Contextual multi-armed bandits with structured payoffs
Qureshi, Muhammad Anjum
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Multi-Armed Bandit (MAB) problems model sequential decision making under uncertainty. In traditional MAB, the learner selects an arm in each round, and then, observes a random reward from the arm’s unknown reward distribution. In the end, the goal is to maximize the cumulative reward by learning to select optimal arms as much as possible. In the contextual MAB—an extension to MAB—the learner observes a context (side-information) in the beginning of each round, selects an arm, and then, observes a random reward whose distribution depends on both the arriving context and the chosen arm. Another MAB variant, called unimodal MAB, assumes that the expected reward exhibits a unimodal structure over the arms, and tries to locate the arm with the “peak” reward by learning the direction of increase of the expected reward. In this thesis, we consider an extension to unimodal MAB called contextual unimodal MAB, and demonstrate that it is a powerful tool for designing Artificial Intelligence (AI)- enabled radios by utilizing the special structure of the dependence of the reward to contexts and arms of the wireless environment. While AI-enabled radios are expected to enhance the spectral efficiency of 5th generation (5G) millimeter wave (mmWave) networks by learning to optimize network resources, allocating resources over the mmWave band is extremely challenging due to rapidly-varying channel conditions. We consider several resource allocation problems in this thesis under various design possibilities for mmWave radio networks under unknown channel statistics and without any channel state information (CSI) feedback: i) dynamic rate selection for an energy harvesting transmitter, ii) dynamic power allocation for heterogeneous applications, and iii) distributed resource allocation in a multi-user network. All of these problems exhibit structured payoffs which are unimodal functions over partially ordered arms (transmission parameters) as well as unimodal or monotone functions over partially ordered contexts (side-information). Structure over arms helps in reducing the number of arms to be explored, while structure over contexts helps in using past information from nearby contexts to make better selections. We formalize dynamic adaptation of transmission parameters as a structured MAB, and propose frequentist and Bayesian online learning algorithms. We show that both approaches yield logarithmic in time regret. We also investigate dynamic rate and channel adaptation in a cognitive radio network serving heterogeneous applications under dynamically varying channel availability and rate constraints. We formalize the problem as a Bayesian learning problem, and propose a novel learning algorithm which considers each rate-channel pair as a two-dimensional action. The set of available actions varies dynamically over time due to variations in primary user activity and rate requirements of the applications served by the users. Additionally, we extend the work to cater to thescenario when the arms belong to a continuous interval as well as the contexts. Finally, we show via simulations that our algorithms significantly improve the performance in the aforementioned radio resource allocation problems.
Cognitive radio networks