The Restless Hidden Markov Bandit with Linear Rewards and Side Information
This provides a practical solution for decision-making under uncertainty in high-dimensional bandit problems, though it is incremental by extending existing Markovian bandit frameworks with structural side information.
The paper tackles the hidden Markovian bandit problem with linear rewards by introducing a model where the state is unknown and includes both common Markovian and arm-specific i.i.d. components, resulting in an algorithm that achieves logarithmic regret and independence from the action space's extreme points in high dimensions.
In this paper we present a model for the hidden Markovian bandit problem with linear rewards. As opposed to current work on Markovian bandits, we do not assume that the state is known to the decision maker before making the decision. Furthermore, we assume structural side information where the decision maker knows in advance that there are two types of hidden states; one is common to all arms and evolves according to a Markovian distribution, and the other is unique to each arm and is distributed according to an i.i.d. process that is unique to each arm. We present an algorithm and regret analysis to this problem. Surprisingly, we can recover the hidden states and maintain logarithmic regret in the case of a convex polytope action set. Furthermore, we show that the structural side information leads to expected regret that does not depend on the number of extreme points in the action space. Therefore, we obtain practical solutions even in high dimensional problems.