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Frank Shih

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3 papers

2 author rows

TMLR Journal 2025 Journal Article

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

Frank Shih
Faming Liang

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.

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NeurIPS Conference 2025 Conference Paper

Uncertainty Quantification for Physics-Informed Neural Networks with Extended Fiducial Inference

Frank Shih
Zhenghao Jiang
Faming Liang

Uncertainty quantification (UQ) in scientific machine learning is increasingly critical as neural networks are widely adopted to tackle complex problems across diverse scientific disciplines. For physics-informed neural networks (PINNs), a prominent model in scientific machine learning, uncertainty is typically quantified using Bayesian or dropout methods. However, both approaches suffer from a fundamental limitation: the prior distribution or dropout rate required to construct honest confidence sets cannot be determined without additional information. In this paper, we propose a novel method within the framework of extended fiducial inference (EFI) to provide rigorous uncertainty quantification for PINNs. The proposed method leverages a narrow-neck hyper-network to learn the parameters of the PINN and quantify their uncertainty based on imputed random errors in the observations. This approach overcomes the limitations of Bayesian and dropout methods, enabling the construction of honest confidence sets based solely on observed data. This advancement represents a significant breakthrough for PINNs, greatly enhancing their reliability, interpretability, and applicability to real-world scientific and engineering challenges. Moreover, it establishes a new theoretical framework for EFI, extending its application to large-scale models, eliminating the need for sparse hyper-networks, and significantly improving the automaticity and robustness of statistical inference.

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ICLR Conference 2024 Conference Paper

Fast Value Tracking for Deep Reinforcement Learning

Frank Shih
Faming Liang

Reinforcement learning (RL) tackles sequential decision-making problems by creating agents that interacts with their environment. However, existing algorithms often view these problem as static, focusing on point estimates for model parameters to maximize expected rewards, neglecting the stochastic dynamics of agent-environment interactions and the critical role of uncertainty quantification. Our research leverages the Kalman filtering paradigm to introduce a novel and scalable sampling algorithm called Langevinized Kalman Temporal-Difference (LKTD) for deep reinforcement learning. This algorithm, grounded in Stochastic Gradient Markov Chain Monte Carlo (SGMCMC), efficiently draws samples from the posterior distribution of deep neural network parameters. Under mild conditions, we prove that the posterior samples generated by the LKTD algorithm converge to a stationary distribution. This convergence not only enables us to quantify uncertainties associated with the value function and model parameters but also allows us to monitor these uncertainties during policy updates throughout the training phase. The LKTD algorithm paves the way for more robust and adaptable reinforcement learning approaches.

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