  We study online learning for optimal allocation when the resource to be
allocated is time. %Examples of possible applications include job scheduling
for a computing server, a driver filling a day with rides, a landlord renting
an estate, etc. An agent receives task proposals sequentially according to a
Poisson process and can either accept or reject a proposed task. If she accepts
the proposal, she is busy for the duration of the task and obtains a reward
that depends on the task duration. If she rejects it, she remains on hold until
a new task proposal arrives. We study the regret incurred by the agent, first
when she knows her reward function but does not know the distribution of the
task duration, and then when she does not know her reward function, either.
This natural setting bears similarities with contextual (one-armed) bandits,
but with the crucial difference that the normalized reward associated to a
context depends on the whole distribution of contexts.
