Dzhoha A. Sequential resource allocation in a stochastic environment

The focus of this dissertation study lies in the asymptotic analysis of policies within the context of sequential resource allocation tasks in a stochastic environment. This environment is characterized by a collection of beta distributions with unknown parameters, resembling a stochastic multi-armed bandit model. The central aim of this study is twofold: firstly, to conduct an asymptotic analysis of policies and adapt algorithms tailored to the specific environment; and secondly, to explore the impact of contextual information on the effectiveness of these strategies. The problem at hand pertains to decision-making under uncertainty, involving a sequential interaction between a decision-maker (referred to as the agent) and the stochastic environment. This interaction unfolds over a finite time horizon. At each step, the agent selects an action from a predefined set and, in return, receives a reward from the environment. The agent’s objective is to consistently select actions that maximize the cumulative reward over the entire horizon. The primary challenge in this task is the lack of prior knowledge regarding the parameters governing the reward process.