  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. Last, we strive to preserve tractability at any stage of
the method, that we illustrate on two challenging simulated environments.
