Convergent learning algorithms for potential games with unknown noisy rewards

In this paper, we address the problem of convergence to Nash equilibria in games with rewards that are initially unknown and which must be estimated over time from noisy observations. These games arise in many real-world applications, whenever rewards for actions cannot be prespecified and must be learned on-line. Standard results in game theory, however, do not consider such settings. Specifically, using results from stochastic approximation and differential inclusions, we prove the convergence of variants of fictitious play and adaptive play to Nash equilibria in potential games and weakly acyclic games, respectively. These variants all use a multi-agent version of Q-learning to estimate the reward functions and a novel form of the e-greedy decision rule to select an action. Furthermore, we derive e-greedy decision rules that exploit the sparse interaction structure encoded in two compact graphical representations of games, known as graphical and hypergraphical normal form, to improve the convergence rate of the learning algorithms. The structure captured in these representations naturally occurs in many distributed optimisation and control applications. Finally, we demonstrate the efficacy of the algorithms in a simulated ad hoc wireless sensor network management problem

Large-scale Multi-agent Decision-making Using Mean Field Game Theory and Reinforcement Learning

The Multi-agent system (MAS) optimal control problem is a recently emerging research topic that benefits industries such as robotics, communication, and power systems. The traditional MAS control algorithms are developed by extending the single agent optimal controllers, requiring heavy information exchange. Moreover, the information exchanged within the MAS needs to be used to compute the optimal control resulting in the coupling between the computational complexity and the agent number. With the increasing need for large-scale MAS in practical applications, the existing MAS optimal control algorithms suffer from the ``curse of dimensionality" problem and limited communication resources. Therefore, a new type of MAS optimal control framework that features a decentralized and computational friendly decision process is desperately needed. To deal with the aforementioned problems, the mean field game theory is introduced to generate a decentralized optimal control framework named the Actor-critic-mass (ACM). Moreover, the ACM algorithm is improved by eliminating constraints such as homogeneous agents and cost functions. Finally, the ACM algorithm is utilized in two applications

Optimization and Communication in UAV Networks

UAVs are becoming a reality and attract increasing attention. They can be remotely controlled or completely autonomous and be used alone or as a fleet and in a large set of applications. They are constrained by hardware since they cannot be too heavy and rely on batteries. Their use still raises a large set of exciting new challenges in terms of trajectory optimization and positioning when they are used alone or in cooperation, and communication when they evolve in swarm, to name but a few examples. This book presents some new original contributions regarding UAV or UAV swarm optimization and communication aspects

Graph Attention-based Reinforcement Learning for Trajectory Design and Resource Assignment in Multi-UAV Assisted Communication

In the multiple unmanned aerial vehicle (UAV)- assisted downlink communication, it is challenging for UAV base stations (UAV BSs) to realize trajectory design and resource assignment in unknown environments. The cooperation and competition between UAV BSs in the communication network leads to a Markov game problem. Multi-agent reinforcement learning is a significant solution for the above decision-making. However, there are still many common issues, such as the instability of the system and low utilization of historical data, that limit its application. In this paper, a novel graph-attention multi-agent trust region (GA-MATR) reinforcement learning framework is proposed to solve the multi-UAV assisted communication problem. Graph recurrent network is introduced to process and analyze complex topology of the communication network, so as to extract useful information and patterns from observational information. The attention mechanism provides additional weighting for conveyed information, so that the critic network can accurately evaluate the value of behavior for UAV BSs. This provides more reliable feedback signals and helps the actor network update the strategy more effectively. Ablation simulations indicate that the proposed approach attains improved convergence over the baselines. UAV BSs learn the optimal communication strategies to achieve their maximum cumulative rewards. Additionally, multi-agent trust region method with monotonic convergence provides an estimated Nash equilibrium for the multi-UAV assisted communication Markov game.Comment: 13 page

Human-Machine Cooperative Decision Making

The research reported in this thesis focuses on the decision making aspect of human-machine cooperation and reveals new insights from theoretical modeling to experimental evaluations: Two mathematical behavior models of two emancipated cooperation partners in a cooperative decision making process are introduced. The model-based automation designs are experimentally evaluated and thereby demonstrate their benefits compared to state-of-the-art approaches

Human-Machine Cooperative Decision Making

Diese Dissertation beschäftigt sich mit der gemeinsamen Entscheidungsfindung in der Mensch-Maschine-Kooperation und liefert neue Erkenntnisse, welche von der theoretischen Modellierung bis zu experimentellen Untersuchungen reichen. Zunächst wird eine methodische Klassifikation bestehender Forschung zur Mensch-Maschine-Kooperation vorgenommen und der Forschungsfokus dieser Dissertation mithilfe eines vorgestellten Taxonomiemodells der Mensch-Maschine-Kooperation, dem Butterfly-Modell, abgegrenzt. Darauffolgend stellt die Dissertation zwei mathematische Verhaltensmodelle der gemeinsamen Entscheidungsfindung von Mensch und Maschine vor: das Adaptive Verhandlungsmodell und den n-stufigen War of Attrition. Beide modellieren den Einigungsprozess zweier emanzipierter Kooperationspartner und unterscheiden sich hinsichtlich ihrer Ursprünge, welche in der Verhandlungs- beziehungsweise Spieltheorie liegen. Zusätzlich wird eine Studie vorgestellt, die die Eignung der vorgeschlagenen mathematischen Modelle zur Beschreibung des menschlichen Nachgebeverhaltens in kooperativen Entscheidungsfindungs-Prozessen nachweist. Darauf aufbauend werden zwei modellbasierte Automationsdesigns bereitgestellt, welche die Entwicklung von Maschinen ermöglichen, die an einem Einigungsprozess mit einem Menschen teilnehmen können. Zuletzt werden zwei experimentelle Untersuchungen der vorgeschlagenen Automationsdesigns im Kontext von teleoperierten mobilen Robotern in Such- und Rettungsszenarien und anhand einer Anwendung in einem hochautomatisierten Fahrzeug präsentiert. Die experimentellen Ergebnisse liefern empirische Evidenz für die Überlegenheit der vorgestellten modellbasierten Automationsdesigns gegenüber den bisherigen Ansätzen in den Aspekten der objektiven kooperativen Performanz, des menschlichen Vertrauens in die Interaktion mit der Maschine und der Nutzerzufriedenheit. So zeigt diese Dissertation, dass Menschen eine emanzipierte Interaktion mit Bezug auf die Entscheidungsfindung bevorzugen, und leistet einen wertvollen Beitrag zur vollumfänglichen Betrachtung und Verwirklichung von Mensch-Maschine-Kooperationen

Game Theory Relaunched

The game is on. Do you know how to play? Game theory sets out to explore what can be said about making decisions which go beyond accepting the rules of a game. Since 1942, a well elaborated mathematical apparatus has been developed to do so; but there is more. During the last three decades game theoretic reasoning has popped up in many other fields as well - from engineering to biology and psychology. New simulation tools and network analysis have made game theory omnipresent these days. This book collects recent research papers in game theory, which come from diverse scientific communities all across the world; they combine many different fields like economics, politics, history, engineering, mathematics, physics, and psychology. All of them have as a common denominator some method of game theory. Enjoy