This thesis presents a rough set approach to reinforcement learning. This is made possible by considering behaviour patterns of learning agents in the context of approximation spaces. Rough set theory introduced by Zdzisław Pawlak in the early 1980s provides a ground for deriving pattern-based rewards within approximation spaces. Learning can be considered episodic. The framework provided by an approximation space makes it possible to derive pattern-based reference rewards at the end of each episode. Reference rewards provide a standard for reinforcement comparison as well as the actor-critic method of reinforcement learning. In addition, approximation spaces provide a basis for deriving episodic weights that provide a basis for a new form of off-policy Monte Carlo learning control method. A number of conventional and pattern-based reinforcement learning methods are investigated in this thesis. In addition, this thesis introduces two learning environments used to compare the algorithms. The first is a Monocular Vision System used to track a moving target. The second is an artificial ecosystem testbed that makes it possible to study swarm behaviour by collections of biologically-inspired bots. The simulated ecosystem has an ethological basis inspired by the work of Niko Tinbergen, who introduced in the 1960s methods of observing and explaining the behaviour of biological organisms that carry over into the study of the behaviour of interacting robotic devices that cooperate to survive and to carry out highly specialized tasks. Agent behaviour during each episode is recorded in a decision table called an ethogram, which records features such as states, proximate causes, responses (actions), action preferences, rewards and decisions (actions chosen and actions rejected). At all times an agent follows a policy that maps perceived states of the environment to actions. The goal of the learning algorithms is to find an optimal policy in a non-stationary environment. The results of the learning experiments with seven forms of reinforcement learning are given. The contribution of this thesis is a comprehensive introduction to a pattern-based evaluation of behaviour during reinforcement learning using approximation spaces. / May 2006

This thesis presents a rough set approach to reinforcement learning. This is made possible by considering behaviour patterns of learning agents in the context of approximation spaces. Rough set theory introduced by Zdzisław Pawlak in the early 1980s provides a ground for deriving pattern-based rewards within approximation spaces. Learning can be considered episodic. The framework provided by an approximation space makes it possible to derive pattern-based reference rewards at the end of each episode. Reference rewards provide a standard for reinforcement comparison as well as the actor-critic method of reinforcement learning. In addition, approximation spaces provide a basis for deriving episodic weights that provide a basis for a new form of off-policy Monte Carlo learning control method. A number of conventional and pattern-based reinforcement learning methods are investigated in this thesis. In addition, this thesis introduces two learning environments used to compare the algorithms. The first is a Monocular Vision System used to track a moving target. The second is an artificial ecosystem testbed that makes it possible to study swarm behaviour by collections of biologically-inspired bots. The simulated ecosystem has an ethological basis inspired by the work of Niko Tinbergen, who introduced in the 1960s methods of observing and explaining the behaviour of biological organisms that carry over into the study of the behaviour of interacting robotic devices that cooperate to survive and to carry out highly specialized tasks. Agent behaviour during each episode is recorded in a decision table called an ethogram, which records features such as states, proximate causes, responses (actions), action preferences, rewards and decisions (actions chosen and actions rejected). At all times an agent follows a policy that maps perceived states of the environment to actions. The goal of the learning algorithms is to find an optimal policy in a non-stationary environment. The results of the learning experiments with seven forms of reinforcement learning are given. The contribution of this thesis is a comprehensive introduction to a pattern-based evaluation of behaviour during reinforcement learning using approximation spaces.

This thesis presents a rough set approach to reinforcement learning. This is made possible by considering behaviour patterns of learning agents in the context of approximation spaces. Rough set theory introduced by Zdzisław Pawlak in the early 1980s provides a ground for deriving pattern-based rewards within approximation spaces. Learning can be considered episodic. The framework provided by an approximation space makes it possible to derive pattern-based reference rewards at the end of each episode. Reference rewards provide a standard for reinforcement comparison as well as the actor-critic method of reinforcement learning. In addition, approximation spaces provide a basis for deriving episodic weights that provide a basis for a new form of off-policy Monte Carlo learning control method. A number of conventional and pattern-based reinforcement learning methods are investigated in this thesis. In addition, this thesis introduces two learning environments used to compare the algorithms. The first is a Monocular Vision System used to track a moving target. The second is an artificial ecosystem testbed that makes it possible to study swarm behaviour by collections of biologically-inspired bots. The simulated ecosystem has an ethological basis inspired by the work of Niko Tinbergen, who introduced in the 1960s methods of observing and explaining the behaviour of biological organisms that carry over into the study of the behaviour of interacting robotic devices that cooperate to survive and to carry out highly specialized tasks. Agent behaviour during each episode is recorded in a decision table called an ethogram, which records features such as states, proximate causes, responses (actions), action preferences, rewards and decisions (actions chosen and actions rejected). At all times an agent follows a policy that maps perceived states of the environment to actions. The goal of the learning algorithms is to find an optimal policy in a non-stationary environment. The results of the learning experiments with seven forms of reinforcement learning are given. The contribution of this thesis is a comprehensive introduction to a pattern-based evaluation of behaviour during reinforcement learning using approximation spaces.

Un préconditionneur à deux niveaux, reposant sur la technique d’accélération d’Aitken d’une suite de q vecteurs solutions de l’interface d’un pro- cessus itératif de Schwarz Additif Restreint, est conçu. Cette nouvelle technique, dénomée ARAS(q), utilise une approximation grossière de la solution sur l’interface. Différentes méthodes sont proposées, aboutissant au développement d’une tech- nique d’approximation par Décomposition en Valeures Singulières de la suite de vecteurs. Des implémentations parallèles des méthodes d’Aitken-Schwarz sont pro- posées et l’étude conduit à l’implémentation d’un code totalement algébrique, sur un ou deux niveaux de parallélisation MPI, écrit dans l’environnement de la biblio- thèque PETSc. Cette implémentation pleinement parallèle et algébrique procure un outil flexible pour la résolution de systèmes linéaires tels que ceux issus de la dif- férentiation automatique des solutions de Navier-Stokes dépendant des paramètres de la simulation / A two level preconditioner, based on the Aitken acceleration technique of a sequence of q interface’s solution vectors of the Restricted Additive Schwarz iterative process, is designed. This new technique, called ARAS(q), uses a coarse approximation of the solution on the interface. Different methods are discussed, leading to the development of an approximation technique by Singular Value De- composition of the sequence of vectors. Parallel implementations of Aitken-Schwarz methods are proposed, and the study leads to a fully algebraic one-level and two- level MPI implementation of ARAS(q) written into the PETSc library framework. This fully parallel and algebraic code gives an adaptive tool to solve linear systems such as those arising from automatic differentiation of compressible Navier-Stokes solution with respect to the simulation’s parameters