In continual learning (CL) -- where a learner trains on a stream of data -- standard hyperparameter optimisation (HPO) cannot be applied, as a learner does not have access to all of the data at the same time. This has prompted the development of CL-specific HPO frameworks. The most popular way to tune hyperparameters in CL is to repeatedly train over the whole data stream with different hyperparameter settings. However, this end-of-training HPO is unrealistic as in practice a learner can only see the stream once. Hence, there is an open question: what HPO framework should a practitioner use for a CL problem in reality? This paper answers this question by evaluating several realistic HPO frameworks. We find that all the HPO frameworks considered, including end-of-training HPO, perform similarly. We therefore advocate using the realistic and most computationally efficient method: fitting the hyperparameters on the first task and then fixing them throughout training.

Transfer learning for Bayesian optimisation has generally assumed a strong similarity between optimisation tasks, with at least a subset having similar optimal inputs. This assumption can reduce computational costs, but it is violated in a wide range of optimisation problems where transfer learning may nonetheless be useful. We replace this assumption with a weaker one only requiring the shape of the optimisation landscape to be similar, and analyse the recent method Prior Learning for Bayesian Optimisation - PLeBO - in this setting. By learning priors for the hyperparameters of the Gaussian process surrogate model we can better approximate the underlying function, especially for few function evaluations. We validate the learned priors and compare to a breadth of transfer learning approaches, using synthetic data and a recent air pollution optimisation problem as benchmarks. We show that PLeBO and prior transfer find good inputs in fewer evaluations.

We introduce ordered transfer hyperparameter optimisation (OTHPO), a version of transfer learning for hyperparameter optimisation (HPO) where the tasks follow a sequential order. Unlike for state-of-the-art transfer HPO, the assumption is that each task is most correlated to those immediately before it. This matches many deployed settings, where hyperparameters are retuned as more data is collected; for instance tuning a sequence of movie recommendation systems as more movies and ratings are added. We propose a formal definition, outline the differences to related problems and propose a basic OTHPO method that outperforms state-of-the-art transfer HPO. We empirically show the importance of taking order into account using ten benchmarks. The benchmarks are in the setting of gradually accumulating data, and span XGBoost, random forest, approximate k-nearest neighbor, elastic net, support vector machines and a separate real-world motivated optimisation problem. We open source the benchmarks to foster future research on ordered transfer HPO.

Bayesian optimisation is a powerful method for optimising black-box functions, popular in settings where the true function is expensive to evaluate and no gradient information is available. Bayesian optimisation can improve responses to many optimisation problems within climate change for which simulator models are unavailable or expensive to sample from. While there have been several feasibility demonstrations of Bayesian optimisation in climate-related applications, there has been no unifying review of applications and benchmarks. We provide such a review here, to encourage the use of Bayesian optimisation in important and well-suited application domains. We identify four main application domains: material discovery, wind farm layout, optimal renewable control and environmental monitoring. For each domain we identify a public benchmark or data set that is easy to use and evaluate systems against, while being representative of real-world problems. Due to the lack of a suitable benchmark for environmental monitoring, we propose LAQN-BO, based on air pollution data. Our contributions are: a) identifying a representative range of benchmarks, providing example code where necessary; b) introducing a new benchmark, LAQN-BO; and c) promoting a wider use of climate change applications among Bayesian optimisation practitioners.