Heteroscedastic Bayesian Optimisation for Stochastic Model Predictive Control

TL;DR

This paper introduces a heteroscedastic Bayesian optimization framework tailored for stochastic model predictive control, effectively tuning hyper-parameters in noisy, input-dependent environments, demonstrated on benchmarks and real robots.

Contribution

It presents a novel Bayesian optimization method that models input-dependent noise for hyper-parameter tuning in stochastic MPC, improving performance over traditional methods.

Findings

Outperforms baseline tuning methods in benchmark tasks

Effectively handles input-dependent noise in control scenarios

Validates approach on physical robot experiments

Abstract

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.