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Cuichen Li Tommy

Disciplinary expertise : Statistics and Machine learning

Page: Bayesian optimization

Content gap: The historical part of Bayesian optimization

Early Mathematics Foundations

From 1960s to 1980s

The earliest idea of Bayesian optimization sprang in 1964, from a paper by American applied mathematician Harold J. Kushner, “A New Method of Locating the Maximum Point of an Arbitrary Multipeak Curve in the Presence of Noise”. Although not directly proposing Bayesian optimization, in this paper, he first proposed a new method of locating the maximum point of an arbitrary multipeak curve in a noisy environment. This method provided an important theoretical foundation for subsequent Bayesian optimization.

By the 1980s, the framework we now use for Bayesian optimization was explicitly established. In 1978, the Soviet scientist Jonas Mockus, in his paper “The Application of Bayesian Methods for Seeking the Extremum”, discussed how to use Bayesian methods to find the extreme value of a function under various uncertain conditions. In his paper, Mockus first proposed the Expected Improvement principle (EI), which is one of the core sampling strategies of Bayesian optimization. This criterion balances exploration while optimizing the function efficiently by maximizing the expected improvement. Because of the usefulness and profound impact of this principle, Jonas Mockus is widely regarded as the founder of Bayesian optimization. Although Expected Improvement principle (IE) is one of the earliest proposed core sampling strategies for Bayesian optimization, it is not the only one, with the development of modern society, we also have Probability of Improvement (PI), or Upper Confidence Bound (UCB) and so on.

From Theory to Practice

In the 1990s, Bayesian optimization began to gradually transition from pure theory to real-world applications. In 1998, Donald R. Jones and his coworkers published a paper titled “Gaussian Optimization”. In this paper, they proposed the Gaussian Process(GP) and elaborated on the Expected Improvement principle(EI) proposed by Jonas Mockus in 1978. Through the efforts of Donald R. Jones and his colleagues, Bayesian Optimization began to shine in the fields like computers science and engineering. However, the computational complexity of Bayesian optimization for the computing power at that time still affected its development to a large extent.

In the 21st century, with the gradual rise of artificial intelligence and bionic robots, Bayesian optimization has been widely used in mechanical learning and deep learning, and has become an important tool for Hyperparameter Tuning. Companies such as Google, Facebook and OpenAI have added Bayesian optimization to their deep learning frameworks to improve search efficiency. However, Bayesian optimization still faces many challenges, for example, because of the use of Gaussian Process as a proxy model for optimization, when there is a lot of data, the training of Gaussian Process will be very slow and the computational cost is very high. This makes it difficult for this optimization method to work well in more complex drug development and medical experiments.

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