Local Bayesian optimization via maximizing probability of descent
Local Bayesian optimization via maximizing probability of descent
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DOI：
10.48550/arxiv.2210.11662
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发表时间：
2022-10
期刊：
影响因子：
--
通讯作者：
Quan Nguyen;Kaiwen Wu;J. Gardner;R. Garnett
中科院分区：
文献类型：
--
作者：
Quan Nguyen;Kaiwen Wu;J. Gardner;R. Garnett
局部优化通过避免全局搜索空间的需要，为昂贵的高维黑盒优化提供了一种很有前途的方法。对于不能直接评估梯度的目标函数，贝叶斯优化提供了一种解决方案--我们构建目标的概率模型，设计一种策略来学习当前位置的梯度，并使用得到的信息来导航目标景观。以前的工作是通过最小化梯度估计中的方差，然后沿着期望梯度的方向移动来实现该方案。在这篇文章中，我们重新审视和提炼了这种方法。我们证明了，令人惊讶的是，梯度的期望值并不总是使下降概率最大化的方向，事实上，这些方向可能是近乎正交的。然后，这种观察激发了一种优雅的优化方案，寻求最大化下降的可能性，同时朝着最有可能下降的方向移动。在合成目标和真实目标上的实验表明，我们的方法比以前实现的这种优化方案性能更好，并且与其他明显更复杂的基线相比具有竞争力。
Local optimization presents a promising approach to expensive, high-dimensional black-box optimization by sidestepping the need to globally explore the search space. For objective functions whose gradient cannot be evaluated directly, Bayesian optimization offers one solution -- we construct a probabilistic model of the objective, design a policy to learn about the gradient at the current location, and use the resulting information to navigate the objective landscape. Previous work has realized this scheme by minimizing the variance in the estimate of the gradient, then moving in the direction of the expected gradient. In this paper, we re-examine and refine this approach. We demonstrate that, surprisingly, the expected value of the gradient is not always the direction maximizing the probability of descent, and in fact, these directions may be nearly orthogonal. This observation then inspires an elegant optimization scheme seeking to maximize the probability of descent while moving in the direction of most-probable descent. Experiments on both synthetic and real-world objectives show that our method outperforms previous realizations of this optimization scheme and is competitive against other, significantly more complicated baselines.