Bayesian Neural Networks via Dirichlet Process Priors on the Data-Generating Distribution for Randomized Value Functions in Deep Reinforcement Learning

Bayesian neural networks (BNNs) offer a principled framework for quantifying epistemic uncertainty. However, standard weight-space priors yield complex, high-dimensional neural network posteriors that are computationally prohibitive to sample from, and popular approximate inference schemes often fail to capture epistemic uncertainty effectively—a failure mode particularly acute in reinforcement learning (RL) \citep{osband2018randomized}. To resolve this challenge, we introduce a new class of BNNs that quantify uncertainty by placing Bayesian nonparametric Dirichlet Process (DP) priors directly on the underlying data-generating distribution rather than on network parameters. Building on this foundation, we develop DP-DQN, a reinforcement learning algorithm that leverages DP-BNNs to maintain posterior distributions over value functions and perform efficient Thompson sampling. By grounding randomized value functions in Bayesian nonparametrics, DP-DQN unifies data-driven posterior reweighting (via the Bayesian Bootstrap) with generative prior hypotheses injected directly through the DP base measure, enabling decisive ``deep exploration'' with a single neural network without the overhead of multi-network ensembles.