Supervisors info:
Αντώνης Οικονόμου, Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Summary:
Reinforcement Learning is one of the most important and up-and-coming categories of Machine Learning, due to the great flexibility of its algorithms, in managing large state spaces and unknown transition probabilities, to problems modeled as Markov Decision Processes. The aim of this postgraduate Thesis is to present the basic principles of Reinforcement Learning, emphasizing both the necessary mathematical framework in which it is structured, and algorithms, many of which are implemented in R software for better understanding. Although the highly technical mathematical proofs are absent in the light of an introduction, an attempt has been made to include those which are mainly based on arguments of Probability Theory, that one can encounter in an undergraduate level of studies.
This Thesis is structured in 3 Chapters. Chapter 1, is a brief overview of the 3 main types of Machine Learning: Supervised Learning, Unsupervised Learning, and Reinforcement Learning, so that the reader can distinguish what the goal of each type is, and in which cases each of them is more appropriate. In Chapter 2, an introduction is made to a simplified subset of the Reinforcement Learning Problem also known as the Multi-Armed Bandit Problem, a key feature of which is that the set of possible actions at each time step remains unchanged. In addition, at the end of the Chapter, the algorithms formulated are implemented in the R software, in order to experimentally verify their theoretical properties.
Lastly, Chapter 3 is devoted to the general context of Reinforcement Learning where each state is characterized by its own set of actions. Having clearly articulated critical concepts such as the Bellman Equations, optimal value functions, and optimal policies, we will proceed to formulate some of the most important Reinforcement Learning Algorithms that approach optimal policies, both in the case of known and unknown transition probabilities.
Keywords:
Reinforcement Learning, Machine Learning, Statistics, Artificial Intelligence
