A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes
A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes
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发表时间：
2018-11
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通讯作者：
Jialin Song;Yuxin Chen;Yisong Yue
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作者：
Jialin Song;Yuxin Chen;Yisong Yue
我们如何有效地收集信息，以优化一个未知的功能，当有多个，相互依赖的信息源，不同的成本？例如，在优化机器人系统时，智能地权衡计算机模拟和真实的机器人测试可以带来显著的节省。现有的方法，如多保真度GP-UCB或基于熵搜索的方法，要么对不同属性之间的相互作用进行简单的假设，要么使用缺乏理论保证的简单的算法。在本文中，我们研究了多个输出之间的复杂结构依赖的多保真度贝叶斯优化，并提出了MF-MI-Greedy，一个原则性的算法框架来解决这个问题。特别是，我们使用加性高斯过程的基础上共享的潜在结构与目标函数不同的并行性建模。然后，我们使用成本敏感的互信息增益有效的贝叶斯全局优化。我们提出了一个简单的概念，后悔，其中包括成本的不同qualities，并证明MF-MI-Greedy实现低后悔。我们证明了我们的算法在合成和真实世界的数据集上的强大的经验性能。
How can we efficiently gather information to optimize an unknown function, when presented with multiple, mutually dependent information sources with different costs? For example, when optimizing a robotic system, intelligently trading off computer simulations and real robot testings can lead to significant savings. Existing methods, such as multi-fidelity GP-UCB or Entropy Search-based approaches, either make simplistic assumptions on the interaction among different fidelities or use simple heuristics that lack theoretical guarantees. In this paper, we study multi-fidelity Bayesian optimization with complex structural dependencies among multiple outputs, and propose MF-MI-Greedy, a principled algorithmic framework for addressing this problem. In particular, we model different fidelities using additive Gaussian processes based on shared latent structures with the target function. Then we use cost-sensitive mutual information gain for efficient Bayesian global optimization. We propose a simple notion of regret which incorporates the cost of different fidelities, and prove that MF-MI-Greedy achieves low regret. We demonstrate the strong empirical performance of our algorithm on both synthetic and real-world datasets.