Maximizing acquisition functions for Bayesian optimization

By James T. Wilson, Frank Hutter, Marc Peter Deisenroth. 2018

316 citations recorded by the source corpus.

Bayesian optimization is a sample-efficient approach to global optimization that relies on theoretically motivated value heuristics (acquisition functions) to guide its search process. Fully maximizing acquisition functions produces the Bayes' decision rule, but this ideal is difficult to achieve since these functions are frequently non-trivial to optimize. This statement is especially true when evaluating queries in parallel, where acquisition functions are routinely non-convex, high-dimensional, and intractable. We first show that acquisition functions estimated via Monte Carlo integration are consistently amenable to gradient-based optimization. Subsequently, we identify a common family of acquisition functions, including EI and UCB, whose characteristics not only facilitate but justify use of greedy approaches for their maximization.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Management Science and Operations Research

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Eric P. Xing
2. Barnab'as P'oczos
3. Colin White
4. Yash Savani
5. Jeff Schneider
6. Yoshua Bengio
7. Willie Neiswanger
8. Ruslan Salakhutdinov

In Computational Theory and Mathematics

1. Yash Savani
2. Colin White
3. Kirthevasan Kandasamy
4. Willie Neiswanger
5. Eric P. Xing
6. Maximilian Balandat
7. Sam Daulton
8. Jeff Schneider

In Management Science and Operations Research

1. Kirthevasan Kandasamy
2. Barnab'as P'oczos
3. Jeff Schneider
4. Maximilian Balandat
5. Sam Daulton
6. Willie Neiswanger
7. Eric P. Xing
8. Eytan Bakshy

Citations in the corpus

• BANANAS: Bayesian Optimization with Neural Architectures for Neural Architecture Search (2019, methodology): “[68] James Wilson, Frank Hutter, and Marc Deisenroth.”
• ProBO: Versatile Bayesian Optimization Using Any Probabilistic Programming Language (2019, methodology): “Note that post and gen are not in general analytically differentiable, so in contrast with [53], we cannot optimize a ( x ) with gradient-based methods.”
• ProBO: a Framework for Using Probabilistic Programming in Bayesian Optimization (2019, methodology): “Special cases of sample-based (Monte Carlo) estimates of certain acquisition functions have been described in prior work (Snoek et al., 2012; Wilson et al., 2018; Hern´andez-Lobato et al., 2015).”
• Learning search spaces for Bayesian optimization: Another view of hyperparameter transfer learning (2019, methodology): “Beyond those we used in our experiments, we can further mention recent resource-aware optimizers [2, 8], evolutionary-based techniques [18, 34] and virtually any core improvement of BO, be it related to the acquisition function [48] or efficient parallelism [23, 47].”
• BoTorch: Programmable Bayesian Optimization in PyTorch (2019, methodology): “The classic case considered in the literature is a single-output ( m = 1 ) model with a single candidate ( q = 1 ) point x , a Gaussian model posterior 2 ) , and the identity objective g ( ξ ) = ξ .”
• Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization (2020, methodology): “[60] note that in similar scenarios, submodularity has been extended to infinite sets X (e.”
• Monte Carlo Gradient Estimation in Machine Learning (2019, methodology): “, 2017), in Bayesian optimisation (Wilson et al., 2018) and in probabilistic programming (Ritchie et al.”