J. C. Schoeman

E. Visser, C. E. van Daalen, J. C. Schoeman

Bayesian optimization (BO) is a popular method for optimizing expensive black-box functions. BO has several well-documented shortcomings, including computational slowdown with longer optimization runs, poor suitability for non-stationary or ill-conditioned objective functions, and poor convergence characteristics. Several algorithms have been proposed that incorporate local strategies, such as trust regions, into BO to mitigate these limitations; however, none address all of them satisfactorily. To address these shortcomings, we propose the LABCAT algorithm, which extends trust-region-based BO by adding a rotation aligning the trust region with the weighted principal components and an adaptive rescaling strategy based on the length-scales of a local Gaussian process surrogate model with automatic relevance determination. Through extensive numerical experiments using a set of synthetic test functions and the well-known COCO benchmarking software, we show that the LABCAT algorithm outperforms several state-of-the-art BO and other black-box optimization algorithms.

Andrew Murdoch, Johannes Cornelius Schoeman, Hendrik Willem Jordaan

In this paper, we address the issue of increasing the performance of reinforcement learning (RL) solutions for autonomous racing cars when navigating under conditions where practical vehicle modelling errors (commonly known as \emph{model mismatches}) are present. To address this challenge, we propose a partial end-to-end algorithm that decouples the planning and control tasks. Within this framework, an RL agent generates a trajectory comprising a path and velocity, which is subsequently tracked using a pure pursuit steering controller and a proportional velocity controller, respectively. In contrast, many current learning-based (i.e., reinforcement and imitation learning) algorithms utilise an end-to-end approach whereby a deep neural network directly maps from sensor data to control commands. By leveraging the robustness of a classical controller, our partial end-to-end driving algorithm exhibits better robustness towards model mismatches than standard end-to-end algorithms.

J. C. Schoeman, C. E. van Daalen, J. A. du Preez

In this paper, we propose a parametrised factor that enables inference on Gaussian networks where linear dependencies exist among the random variables. Our factor representation is effectively a generalisation of traditional Gaussian parametrisations where the positive-definite constraint of the covariance matrix has been relaxed. For this purpose, we derive various statistical operations and results (such as marginalisation, multiplication and affine transformations of random variables) that extend the capabilities of Gaussian factors to these degenerate settings. By using this principled factor definition, degeneracies can be accommodated accurately and automatically at little additional computational cost. As illustration, we apply our methodology to a representative example involving recursive state estimation of cooperative mobile robots.