Summary and Contributions: Post-rebuttal: I would like to thank the authors for their response. As stated in the original review, I think comparing to DQN will improve the paper. This paper address the problem of robust control of continuous dynamic systems, where the system's dynamics is unknown but assumed to have a linear structure, with external polytopic disturbance. The proposed approach consists of several steps for each action, first model and confidence region estimation (or refinement), then worst case reward extraction and state estimation bounds, a conservative planning step based on the reward and state bounds, finally one step execution, and repeating the process in an MPC like manner. The paper presents an end to end approach to the robust control problem for unknown dynamics (only the system dynamic matrix is unknown) in an adaptive manner.

We consider the problem of robust and adaptive model predictive control (MPC) of a linear system, with unknown parameters that are learned along the way (adaptive), in a critical setting where failures must be prevented (robust). This problem has been studied from different perspectives by different communities. However, the existing theory deals only with the case of quadratic costs (the LQ problem), which limits applications to stabilisation and tracking tasks only. In order to handle more general (non-convex) costs that naturally arise in many practical problems, we carefully select and bring together several tools from different communities, namely non-asymptotic linear regression, recent results in interval prediction, and tree-based planning. Combining and adapting the theoretical guarantees at each layer is non trivial, and we provide the first end-to-end suboptimality analysis for this setting. Interestingly, our analysis naturally adapts to handle many models and combines with a data-driven robust model selection strategy, which enables to relax the modelling assumptions.