  We study a variant of causal contextual bandits where the context is chosen
based on an initial intervention chosen by the learner. At the beginning of
each round, the learner selects an initial action, depending on which a
stochastic context is revealed by the environment. Following this, the learner
then selects a final action and receives a reward. Given $T$ rounds of
interactions with the environment, the objective of the learner is to learn a
policy (of selecting the initial and the final action) with maximum expected
reward. In this paper we study the specific situation where every action
corresponds to intervening on a node in some known causal graph. We extend
prior work from the deterministic context setting to obtain simple regret
minimization guarantees. This is achieved through an instance-dependent causal
parameter, $\lambda$, which characterizes our upper bound. Furthermore, we
prove that our simple regret is essentially tight for a large class of
instances. A key feature of our work is that we use convex optimization to
address the bandit exploration problem. We also conduct experiments to validate
our theoretical results, and release our code at our project GitHub repository:
https://github.com/adaptiveContextualCausalBandits/aCCB.
