  We address the problem of learning in an online setting where the learner
repeatedly observes features, selects among a set of actions, and receives
reward for the action taken. We provide the first efficient algorithm with an
optimal regret. Our algorithm uses a cost sensitive classification learner as
an oracle and has a running time $\mathrm{polylog}(N)$, where $N$ is the number
of classification rules among which the oracle might choose. This is
exponentially faster than all previous algorithms that achieve optimal regret
in this setting. Our formulation also enables us to create an algorithm with
regret that is additive rather than multiplicative in feedback delay as in all
previous work.
