  In many fields such as digital marketing, healthcare, finance, and robotics,
it is common to have a well-tested and reliable baseline policy running in
production (e.g., a recommender system). Nonetheless, the baseline policy is
often suboptimal. In this case, it is desirable to deploy online learning
algorithms (e.g., a multi-armed bandit algorithm) that interact with the system
to learn a better/optimal policy under the constraint that during the learning
process the performance is almost never worse than the performance of the
baseline itself. In this paper, we study the conservative learning problem in
the contextual linear bandit setting and introduce a novel algorithm, the
Conservative Constrained LinUCB (CLUCB2). We derive regret bounds for CLUCB2
that match existing results and empirically show that it outperforms
state-of-the-art conservative bandit algorithms in a number of synthetic and
real-world problems. Finally, we consider a more realistic constraint where the
performance is verified only at predefined checkpoints (instead of at every
step) and show how this relaxed constraint favorably impacts the regret and
empirical performance of CLUCB2.
