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

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 .

Bag of Policies for Distributional Deep Exploration

Efficient exploration in complex environments remains a major challenge for reinforcement learning (RL). Compared to previous Thompson sampling-inspired mechanisms that enable temporally extended exploration, i.e., deep exploration, we focus on deep exploration in distributional RL. We develop here a general purpose approach, Bag of Policies (BoP), that can be built on top of any return distribution estimator by maintaining a population of its copies. BoP consists of an ensemble of multiple heads that are updated independently. During training, each episode is controlled by only one of the heads and the collected state-action pairs are used to update all heads off-policy, leading to distinct learning signals for each head which diversify learning and behaviour. To test whether optimistic ensemble method can improve on distributional RL as did on scalar RL, by e.g. Bootstrapped DQN, we implement the BoP approach with a population of distributional actor-critics using Bayesian Distributional Policy Gradients (BDPG). The population thus approximates a posterior distribution of return distributions along with a posterior distribution of policies. Another benefit of building upon BDPG is that it allows to analyze global posterior uncertainty along with local curiosity bonus simultaneously for exploration. As BDPG is already an optimistic method, this pairing helps to investigate if optimism is accumulatable in distributional RL. Overall BoP results in greater robustness and speed during learning as demonstrated by our experimental results on ALE Atari games.