Richard M. Everson

George De Ath, Richard M. Everson, Jonathan E. Fieldsend

Batch Bayesian optimisation (BO) is a successful technique for the optimisation of expensive black-box functions. Asynchronous BO can reduce wallclock time by starting a new evaluation as soon as another finishes, thus maximising resource utilisation. To maximise resource allocation, we develop a novel asynchronous BO method, AEGiS (Asynchronous $ε$-Greedy Global Search) that combines greedy search, exploiting the surrogate's mean prediction, with Thompson sampling and random selection from the approximate Pareto set describing the trade-off between exploitation (surrogate mean prediction) and exploration (surrogate posterior variance). We demonstrate empirically the efficacy of AEGiS on synthetic benchmark problems, meta-surrogate hyperparameter tuning problems and real-world problems, showing that AEGiS generally outperforms existing methods for asynchronous BO. When a single worker is available performance is no worse than BO using expected improvement.

George De Ath, Jonathan E. Fieldsend, Richard M. Everson

Bayesian optimisation is a popular approach for optimising expensive black-box functions. The next location to be evaluated is selected via maximising an acquisition function that balances exploitation and exploration. Gaussian processes, the surrogate models of choice in Bayesian optimisation, are often used with a constant prior mean function equal to the arithmetic mean of the observed function values. We show that the rate of convergence can depend sensitively on the choice of mean function. We empirically investigate 8 mean functions (constant functions equal to the arithmetic mean, minimum, median and maximum of the observed function evaluations, linear, quadratic polynomials, random forests and RBF networks), using 10 synthetic test problems and two real-world problems, and using the Expected Improvement and Upper Confidence Bound acquisition functions. We find that for design dimensions $\ge5$ using a constant mean function equal to the worst observed quality value is consistently the best choice on the synthetic problems considered. We argue that this worst-observed-quality function promotes exploitation leading to more rapid convergence. However, for the real-world tasks the more complex mean functions capable of modelling the fitness landscape may be effective, although there is no clearly optimum choice.

George De Ath, Richard M. Everson, Jonathan E. Fieldsend et al.

Bayesian optimisation is a popular, surrogate model-based approach for optimising expensive black-box functions. Given a surrogate model, the next location to expensively evaluate is chosen via maximisation of a cheap-to-query acquisition function. We present an $ε$-greedy procedure for Bayesian optimisation in batch settings in which the black-box function can be evaluated multiple times in parallel. Our $ε$-shotgun algorithm leverages the model's prediction, uncertainty, and the approximated rate of change of the landscape to determine the spread of batch solutions to be distributed around a putative location. The initial target location is selected either in an exploitative fashion on the mean prediction, or -- with probability $ε$ -- from elsewhere in the design space. This results in locations that are more densely sampled in regions where the function is changing rapidly and in locations predicted to be good (i.e close to predicted optima), with more scattered samples in regions where the function is flatter and/or of poorer quality. We empirically evaluate the $ε$-shotgun methods on a range of synthetic functions and two real-world problems, finding that they perform at least as well as state-of-the-art batch methods and in many cases exceed their performance.

George De Ath, Richard M. Everson, Alma A. M. Rahat et al.

The performance of acquisition functions for Bayesian optimisation to locate the global optimum of continuous functions is investigated in terms of the Pareto front between exploration and exploitation. We show that Expected Improvement (EI) and the Upper Confidence Bound (UCB) always select solutions to be expensively evaluated on the Pareto front, but Probability of Improvement is not guaranteed to do so and Weighted Expected Improvement does so only for a restricted range of weights. We introduce two novel $ε$-greedy acquisition functions. Extensive empirical evaluation of these together with random search, purely exploratory, and purely exploitative search on 10 benchmark problems in 1 to 10 dimensions shows that $ε$-greedy algorithms are generally at least as effective as conventional acquisition functions (e.g., EI and UCB), particularly with a limited budget. In higher dimensions $ε$-greedy approaches are shown to have improved performance over conventional approaches. These results are borne out on a real world computational fluid dynamics optimisation problem and a robotics active learning problem. Our analysis and experiments suggest that the most effective strategy, particularly in higher dimensions, is to be mostly greedy, occasionally selecting a random exploratory solution.

Nicholas D. Sanders, Richard M. Everson, Jonathan E. Fieldsend et al.

Many expensive black-box optimisation problems are sensitive to their inputs. In these problems it makes more sense to locate a region of good designs, than a single-possibly fragile-optimal design. Expensive black-box functions can be optimised effectively with Bayesian optimisation, where a Gaussian process is a popular choice as a prior over the expensive function. We propose a method for robust optimisation using Bayesian optimisation to find a region of design space in which the expensive function's performance is relatively insensitive to the inputs whilst retaining a good quality. This is achieved by sampling realisations from a Gaussian process that is modelling the expensive function, and evaluating the improvement for each realisation. The expectation of these improvements can be optimised cheaply with an evolutionary algorithm to determine the next location at which to evaluate the expensive function. We describe an efficient process to locate the optimum expected improvement. We show empirically that evaluating the expensive function at the location in the candidate uncertainty region about which the model is most uncertain, or at random, yield the best convergence in contrast to exploitative schemes. We illustrate our method on six test functions in two, five, and ten dimensions, and demonstrate that it is able to outperform two state-of-the-art approaches from the literature. We also demonstrate our method one two real-world problems in 4 and 8 dimensions, which involve training robot arms to push objects onto targets.

George De Ath, Richard M. Everson

We propose a novel part-based method for tracking an arbitrary object in challenging video sequences. The colour distribution of tracked image patches on the target object are represented by pairs of RGB samples and counts of how many pixels in the patch are similar to them. Patches are placed by segmenting the object in the given bounding box and placing patches in homogeneous regions of the object. These are located in subsequent image frames by applying non-shearing affine transformations to the patches' previous locations, locally optimising the best of these, and evaluating their quality using a modified Bhattacharyya distance. In experiments carried out on VOT2018 and OTB100 benchmarks, the tracker achieves higher performance than all other part-based trackers. An ablation study is used to reveal the effectiveness of each tracking component, with largest performance gains found when using the patch placement scheme.