Machine Learning (stat.ML)

Abstract: Nonlinear systems, such as with degrading hysteretic behavior, are often encountered in engineering applications. In addition, due to the ubiquitous presence of uncertainty and the modeling of such systems becomes increasingly difficult. On the other hand, datasets from pristine models developed without knowing the nature of the degrading effects can be easily obtained. In this paper, we use datasets from pristine models without considering the degrading effects of hysteretic systems as low-fidelity representations that capture many of the important characteristics of the true system's behavior to train a deep operator network (DeepONet). Three numerical examples are used to show that the proposed use of the DeepONets to model the discrepancies between the low-fidelity model and the true system's response leads to significant improvements in the prediction error in the presence of uncertainty in the model parameters for degrading hysteretic systems.

Abstract: In online reinforcement learning (RL), instead of employing standard structural assumptions on Markov decision processes (MDPs), using a certain coverage condition (original from offline RL) is enough to ensure sample-efficient guarantees (Xie et al. 2023). In this work, we focus on this new direction by digging more possible and general coverage conditions, and study the potential and the utility of them in efficient online RL. We identify more concepts, including the $L^p$ variant of concentrability, the density ratio realizability, and trade-off on the partial/rest coverage condition, that can be also beneficial to sample-efficient online RL, achieving improved regret bound. Furthermore, if exploratory offline data are used, under our coverage conditions, both statistically and computationally efficient guarantees can be achieved for online RL. Besides, even though the MDP structure is given, e.g., linear MDP, we elucidate that, good coverage conditions are still beneficial to obtain faster regret bound beyond $\widetilde{O}(\sqrt{T})$ and even a logarithmic order regret. These results provide a good justification for the usage of general coverage conditions in efficient online RL.