A Continuous Relaxation for Discrete Bayesian Optimization

• URL: http://arxiv.org/abs/2404.17452v1
• Date: Fri, 26 Apr 2024 14:47:40 GMT
• Title: A Continuous Relaxation for Discrete Bayesian Optimization
• Authors: Richard Michael, Simon Bartels, Miguel González-Duque, Yevgen Zainchkovskyy, Jes Frellsen, Søren Hauberg, Wouter Boomsma,
• Abstract summary: We show that inference and optimization can be computationally tractable. We consider in particular the optimization domain where very few observations and strict budgets exist. We show that the resulting acquisition function can be optimized with both continuous or discrete optimization algorithms.
• Score: 17.312618575552
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: To optimize efficiently over discrete data and with only few available target observations is a challenge in Bayesian optimization. We propose a continuous relaxation of the objective function and show that inference and optimization can be computationally tractable. We consider in particular the optimization domain where very few observations and strict budgets exist; motivated by optimizing protein sequences for expensive to evaluate bio-chemical properties. The advantages of our approach are two-fold: the problem is treated in the continuous setting, and available prior knowledge over sequences can be incorporated directly. More specifically, we utilize available and learned distributions over the problem domain for a weighting of the Hellinger distance which yields a covariance function. We show that the resulting acquisition function can be optimized with both continuous or discrete optimization algorithms and empirically assess our method on two bio-chemical sequence optimization tasks.

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