# Multi-Agent Reinforcement Learning: Analysis and Application

With the increasing availability of data and the rise of networked systems such as autonomous vehicles, drones, and smart girds, the application of data-driven, machine learning methods with multi-agents systems have become an important topic. In particular, reinforcement learning has gained a lot of popularity due to its similarities with optimal control, with the potential of allowing us to develop optimal control systems using only observed data and without the need for a model of a system's state dynamics. In this thesis work, we explore the application of reinforcement learning with multi-agents systems, which is known as multi-agent reinforcement learning (MARL). We have developed algorithms that address some challenges in the cooperative setting of MARL. We have also done work on better understanding the convergence guarantees of some known multi-agent reinforcement learning algorithms, which combine reinforcement learning with distributed consensus methods. And, with the aim of making MARL better suited to real-world problems, we have also developed algorithms to address some practical challenges with MARL and we have applied MARL on a real-world problem.

In the first part of this thesis, we focus on developing algorithms to address some open problems in MARL. One of these challenges is learning with output feedback, which is known as partial observability in the reinforcement learning literature. One of the main assumptions of reinforcement learning in the singles agent case is that the agent can fully observe the state of the plant it is controlling (we note the “plant" is often referred to as the “environment" in the reinforcement learning literature. We will use these terms interchangeably). In the single agent case this assumption can be reasonable since it only requires one agent to fully observe its environment. In the multi-agent setting, however, this assumption would require all agents to fully observe the state and furthermore since each agent could affect the plant (or environment) with its actions, the assumption would also require that agent's know the actions of other agents. We have also developed algorithms to address practical issues that may arise when applying reinforcement learning (RL) or MARL on large-scale real-world systems. One such algorithm is a distributed reinforcement learning algorithm that allows us to learn in cases where the states and actions are both continuous and of large dimensionality, which is the case for many real-world applications. Without the ability to handle continuous states and actions, many algorithms require discretization, which with high dimensional systems can become impractical. We have also developed a distributed reinforcement learning algorithm that addresses data scalability of RL. By data scalability we mean how to learn from a very large dataset that cannot be efficiently processed by a single agent with limited resources.

In the second part of this thesis, we provide a finite-sample analysis of some distributed reinforcement learning algorithms. By finite-sample analysis, we mean we provide an upper bound on the squared error of the algorithm for a given iteration of the algorithm. Or equivalently, since each iteration uses one data sample, we provide an upper bound of the squared error for a given number of data samples used. This type of analysis had been missing in the MARL literature, where most works on MARL have only provided asymptotic results for their proposed algorithms, which only tells us how the algorithmic error behaves as the number of samples used goes to infinity.

The third part of this thesis focuses on applications with real-world systems. We have explored a real-world problem, namely transactive energy systems (TES), which can be represented as a multi-agent system. We have applied various reinforcement learning algorithms with the aim of learning an optimal control policy for this system. Through simulations, we have compared the performance of these algorithms and have illustrated the effect of partial observability (output feedback) when compared to full state feedback.

In the last part we present some other work, specifically we present a distributed observer that aims to address learning with output feedback by estimating the state. The proposed algorithm is designed so that we do not require a complete model of state dynamics, and instead we use a parameterized model where the parameters are estimated along with the state.