Latent Trajectory: A New Framework for Deep Actor-Critic Reinforcement Learning with Uncertainty Quantification

Uncertainty quantification in deep learning is challenging due to the complexity of deep neural networks. This challenge is particularly pronounced in deep reinforcement learning (RL), where agents interact with stochastic environments. In deep actor-critic RL, this challenge is further exacerbated due to the interdependence between the actor and critic updates. Existing uncertainty quantification methods for RL are predominantly developed within the Bayesian framework. While these methods estimate the uncertainty of the value function, their confidence intervals are often misleading, with the coverage rate frequently falling well below the nominal level. To address this issue, we introduce a novel deep RL framework that treats transition trajectories as latent variables. Leveraging this framework, we propose an adaptive Stochastic Gradient Markov Chain Monte Carlo algorithm to train deep actor-critic models, which naturally accounts for the interdependence between the actor and critic updates. We provide theoretical guarantees for the convergence of the proposed method and offer empirical evidence for its effectiveness in uncertainty quantification of the value function. The proposed latent trajectory framework is highly flexible, allowing for the integration of advanced RL strategies to further enhance deep actor-critic learning.