Is it possible to pick more than 1 sample point in each iteration of bayesian optimisation? I want to use Bayesian optimisation for my project and I plan to build a closed-loop system, such that there is a model, robot to conduct experiments, measurement of experimental data which updates the model and continues to iterate until the optimise output is produced.
The experiment part involves a liquid handling robot that can produce +50 different components for the experiment in a high throughput manner.
I have been reading a lot about Bayesian optimisation and for successive iterations, it only picks 1 point to explore/exploit. I wanted to ask if it is possible to select more than 1  point,such as 20, for successive experiments as I want to utilise the capability of the liquid handling robot as much as possible?
Thanks.
 A: Yes, you can. There are several Bayesian optimization algorithms, but let's use the Gaussian process as an example as it is the most popular one. The Gaussian process learns to approximate the distribution of the functions that you want to optimize. Next, given the learned distribution you have some optimization criteria, the acquisition function, that is used to pick a candidate to check next. The candidate is evaluated "in the wild" and the result is fed to the Gaussian process so it can update with new data and generate a new candidate.
The acquisition function is something like upper confidence bound, expected improvement, probability of improvement, etc, or out can use Thompson sampling (Russo et al, 2017) and pick the candidate at random, with the probability proportional to the probabilities learned by the Gaussian process. Nothing prohibits you from picking the $k$ highest values according to the acquisition function or sampling $k$ values using Thompson sampling, instead of a single value. Same, you can do a Bayesian update of the learned distribution with multiple values, not only with a single value.
The downside is that by checking a single value you can update your knowledge (the learned distribution) instantly, while with many values you update it in batch. What this means is that in exploration-exploitation you focus more on exploration. It can have pros and cons, with more data you gain more knowledge about the explored region of the distribution. On another hand, it can make you slower as you may unnecessarily check all those scenarios while checking a single one might be enough to learn that it was a bad idea. Using Thompson sampling in such a case would enable you to be more explorative.
