Policy Optimization of Finite-Horizon Kalman Filter with Unknown Noise Covariance

This paper is on learning the Kalman gain by policy optimization method. Firstly, we reformulate the finite-horizon Kalman filter as a policy optimization problem of the dual system. Secondly, we obtain the global linear convergence of exact gradient descent method in the setting of known parameters. Thirdly, the gradient estimation and stochastic gradient descent method are proposed to solve the policy optimization problem, and further the global linear convergence and sample complexity of stochastic gradient descent are provided for the setting of unknown noise covariance matrices and known model parameters

A Policy-Guided Imitation Approach for Offline Reinforcement Learning

Offline reinforcement learning (RL) methods can generally be categorized into two types: RL-based and Imitation-based. RL-based methods could in principle enjoy out-of-distribution generalization but suffer from erroneous off-policy evaluation. Imitation-based methods avoid off-policy evaluation but are too conservative to surpass the dataset. In this study, we propose an alternative approach, inheriting the training stability of imitation-style methods while still allowing logical out-of-distribution generalization. We decompose the conventional reward-maximizing policy in offline RL into a guide-policy and an execute-policy. During training, the guide-poicy and execute-policy are learned using only data from the dataset, in a supervised and decoupled manner. During evaluation, the guide-policy guides the execute-policy by telling where it should go so that the reward can be maximized, serving as the \textit{Prophet}. By doing so, our algorithm allows \textit{state-compositionality} from the dataset, rather than \textit{action-compositionality} conducted in prior imitation-style methods. We dumb this new approach Policy-guided Offline RL (\texttt{POR}). \texttt{POR} demonstrates the state-of-the-art performance on D4RL, a standard benchmark for offline RL. We also highlight the benefits of \texttt{POR} in terms of improving with supplementary suboptimal data and easily adapting to new tasks by only changing the guide-poicy.Comment: Oral @ NeurIPS 2022, code at https://github.com/ryanxhr/PO