  Multi-armed bandits (MAB) and causal MABs (CMAB) are established frameworks
for decision-making problems. The majority of prior work typically studies and
solves individual MAB and CMAB in isolation for a given problem and associated
data. However, decision-makers are often faced with multiple related problems
and multi-scale observations where joint formulations are needed in order to
efficiently exploit the problem structures and data dependencies. Transfer
learning for CMABs addresses the situation where models are defined on
identical variables, although causal connections may differ. In this work, we
extend transfer learning to setups involving CMABs defined on potentially
different variables, with varying degrees of granularity, and related via an
abstraction map. Formally, we introduce the problem of causally abstracted MABs
(CAMABs) by relying on the theory of causal abstraction in order to express a
rigorous abstraction map. We propose algorithms to learn in a CAMAB, and study
their regret. We illustrate the limitations and the strengths of our algorithms
on a real-world scenario related to online advertising.
