  We consider the linear contextual multi-class multi-period packing problem
(LMMP) where the goal is to pack items such that the total vector of
consumption is below a given budget vector and the total value is as large as
possible. We consider the setting where the reward and the consumption vector
associated with each action is a class-dependent linear function of the
context, and the decision-maker receives bandit feedback. LMMP includes linear
contextual bandits with knapsacks and online revenue management as special
cases. We establish a new estimator which guarantees a faster convergence rate,
and consequently, a lower regret in such problems. We propose a bandit policy
that is a closed-form function of said estimated parameters. When the contexts
are non-degenerate, the regret of the proposed policy is sublinear in the
context dimension, the number of classes, and the time horizon $T$ when the
budget grows at least as $\sqrt{T}$. We also resolve an open problem posed by
Agrawal & Devanur (2016) and extend the result to a multi-class setting. Our
numerical experiments clearly demonstrate that the performance of our policy is
superior to other benchmarks in the literature.
