通过变分下界优化，提升多目标贝叶斯优化中帕累托前沿的熵搜索精度。
Pareto-frontier Entropy Search with Variational Lower Bound Maximization
- 用混合分布近似帕累托前沿截断分布，解决连续域无法完整获取前沿的问题。
- 在多目标数量大时，相比基线方法，信息增益更准确，优化效率显著提升。
- 适合高维多目标优化场景，尤其适用于需高效探索复杂权衡面的任务。
本文研究基于帕累托前沿信息增益的多目标贝叶斯优化（MOBO）。计算信息增益的关键在于以帕累托前沿为条件的预测分布，该分布定义为被帕累托前沿截断的分布。然而，在连续域中通常无法获得完整的帕累托前沿，因此完整截断难以确定。为此，我们采用由帕累托前沿子集导出的过截断与欠截断两种近似截断构成的混合分布来逼近真实截断分布。由于混合系数的最优值事先未知，我们提出通过变分下界最大化框架优化该系数，从而最小化信息增益的近似误差。实验表明，该方法在目标函数数量较多时表现尤为出色。
原文摘要 · Abstract (English)
This study considers multi-objective Bayesian optimization (MOBO) through the information gain of the Pareto-frontier. To calculate the information gain, a predictive distribution conditioned on the Pareto-frontier plays a key role, which is defined as a distribution truncated by the Pareto-frontier. However, it is usually impossible to obtain the entire Pareto-frontier in a continuous domain, and therefore, the complete truncation cannot be known. We consider an approximation of the truncate distribution by using a mixture distribution consisting of two possible approximate truncation obtainable from a subset of the Pareto-frontier, which we call over- and under-truncation. Since the optimal balance of the mixture is unknown beforehand, we propose optimizing the balancing coefficient through the variational lower bound maximization framework, by which the approximation error of the information gain can be minimized. Our empirical evaluation demonstrates the effectiveness of the proposed method particularly when the number of objective functions is large.
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