Prior Optimizers#
This section concerns optimizers that utilize priors to guide the search process. Priors are explained in detail here.
1 PiBO#
PiBO (see paper) is an extension of Bayesian Optimization (BO) that uses a specific acquisition function that incorporates Priors, by including a Prior-factor that decays over time. This way, the optimizer first relies on the Prior knowledge, before shifting focus to the data acquired during the optimization process.
The altered acquisition function takes this form:
where after \(n\) evaluations, the Prior-function \(\pi(\boldsymbol{x})\) is decayed by the factor \(\beta/n\) and multiplied with the acquisition function \(\alpha(\boldsymbol{x},\mathcal{D}_n)\). In our PiBO implementation, we use Expected Improvement as the acquisition function.
The following illustration from the PiBO-paper shows the influence of a well-chosen and a bad, decaying Prior on the optimization process:
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| Left: A well-located Prior influences the acquisition function leading to quicker convergence and even more exploration. Right: An off-center Prior slows down, but does not prevent convergence. (Image Source: PiBO-paper, Jan 27, 2025) |
In both cases, the optimization process uses the additional information provided by the Prior to arrive at the solution, however, the bad Prior (right) results in a slower convergence to the optimum.
Practical Tips
TODO Write about what to consider when using PiBO in NePS.
Info
PiBO is chosen as the default optimizer in NePS when there is only Prior, but no Multi-Fidelity information available.
For optimizers using both Priors and Multi-Fidelity, please refer here.