uncertainty Estimation in RL Confidence Region Estimation

Mar 19, 2026

RE-SAC: Disentangling aleatoric and epistemic risks in bus fleet control: A stable and robust ensemble DRL approach

Bus holding control is challenging due to stochastic traffic and passenger demand. While deep reinforcement learning (DRL) shows promise, standard actor-critic algorithms suffer from Q-value instability in volatile environments. A key source of this instability is the conflation of two distinct uncertainties: aleatoric uncertainty (irreducible noise) and epistemic uncertainty (data insufficiency). Treating these as a single risk leads to value underestimation in noisy states, causing catastrophic policy collapse. We propose a robust ensemble soft actor-critic (RE-SAC) framework to explicitly disentangle these uncertainties. RE-SAC applies Integral Probability Metric (IPM)-based weight regularization to the critic network to hedge against aleatoric risk, providing a smooth analytical lower bound for the robust Bellman operator without expensive inner-loop perturbations. To address epistemic risk, a diversified Q-ensemble penalizes overconfident value estimates in sparsely covered regions. This dual mechanism prevents the ensemble variance from misidentifying noise as a data gap, a failure mode identified in our ablation study. Experiments in a realistic bidirectional bus corridor simulation demonstrate that RE-SAC achieves the highest cumulative reward (approx. -0.4e6) compared to vanilla SAC (-0.55e6). Mahalanobis rareness analysis confirms that RE-SAC reduces Oracle Q-value estimation error by up to 62% in rare out-of-distribution states (MAE of 1647 vs. 4343), demonstrating superior robustness under high traffic variability.

Yifan Zhang, Liang Zheng, Qifan Zhang

Central South University

Uncertainty Estimation in RL Reinforcement Learning Robust RL Soft Actor-Critic Distributionally Robust RL

Feb 23, 2026

Uncertainty-Aware Rank-One MIMO Q Network Framework for Accelerated Offline Reinforcement Learning

Offline reinforcement learning (RL) has garnered significant interest due to its safe and easily scalable paradigm. However, training under this paradigm presents its own challenge: the extrapolation error stemming from out-of-distribution (OOD) data. Existing methodologies have endeavored to address this issue through means like penalizing OOD Q-values or imposing similarity constraints on the learned policy and the behavior policy. Nonetheless, these approaches are often beset by limitations such as being overly conservative in utilizing OOD data, imprecise OOD data characterization, and significant computational overhead. To address these challenges, this paper introduces an Uncertainty-Aware Rank-One Multi-Input Multi-Output (MIMO) Q Network framework. The framework aims to enhance Offline Reinforcement Learning by fully leveraging the potential of OOD data while still ensuring efficiency in the learning process. Specifically, the framework quantifies data uncertainty and harnesses it in the training losses, aiming to train a policy that maximizes the lower confidence bound of the corresponding Q-function. Furthermore, a Rank-One MIMO architecture is introduced to model the uncertainty-aware Q-function, \TP{offering the same ability for uncertainty quantification as an ensemble of networks but with a cost nearly equivalent to that of a single network}. Consequently, this framework strikes a harmonious balance between precision, speed, and memory efficiency, culminating in improved overall performance. Extensive experimentation on the D4RL benchmark demonstrates that the framework attains state-of-the-art performance while remaining computationally efficient. By incorporating the concept of uncertainty quantification, our framework offers a promising avenue to alleviate extrapolation errors and enhance the efficiency of offline RL.

Thanh Nguyen, Tung Luu, Tri Ton +2

School of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea · Department of Artificial Intelligence, Korea University, Seoul 02841, Republic of Korea

Uncertainty Estimation in RL Offline RL

Oct 21, 2024

Statistical Inference for Policy Evaluation with Temporal Difference Learning

We investigate the statistical properties of Temporal Difference (TD) learning with Polyak-Ruppert averaging, arguably one of the most widely used algorithms in reinforcement learning, for the task of estimating the parameters of the optimal linear approximation to the value function. Assuming independent samples, we make three theoretical contributions that improve upon the current state-of-the-art results: (i) we establish refined high-dimensional Berry-Esseen bounds over the class of convex sets, achieving faster rates than the best known results, and (ii) we propose and analyze a novel, computationally efficient online plug-in estimator of the asymptotic covariance matrix; (iii) we derive sharper high probability convergence guarantees that depend explicitly on the asymptotic variance and hold under weaker conditions than those adopted in the literature. These results enable the construction of confidence regions and simultaneous confidence intervals for the linear parameters of the value function approximation, with guaranteed finite-sample coverage. We demonstrate the applicability of our theoretical findings through numerical experiments.

Weichen Wu, Gen Li, Yuting Wei +1

The Voleon Group, New York, NY, USA · Department of Statistics, The Chinese University of Hong Kong, Hong Kong SAR. · Department of Statistics and Data Science, The Wharton School, University of Pennsylvania, Philadelphia, PA, USA. +1

Parameter Estimation Confidence Region Estimation Value Function Estimation Stochastic Approximation Policy Evaluation Temporal-Difference Learning+3