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Maybe one usage could be in Thompson sampling. You're trying to guess the maximum of a function, so you sample a random function from the GP, find its maximum,
by man-and-laptop 8y ago
Maybe one usage could be in Thompson sampling. You're trying to guess the maximum of a function, so you sample a random function from the GP, find its maximum, test it out, get back a y value, and then update your GP.
Maybe that's what the above comment meant by Bayesian optimisation.
- Zephyr314 8y agoThis is close to how Bayesian optimization usually works, except you can sample many functions from the GP at once and apply different "acquisition functions" instead of just looking for the maximum. Classic examples are "Expected Improvement" (which point is expected to beat the current best point by the most) or "Probability of Improvement" (which point has the best odds of beating the current best point). You then sample and repeat. I gave a high level talk that walks through this here [0]. A deeper dive into acquisition functions can be found here [1] and here [2]. [0]: https://www.youtube.com/watch?v=J6UcAdH54RE&list=PLbSwfqjMfjGc6Z-WP9VYBCZsHHyOImabQ https://www.youtube.com/watch?v=J6UcAdH54RE&list=PLbSwfqjMfj... [1]: https://sigopt.com/blog/expected-improvement-vs-knowledge-gradient/ https://sigopt.com/blog/expected-improvement-vs-knowledge-gr... [2]: https://sigopt.com/blog/clustering-applied-to-acquisition-functions/ https://sigopt.com/blog/clustering-applied-to-acquisition-fu... (edit: fixed a typo)