Bayesian active learning of failure or feasibility regions#

When designing a system it is important to identify design parameters that may affect the reliability of the system and cause failures, or lead to unsatisfactory performance. Consider designing a communication network that for some design parameters would lead to too long delays for users. A designer of the system would then decide what is the maximum acceptable delay and want to identify a failure region in the parameter space that would lead to longer delays., or conversely, a feasible region with safe performance.

When evaluating the system is expensive (e.g. lengthy computer simulations), identification of the failure region needs to be performed with a limited number of evaluations. Traditional Monte Carlo based methods are not suitable here as they require too many evaluations. Bayesian active learning methods, however, are well suited for the task. Here we show how Trieste can be used to identify failure or feasible regions with the help of acquisition functions designed with this goal in mind.

%matplotlib inline

# silence TF warnings and info messages, only print errors
import os

os.environ["TF_CPP_MIN_LOG_LEVEL"] = "3"

import tensorflow as tf


import numpy as np


A toy problem#

Throughout the tutorial we will use the standard Branin function as a stand-in for an expensive-to-evaluate system. We create a failure region by thresholding the value at 80, space with value above 80 is considered a failure region. This region needs to be learned as efficiently as possible by the active learning algorithm.

Note that if we are interested in a feasibility region instead, it is simply a complement of the failure region, space with the value below 80.

We illustrate the thresholded Branin function below, you can note that above the threshold of 80 there are no more values observed.

from trieste.objectives import Branin
from trieste.experimental.plotting import plot_function_plotly

branin = Branin.objective
search_space = Branin.search_space

# threshold is arbitrary, but has to be within the range of the function
threshold = 80.0

# define a modified branin function
def thresholded_branin(x):
    y = np.array(branin(x))
    y[y > threshold] = np.nan
    return tf.convert_to_tensor(y.reshape(-1, 1), x.dtype)

# illustrate the thresholded branin function
fig = plot_function_plotly(
    thresholded_branin, search_space.lower, search_space.upper