Sequential Subspace Search for Functional Bayesian Optimization Incorporating Experimenter Intuition

• URL: http://arxiv.org/abs/2009.03543v1
• Date: Tue, 8 Sep 2020 06:54:11 GMT
• Title: Sequential Subspace Search for Functional Bayesian Optimization Incorporating Experimenter Intuition
• Authors: Alistair Shilton, Sunil Gupta, Santu Rana, Svetha Venkatesh
• Abstract summary: Our algorithm generates a sequence of finite-dimensional random subspaces of functional space spanned by a set of draws from the experimenter's Gaussian Process. Standard Bayesian optimisation is applied on each subspace, and the best solution found used as a starting point (origin) for the next subspace. We test our algorithm in simulated and real-world experiments, namely blind function matching, finding the optimal precipitation-strengthening function for an aluminium alloy, and learning rate schedule optimisation for deep networks.
• Score: 63.011641517977644
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose an algorithm for Bayesian functional optimisation - that is, finding the function to optimise a process - guided by experimenter beliefs and intuitions regarding the expected characteristics (length-scale, smoothness, cyclicity etc.) of the optimal solution encoded into the covariance function of a Gaussian Process. Our algorithm generates a sequence of finite-dimensional random subspaces of functional space spanned by a set of draws from the experimenter's Gaussian Process. Standard Bayesian optimisation is applied on each subspace, and the best solution found used as a starting point (origin) for the next subspace. Using the concept of effective dimensionality, we analyse the convergence of our algorithm and provide a regret bound to show that our algorithm converges in sub-linear time provided a finite effective dimension exists. We test our algorithm in simulated and real-world experiments, namely blind function matching, finding the optimal precipitation-strengthening function for an aluminium alloy, and learning rate schedule optimisation for deep networks.

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