BOTier: Multi-Objective Bayesian Optimization with Tiered Composite Objectives

Next to the primary optimization objectives, scientific optimization problems often contain a series of subordinate objectives, which can be expressed as preferences over either the outputs of an experiment, or the experiment inputs (e.g. to minimize the experimental cost). BoTier provides a flexible composite objective to express hierarchical user preferences over both experiment inputs and outputs. The details are described in the corresponding paper.

botieris a lightweight plug-in for botorch, and can be readily integrated with the botorch ecosystem for Bayesian Optimization.

Installation

botier can be readily installed from the Python Package Index (PyPI).

pip install botier

Usage

The following code snippet shows a minimal example of using the hierarchical scalarization objective

In this example, our primary goal is to maximize the $\sin(2\pi x)$ function to a value of min. 0.5. If this is satisfied, the value of x should be minimized.

import torch
from gpytorch.mlls import ExactMarginalLogLikelihood
from botorch.models import SingleTaskGP
from botorch.fit import fit_gpytorch_mll
from botorch.acquisition.monte_carlo import qExpectedImprovement
from botorch.optim import optimize_acqf

import numpy as np
from matplotlib import pyplot as plt

from botier import AuxiliaryObjective, HierarchyScalarizationObjective

# define the 'auxiliary objectives' that eventually make up the overall optimization objective
objectives = [
    AuxiliaryObjective(output_index=0, abs_threshold=0.5, upper_bound=1.0, lower_bound=-1.0),
    AuxiliaryObjective(maximize=False, calculation=lambda y, x: x[..., 0], abs_threshold=0.0, lower_bound=0.0, upper_bound=1.0),
]
global_objective = HierarchyScalarizationObjective(objectives, k=1E2, normalized_objectives=True)

# generate some training data
train_x = torch.rand(5, 1).double()
train_y = torch.sin(2 * torch.pi * train_x)

budget = 20
for n in range(budget):
    
    # fit a simple BoTorch surrogate model
    surrogate = SingleTaskGP(train_x, train_y)
    mll = ExactMarginalLogLikelihood(surrogate.likelihood, surrogate)
    fit_gpytorch_mll(mll)

    # instantiate a BoTorch Monte-Carlo acquisition function using the botier.HierarchyScalarizationObjective as the 'objective' argument
    acqf = qExpectedImprovement(
        model=surrogate,
        objective=global_objective,
        best_f=torch.max(train_y)
    )

    new_candidate, _ = optimize_acqf(acqf, bounds=torch.tensor([[0.0], [1.0]]), q=1, num_restarts=5, raw_samples=512)


    # evaluate the global objective
    new_candidate_y = torch.sin(2 * torch.pi * new_candidate)

    # update the training points
    train_x = torch.cat([train_x, new_candidate])
    train_y = torch.cat([train_y, new_candidate_y])

    print(f"iteration {n + 1}: candidate={new_candidate.item()}, objective={new_candidate_y.item()}")


plt.plot(np.linspace(0, 1, 100), torch.sin(2 * torch.pi * torch.linspace(0, 1, 100)), label="true function", zorder=0)
plt.scatter(train_x.numpy(), train_y.numpy(), s=25, marker="x", cmap="spring", c=np.arange(len(train_x)), label="selected points")
plt.colorbar()
plt.legend()
plt.show()

For more detailed usage examples, see examples.

Contributors

Felix Strieth-Kalthoff (@felix-s-k), Mohammad Haddadnia (@mohaddadnia), Leonie Grashoff (@lgrashoff)