  Model predictive control (MPC) has been successful in applications involving
the control of complex physical systems. This class of controllers leverages
the information provided by an approximate model of the system's dynamics to
simulate the effect of control actions. MPC methods also present a few
hyper-parameters which may require a relatively expensive tuning process by
demanding interactions with the physical system. Therefore, we investigate
fine-tuning MPC methods in the context of stochastic MPC, which presents extra
challenges due to the randomness of the controller's actions. In these
scenarios, performance outcomes present noise, which is not homogeneous across
the domain of possible hyper-parameter settings, but which varies in an
input-dependent way. To address these issues, we propose a Bayesian
optimisation framework that accounts for heteroscedastic noise to tune
hyper-parameters in control problems. Empirical results on benchmark continuous
control tasks and a physical robot support the proposed framework's suitability
relative to baselines, which do not take heteroscedasticity into account.
