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Factorial design with empirical Bayes and Thompson Sampling

This tutorial illustrates how to run a factorial experiment. In such an experiment, each parameter (factor) can be assigned one of multiple discrete values (levels). A full-factorial experiment design explores all possible combinations of factors and levels.

For instance, consider a banner with a title and an image. We are considering two different titles and three different images. A full-factorial experiment will compare all 2*3=6 possible combinations of title and image, to see which version of the banner performs the best.

In this example, we first run an exploratory batch to collect data on all possible combinations. Then we use empirical Bayes to model the data and shrink noisy estimates toward the mean. Next, we use Thompson Sampling to suggest a set of arms (combinations of factors and levels) on which to collect more data. We repeat the process until we have identified the best performing combination(s).

In [1]:
import numpy as np
import pandas as pd
import sklearn as skl
from typing import Dict, Optional, Tuple, Union
from ax import Arm, ChoiceParameter, Models, ParameterType, SearchSpace, Experiment, OptimizationConfig, Objective
from ax.plot.scatter import plot_fitted
from ax.utils.notebook.plotting import render, init_notebook_plotting
from ax.utils.stats.statstools import agresti_coull_sem
In [2]:
init_notebook_plotting()

[INFO 12-16 17:58:25] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell.