  A standard assumption in contextual multi-arm bandit is that the true context
is perfectly known before arm selection. Nonetheless, in many practical
applications (e.g., cloud resource management), prior to arm selection, the
context information can only be acquired by prediction subject to errors or
adversarial modification. In this paper, we study a contextual bandit setting
in which only imperfect context is available for arm selection while the true
context is revealed at the end of each round. We propose two robust arm
selection algorithms: MaxMinUCB (Maximize Minimum UCB) which maximizes the
worst-case reward, and MinWD (Minimize Worst-case Degradation) which minimizes
the worst-case regret. Importantly, we analyze the robustness of MaxMinUCB and
MinWD by deriving both regret and reward bounds compared to an oracle that
knows the true context. Our results show that as time goes on, MaxMinUCB and
MinWD both perform as asymptotically well as their optimal counterparts that
know the reward function. Finally, we apply MaxMinUCB and MinWD to online edge
datacenter selection, and run synthetic simulations to validate our theoretical
analysis.
