  We study the sequential resource allocation problem where a decision maker
repeatedly allocates budgets between resources. Motivating examples include
allocating limited computing time or wireless spectrum bands to multiple users
(i.e., resources). At each timestep, the decision maker should distribute its
available budgets among different resources to maximize the expected reward, or
equivalently to minimize the cumulative regret. In doing so, the decision maker
should learn the value of the resources allocated for each user from feedback
on each user's received reward. For example, users may send messages of
different urgency over wireless spectrum bands; the reward generated by
allocating spectrum to a user then depends on the message's urgency. We assume
each user's reward follows a random process that is initially unknown. We
design combinatorial multi-armed bandit algorithms to solve this problem with
discrete or continuous budgets. We prove the proposed algorithms achieve
logarithmic regrets under semi-bandit feedback.
