Optimal data driven resource allocation under multi-armed bandit observations
本文提出了首个在资源约束下多臂老虎机模型的渐近最优策略，推导了可行策略的遗憾下界，并构造了达到该下界的策略，适用于正态分布和离散分布情形。
Abstract This paper introduces the first asymptotically optimal strategy for a multi armed bandit (MAB) model under side constraints. The side constraints model situations in which bandit activations are limited by the availability of certain resources that are replenished at a constant rate. The main result involves the derivation of an asymptotic lower bound for the regret of feasible uniformly fast policies and the construction of policies that achieve this lower bound, under pertinent conditions. Further, we provide the explicit form of such policies for the case in which the unknown distributions are Normal with unknown means and known variances, for the case of Normal distributions with unknown means and unknown variances and for the case of arbitrary discrete distributions with finite support.