Multi-objective Bayesian Optimization using Pareto-frontier Entropy
Multi-objective Bayesian Optimization using Pareto-frontier Entropy
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发表时间：
2019-06
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通讯作者：
Shinya Suzuki;Shion Takeno;T. Tamura;Kazuki Shitara;Masayuki Karasuyama
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作者：
Shinya Suzuki;Shion Takeno;T. Tamura;Kazuki Shitara;Masayuki Karasuyama
研究了一种基于熵的多目标贝叶斯优化算法。熵搜索是贝叶斯优化的一种成功方法。然而，对于目标管理，现有的基于熵的方法忽略了目标之间的权衡或引入不可靠的近似。本文提出了一种新的基于熵的目标优化算法--Pareto-frontier entropy search（PFES）。我们的熵可以将最优值的权衡关系，进一步，我们推导出一个分析公式，而不引入额外的近似或简化的标准熵搜索设置。我们还表明，我们的熵计算实际上是可行的，通过使用递归分解技术，已被称为研究的Pareto超体积计算。除了通常的MBO设置，其中所有的目标是同时观察，我们还考虑了“解耦”设置，其中的目标函数可以单独观察。PFES可以很容易地适应解耦的设置，通过考虑每个输出维度的边际密度的熵。该方法在Pareto边界条件下考虑了目标间的相关性，而现有方法忽略了这一点。我们的数值实验表明PFES通过几个基准数据集的有效性。
This paper studies an entropy-based multi-objective Bayesian optimization (MBO). The entropy search is successful approach to Bayesian optimization. However, for MBO, existing entropy-based methods ignore trade-off among objectives or introduce unreliable approximations. We propose a novel entropy-based MBO called Pareto-frontier entropy search (PFES) by considering the entropy of Pareto-frontier, which is an essential notion of the optimality of the multi-objective problem. Our entropy can incorporate the trade-off relation of the optimal values, and further, we derive an analytical formula without introducing additional approximations or simplifications to the standard entropy search setting. We also show that our entropy computation is practically feasible by using a recursive decomposition technique which has been known in studies of the Pareto hyper-volume computation. Besides the usual MBO setting, in which all the objectives are simultaneously observed, we also consider the "decoupled" setting, in which the objective functions can be observed separately. PFES can easily adapt to the decoupled setting by considering the entropy of the marginal density for each output dimension. This approach incorporates dependency among objectives conditioned on Pareto-frontier, which is ignored by the existing method. Our numerical experiments show effectiveness of PFES through several benchmark datasets.