  Multi-armed bandit problems provide a framework to identify the optimal
intervention over a sequence of repeated experiments. Without additional
assumptions, minimax optimal performance (measured by cumulative regret) is
well-understood. With access to additional observed variables that d-separate
the intervention from the outcome (i.e., they are a d-separator), recent
"causal bandit" algorithms provably incur less regret. However, in practice it
is desirable to be agnostic to whether observed variables are a d-separator.
Ideally, an algorithm should be adaptive; that is, perform nearly as well as an
algorithm with oracle knowledge of the presence or absence of a d-separator. In
this work, we formalize and study this notion of adaptivity, and provide a
novel algorithm that simultaneously achieves (a) optimal regret when a
d-separator is observed, improving on classical minimax algorithms, and (b)
significantly smaller regret than recent causal bandit algorithms when the
observed variables are not a d-separator. Crucially, our algorithm does not
require any oracle knowledge of whether a d-separator is observed. We also
generalize this adaptivity to other conditions, such as the front-door
criterion.
