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

TL;DR

This paper introduces a Bayesian approach to quantify and disentangle aleatoric and epistemic uncertainties in finite-state MDPs, and proposes a method to optimize policies based on posterior expected value, demonstrated on gridworlds and the AI Clinician problem.

Contribution

It presents a novel technique for uncertainty quantification and policy optimization in offline finite-state MDPs without strong distributional assumptions.

Findings

Effective uncertainty disentanglement in simple MDPs

Successful policy optimization using closed-form value expressions

Scalable approach demonstrated on real-world ICU treatment data

Abstract

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 .