Bayesian optimization (BO) has emerged during the last few years as an effective approach to optimize black-box functions where direct queries of the objective are expensive. We consider the case where direct access to the function is not possible, but information about user preferences is. Such scenarios arise in problems where human preferences are modeled, such as A/B tests or recommender systems. We present a new framework for this scenario that we call Preferential Bayesian Optimization (PBO) and that allows to find the optimum of a latent function that can only be queried through pairwise comparisons, so-called duels. PBO extend the applicability of standard BO ideas and generalizes previous discrete dueling approaches by modeling the probability of the the winner of each duel by means of Gaussian process model with a Bernoulli likelihood. The latent preference function is used to define a family of acquisition functions that extend usual policies used in BO. We illustrate the benefits of PBO in a variety of experiments in which we show how the way correlations are modeled is the key ingredient to drastically reduce the number of comparisons to find the optimum of the latent function of interest.

@InProceedings{gonzalez17a,
title = {Preferential {B}ayesian Optimization},
author = {Javier González and Zhenwen Dai and Andreas Damianou and Neil D. Lawrence},
booktitle = {Proceedings of the 34th International Conference on Machine Learning},
pages = {1282},
year = {},
editor = {Doina Precup and Yee Whye Teh},
volume = {70},
series = {Proceedings of Machine Learning Research},
publisher = {PMLR},
edit = {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2017-07-17-gonzalez17a.md},
url = {http://inverseprobability.com/publications/gonzalez17a.html},
pdf = {http://proceedings.mlr.press/v70/gonzalez17a/gonzalez17a.pdf},
abstract = {Bayesian optimization (BO) has emerged during the last few years as an effective approach to optimize black-box functions where direct queries of the objective are expensive. We consider the case where direct access to the function is not possible, but information about user preferences is. Such scenarios arise in problems where human preferences are modeled, such as A/B tests or recommender systems. We present a new framework for this scenario that we call Preferential Bayesian Optimization (PBO) and that allows to find the optimum of a latent function that can only be queried through pairwise comparisons, so-called duels. PBO extend the applicability of standard BO ideas and generalizes previous discrete dueling approaches by modeling the probability of the the winner of each duel by means of Gaussian process model with a Bernoulli likelihood. The latent preference function is used to define a family of acquisition functions that extend usual policies used in BO. We illustrate the benefits of PBO in a variety of experiments in which we show how the way correlations are modeled is the key ingredient to drastically reduce the number of comparisons to find the optimum of the latent function of interest.},
OPTgroup = {}
}

%T Preferential Bayesian Optimization
%A Javier González and Zhenwen Dai and Andreas Damianou and Neil D. Lawrence
%B Proceedings of the 34th International Conference on Machine Learning
%C Proceedings of the 34th International Conference on Machine Learning
%D
%E Doina Precup and Yee Whye Teh
%F gonzalez17a
%I PMLR
%P 1282--1291
%R
%U http://inverseprobability.com/publications/gonzalez17a.html
%V 70
%X Bayesian optimization (BO) has emerged during the last few years as an effective approach to optimize black-box functions where direct queries of the objective are expensive. We consider the case where direct access to the function is not possible, but information about user preferences is. Such scenarios arise in problems where human preferences are modeled, such as A/B tests or recommender systems. We present a new framework for this scenario that we call Preferential Bayesian Optimization (PBO) and that allows to find the optimum of a latent function that can only be queried through pairwise comparisons, so-called duels. PBO extend the applicability of standard BO ideas and generalizes previous discrete dueling approaches by modeling the probability of the the winner of each duel by means of Gaussian process model with a Bernoulli likelihood. The latent preference function is used to define a family of acquisition functions that extend usual policies used in BO. We illustrate the benefits of PBO in a variety of experiments in which we show how the way correlations are modeled is the key ingredient to drastically reduce the number of comparisons to find the optimum of the latent function of interest.

TY - CPAPER
TI - Preferential Bayesian Optimization
AU - Javier González
AU - Zhenwen Dai
AU - Andreas Damianou
AU - Neil D. Lawrence
BT - Proceedings of the 34th International Conference on Machine Learning
PY -
DA -
ED - Doina Precup
ED - Yee Whye Teh
ID - gonzalez17a
PB - PMLR
SP - 1282
EP - 1291
L1 - http://proceedings.mlr.press/v70/gonzalez17a/gonzalez17a.pdf
UR - http://inverseprobability.com/publications/gonzalez17a.html
AB - Bayesian optimization (BO) has emerged during the last few years as an effective approach to optimize black-box functions where direct queries of the objective are expensive. We consider the case where direct access to the function is not possible, but information about user preferences is. Such scenarios arise in problems where human preferences are modeled, such as A/B tests or recommender systems. We present a new framework for this scenario that we call Preferential Bayesian Optimization (PBO) and that allows to find the optimum of a latent function that can only be queried through pairwise comparisons, so-called duels. PBO extend the applicability of standard BO ideas and generalizes previous discrete dueling approaches by modeling the probability of the the winner of each duel by means of Gaussian process model with a Bernoulli likelihood. The latent preference function is used to define a family of acquisition functions that extend usual policies used in BO. We illustrate the benefits of PBO in a variety of experiments in which we show how the way correlations are modeled is the key ingredient to drastically reduce the number of comparisons to find the optimum of the latent function of interest.
ER -

González, J., Dai, Z., Damianou, A. & Lawrence, N.D.. (). Preferential Bayesian Optimization. Proceedings of the 34th International Conference on Machine Learning 70:1282-1291