What is the parameter of optimize_acqf

[makinzm]

1. What I would like to do

• I would like to understand what optimize_acqf does, especially num_restarts , raw_samples and the flow.
• Now, I think I may understand the rough abstract but don't have confidence. I would appreciate it, If you could teach me.

2. What I did

• I read this paper roughly :
  • Balandat, Maximilian, et al. "BoTorch: A Framework for Efficient Monte-Carlo Bayesian Optimization." arXiv preprint arXiv:1910.06403 (2019). (https://arxiv.org/abs/1910.06403)
• I read this issue :
  • What is the role of the 'raw samplers' in optimize_acqf? What is the role of the 'raw samplers' in optimize_acqf? #366
  • (What is the role of the 'raw samplers' in optimize_acqf? #366)

3. How I understand now

If I use the following code :

candidate, _ = optimize_acqf(
    aq, bounds=bounds, q=q,
    num_restarts=num_restarts,
    raw_samples=raw_samples,
)

I think the flow is the following roughtly:

1. Sample $N$(=raw_samples) (in bounds) $\xi_i\sim f(x^q|\mathcal{D})$ by fixing the random variable by SSA and using MCMC.

2. Compute the acquisition function value $\hat{\alpha}(\xi)=\frac{1}{N}\sum\alpha(\xi_i)$ by using $N$ samples.

3. SGD Starts point is $\xi$ and the loop $N'$(=num_restarts) SGD starts ($\xi_{i,j+1}=\xi_{i,j}-\frac{1}{N}\sum\nabla \alpha(\xi_{i,j})$).

4. get $\xi$ and $\hat{\alpha}(\xi)$

I think it is not correct , but I cannot what is right.

I would appreciate it, If you could teach me.

Thank you for reading.

[Balandat]

So the flow is

1. Sample (using QMC) raw_samples points X in bounds.
2. Compute the acquisition function value Z := alpha(X) for each of these samples.
3. Apply a Boltzmann sampling heuristic (this one) that selects num_restarts points from X (without replacement) with probability proportional to exp(eta * Z), where Z = (Y - mean(Y)) / std(Y) and eta is a temperature parameter.
4. Use the points that were picked by the heuristic as initial conditions for multi-start L-BFGS-B optimization.

[makinzm]

Thank you for teaching me.
I will re-think this flow.