Bayesian Neural Networks via Dirichlet Process Priors on the Data-Generating Distribution for Randomized Value Functions in Deep Reinforcement Learning
Abstract
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.
Related
- The First Moment of Dirichlet L-functions over Generators of the Character Group
- Large values of cubic and quartic Dirichlet L-functions of prime moduli
- Central non-vanishing of Dirichlet L-functions
- Bilinear generating functions of the multivariable Al-Salam-Carlitz polynomials and applications
- The Dirichlet Process as sampling distribution
BibTeX
@misc{vashishtha2026bayesian,
title = {{Bayesian Neural Networks via Dirichlet Process Priors on the Data-Generating Distribution for Randomized Value Functions in Deep Reinforcement Learning}},
author = {Sumit Vashishtha},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27570},
eprint = {2610.27570},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27570},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bayesian Neural Networks via Dirichlet Process Priors on the Data-Generating Distribution for Randomized Value Functions in Deep Reinforcement Learning
AU - Sumit Vashishtha
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27570
UR - https://arxiv.org/abs/2610.27570
AB - 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.
ER -