# Offline Bayesian Aleatoric and Epistemic Uncertainty Quantification and Posterior Value Optimisation in Finite-State MDPs

arXiv: https://arxiv.org/abs/2406.02456 · HTML: https://mlsanity.com/paper/2406.02456/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 40 references that are in the map.
- First posted on arXiv 4 Jun 2024.

## Builds on (most cited first, 14 of 14)

- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Stabilizing Off-Policy Q-Learning via Bootstrapping Error Reduction](https://mlsanity.com/paper/1906.00949/) (2019)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [MOPO: Model-based Offline Policy Optimization](https://mlsanity.com/paper/2005.13239/) (2020)
- [MOReL : Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2005.05951/) (2020)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [Uncertainty-Based Offline Reinforcement Learning with Diversified Q-Ensemble](https://mlsanity.com/paper/2110.01548/) (2021)
- [Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach](https://mlsanity.com/paper/1506.02188/) (2015)
- [Estimating Risk and Uncertainty in Deep Reinforcement Learning](https://mlsanity.com/paper/1905.09638/) (2019)
- [Risk-Averse Bayes-Adaptive Reinforcement Learning](https://mlsanity.com/paper/2102.05762/) (2021)
- [Model-Based Offline Reinforcement Learning with Pessimism-Modulated Dynamics Belief](https://mlsanity.com/paper/2210.06692/) (2022)
- [Bayesian Policy Optimization for Model Uncertainty](https://mlsanity.com/paper/1810.01014/) (2018)
- [Optimizing Medical Treatment for Sepsis in Intensive Care: from Reinforcement Learning to Pre-Trial Evaluation](https://mlsanity.com/paper/2003.06474/) (2020)
- [Enabling risk-aware Reinforcement Learning for medical interventions through uncertainty decomposition](https://mlsanity.com/paper/2109.07827/) (2021)

## Abstract (arXiv)

We address the challenge of quantifying Bayesian uncertainty and incorporating it in offline use cases of finite-state Markov Decision Processes (MDPs) with unknown dynamics. Our approach provides a principled method to disentangle epistemic and aleatoric uncertainty, and a novel technique to find policies that optimise Bayesian posterior expected value without relying on strong assumptions about the MDP's posterior distribution. First, we utilise standard Bayesian reinforcement learning methods to capture the posterior uncertainty in MDP parameters based on available data. We then analytically compute the first two moments of the return distribution across posterior samples and apply the law of total variance to disentangle aleatoric and epistemic uncertainties. To find policies that maximise posterior expected value, we leverage the closed-form expression for value as a function of policy. This allows us to propose a stochastic gradient-based approach for solving the problem. We illustrate the uncertainty quantification and Bayesian posterior value optimisation performance of our agent in simple, interpretable gridworlds and validate it through ground-truth evaluations on synthetic MDPs. Finally, we highlight the real-world impact and computational scalability of our method by applying it to the AI Clinician problem, which recommends treatment for patients in intensive care units and has emerged as a key use case of finite-state MDPs with offline data. We discuss the challenges that arise with Bayesian modelling of larger scale MDPs while demonstrating the potential to apply our methods rooted in Bayesian decision theory into the real world. We make our code available at https://github.com/filippovaldettaro/finite-state-mdps .