Warm starting Bayesian optimization

Abstract

We develop a framework for warm-starting Bayesian optimization, that reduces the solution time required to solve an optimization problem that is one in a sequence of related problems. This is useful when optimizing the output of a stochastic simulator that fails to provide derivative information, for which Bayesian optimization methods are well-suited. Solving sequences of related optimization problems arises when making several business decisions using one optimization model and input data collected over different time periods or markets. While many gradient-based methods can be warm started by initiating optimization at the solution to the previous problem, this warm start approach does not apply to Bayesian optimization methods, which carry a full metamodel of the objective function from iteration to iteration. Our approach builds a joint statistical model of the entire collection of related objective functions, and uses a value of information calculation to recommend points to evaluate.

Continuous multi-task Bayesian Optimisation with correlation

“…Morales-Enciso and Branke (2015) consider the optimisation of a changing objective function with EGO, and propose three different ways to re-use information gathered on previous objective functions to speed up optimisation of the current objective function: using the old posterior mean as the new prior mean, treating old samples as noisy, and treating time as an extra input dimension to the learnt function. The latter idea is also used by Poloczek et al (2016) to warm-start Bayesian Optimisation, however with the Knowledge Gradient as the acquisition function for the current optimisation task. A similar problem has been much studied in the field of Contextual multi-armed bandits, an extension of the multi-armed bandit problem where the best arm depends on a context that is randomly changing with time.…”

Towards a unifying theory of generalization

“…In particular, it would be interesting to assess what happens when participants learn in either rougher, smoother, or dynamically changing environments, before assessing them on the same level of smoothness. This could be used to develop and test different hierarchies of function learning models, such as warm starting (i.e., adjusting hyper-parameters over environments Poloczek et al, 2016), mismatched learning (i.e., assuming a fixed length-scale that is either too small or too large for the test set), or even "learning-to-learn"-algorithms (Chen et al, 2017) within environments of the same class over time.…”

GPTuneBand: Multi-task and Multi-fidelity Autotuning for Large-scale High Performance Computing Applications

“…In many tuning scenarios, there are correlated tuning tasks, and one can use such correlation to improve performance on each task. Multitask tuning has been used for continuous sets of tasks [39,38] and discrete tasks [31,54,44,13,35]. In the discrete case, one can use a multi-output GP model, such as the linear coregionalization model (LCM) [3,22] or the intrinsic model of coregionalization (IMC) [3,18,9], to model performance across correlated tasks [54,44,13,35].…”

“…Multitask tuning has been used for continuous sets of tasks [39,38] and discrete tasks [31,54,44,13,35]. In the discrete case, one can use a multi-output GP model, such as the linear coregionalization model (LCM) [3,22] or the intrinsic model of coregionalization (IMC) [3,18,9], to model performance across correlated tasks [54,44,13,35]. Some works further extended acquisition functions in BO to multi-task settings [31,54,44,13].…”