This paper studies an instance of the multi-armed bandit (MAB) problem, specifically where several causal MABs operate chronologically in the same dynamical system. Practically the reward distribution of each bandit is governed by the same non-trivial dependence structure, which is a dynamic causal model. Dynamic because we allow for each causal MAB to depend on the preceding MAB and in doing so are able to transfer information between agents. Our contribution, the Chronological Causal Bandit (CCB), is useful in discrete decision-making settings where the causal effects are changing across time and can be informed by earlier interventions in the same system. In this paper, we present some early findings of the CCB as demonstrated on a toy problem.

Visual representation of model and method.

1. DCBO takes continuous actions (interventions) in a dynamical system modelled as a dynamic causal diagram.
2. CCB (this paper) takes discrete actions (interventions) in a dynamical system modelled as a dynamic causal diagram.

To instal this package; clone this repo and install using

pip install -e .

If you are having trouble with graphviz using a MacOS M1 machine, you may need to install it using the instructions found here:

python3 -m pip install \
                --config-settings="--global-option=build_ext" \
                --config-settings="--global-option=-I$(brew --prefix graphviz)/include/" \
                --config-settings="--global-option=-L$(brew --prefix graphviz)/lib/" \
                pygraphviz

This work was published in this paper.

This implementation builds heavily upon the original SCM-MAB code.

A comprehensive example can be found in notebooks/demo.ipynb or if you really want to hit the ground running, you can use the following code snippet:

from src.examples.example_setup import setup_DynamicIVCD
from src.ccb import CCB

params = setup_DynamicIVCD()
m = CCB(**params)
m.run()

If you use this code in your research, please consider citing:

@inproceedings{CCB,
 author = {Dhir, Neil},
 booktitle = {NeurIPS 2021 workshop Causal Inference Challenges in Sequential Decision Making: Bridging Theory and Practice}
 title = {Chronological Causal Bandits}
 volume = {35},
 year = {2021}
}

This repository is MIT licensed, as found in the LICENSE file.