An efficient, Non-Myopic Acquisition Function for Bayesian Optimisation

This project falls within the EPSRC Artificial Intelligence and Robotics area of research. This DPhil will research into an efficient, yet non-myopic acquisition function for Bayesian Optimisation.

Bayesian Optimisation has widespread applications: from multi-factor stock selection, to accelerating drug discovery and tuning hyper-parameters in automated machine learning. In short, Bayesian Optimisation aims to find the minimum of a black box function by intelligently probing the function, eventually converging on the global minimum. The main algorithm involves using current observations to build a surrogate model of the objective function (with Gaussian Process Regression, for example).

An acquisition function that embeds the surrogate model then determines the next point at which to evaluate the objective function: the acquisition function should trade-off exploring regions of high surrogate model uncertainty with exploiting regions next to where the current minimum lies. In theory, the acquisition function should marginalise not just current evaluations, but the potential impact of future evaluations, which would result in an acquisition function that dynamically tends from favouring exploration to exploitation as the budget of evaluations is exhausted.

The issue is that the dynamic program that must be solved to choose the next input is computationally intractable, as it involves recursive optimisation and quadrature.

The myopic approach is to ignore the potential impact of all future evaluations, and assume that the next evaluation is the last. Though a myopic approximation reduces computational intensity, the algorithm is under-exploratory. Whilst more non-myopic acquisition functions (such as the limited look-ahead) have shown promising empirical performance in initial investigations (particularly in applications with complex high-dimensional objectives that have small, fixed, budgets of evaluations), they have not yet been widely adopted due to their high associated computational costs.

The objective of this DPhil is to therefore create a non-myopic acquisition function with a lower computational cost by artificially recreating the exploration to exploitation shift that would be obtained by solving the intractable dynamic program. This acquisition function could then replace the myopic ones currently being used in the majority of the applications of Bayesian Optimisation.

The research will build on the success of the methods recently introduced by De Ath, who proposes randomly selecting an explorative input with a probability of epsilon on each iteration. This DPhil will dynamically vary this value of epsilon, thereby recreating the exploration-exploitation shift that would be introduced by solving the dynamic program, but at a much lower computational cost. This idea has not yet been suggested in literature.