On learning history based policies for controlling Markov decision processes

Reinforcementlearning(RL)folkloresuggeststhathistory-basedfunctionapproximationmethods,suchas recurrent neural nets or history-based state abstraction, perform better than their memory-less counterparts, due to the fact that function approximation in Markov decision processes (MDP) can be viewed as inducing a Partially observable MDP. However, there has been little formal analysis of such history-based algorithms, as most existing frameworks focus exclusively on memory-less features. In this paper, we introduce a theoretical framework for studying the behaviour of RL algorithms that learn to control an MDP using history-based feature abstraction mappings. Furthermore, we use this framework to design a practical RL algorithm and we numerically evaluate its effectiveness on a set of continuous control tasks

Learning near-optimal policies with Bellman-residual minimization based fitted policy iteration and a single sample path

We consider the problem of finding a near-optimal policy in continuous space, discounted Markovian Decision Problems given the trajectory of some behaviour policy. We study the policy iteration algorithm where in successive iterations the action-value functions of the intermediate policies are obtained by picking a function from some fixed function set (chosen by the user) that minimizes an unbiased finite-sample approximation to a novel loss function that upper-bounds the unmodified Bellman-residual criterion. The main result is a finite-sample, high-probability bound on the performance of the resulting policy that depends on the mixing rate of the trajectory, the capacity of the function set as measured by a novel capacity concept that we call the VC-crossing dimension, the approximation power of the function set and the discounted-average concentrability of the future-state distribution. To the best of our knowledge this is the first theoretical reinforcement learning result for off-policy control learning over continuous state-spaces using a single trajectory

Finite-time bounds for fitted value iteration

In this paper we develop a theoretical analysis of the performance of sampling-based fitted value iteration (FVI) to solve infinite state-space, discounted-reward Markovian decision processes (MDPs) under the assumption that a generative model of the environment is available. Our main results come in the form of finite-time bounds on the performance of two versions of sampling-based FVI.The convergence rate results obtained allow us to show that both versions of FVI are well behaving in the sense that by using a sufficiently large number of samples for a large class of MDPs, arbitrary good performance can be achieved with high probability.An important feature of our proof technique is that it permits the study of weighted $L^p$-norm performance bounds. As a result, our technique applies to a large class of function-approximation methods (e.g., neural networks, adaptive regression trees, kernel machines, locally weighted learning), and our bounds scale well with the effective horizon of the MDP. The bounds show a dependence on the stochastic stability properties of the MDP: they scale with the discounted-average concentrability of the future-state distributions. They also depend on a new measure of the approximation power of the function space, the inherent Bellman residual, which reflects how well the function space is ``aligned'' with the dynamics and rewards of the MDP.The conditions of the main result, as well as the concepts introduced in the analysis, are extensively discussed and compared to previous theoretical results.Numerical experiments are used to substantiate the theoretical findings

A Framework for Aggregation of Multiple Reinforcement Learning Algorithms

Aggregation of multiple Reinforcement Learning (RL) algorithms is a new and effective technique to improve the quality of Sequential Decision Making (SDM). The quality of a SDM depends on long-term rewards rather than the instant rewards. RL methods are often adopted to deal with SDM problems. Although many RL algorithms have been developed, none is consistently better than the others. In addition, the parameters of RL algorithms significantly influence learning performances. There is no universal rule to guide the choice of algorithms and the setting of parameters. To handle this difficulty, a new multiple RL system - Aggregated Multiple Reinforcement Learning System (AMRLS) is developed. In AMRLS, each RL algorithm (learner) learns individually in a learning module and provides its output to an intelligent aggregation module. The aggregation module dynamically aggregates these outputs and provides a final decision. Then, all learners take the action and update their policies individually. The two processes are performed alternatively. AMRLS can deal with dynamic learning problems without the need to search for the optimal learning algorithm or the optimal values of learning parameters. It is claimed that several complementary learning algorithms can be integrated in AMRLS to improve the learning performance in terms of success rate, robustness, confidence, redundance, and complementariness. There are two strategies for learning an optimal policy with RL methods. One is based on Value Function Learning (VFL), which learns an optimal policy expressed as a value function. The Temporal Difference RL (TDRL) methods are examples of this strategy. The other is based on Direct Policy Search (DPS), which directly searches for the optimal policy in the potential policy space. The Genetic Algorithms (GAs)-based RL (GARL) are instances of this strategy. A hybrid learning architecture of GARL and TDRL, HGATDRL, is proposed to combine them together to improve the learning ability. AMRLS and HGATDRL are tested on several SDM problems, including the maze world problem, pursuit domain problem, cart-pole balancing system, mountain car problem, and flight control system. Experimental results show that the proposed framework and method can enhance the learning ability and improve learning performance of a multiple RL system

Kernel-based approximate dynamic programming using Bellman residual elimination

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2010.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 207-221).Many sequential decision-making problems related to multi-agent robotic systems can be naturally posed as Markov Decision Processes (MDPs). An important advantage of the MDP framework is the ability to utilize stochastic system models, thereby allowing the system to make sound decisions even if there is randomness in the system evolution over time. Unfortunately, the curse of dimensionality prevents most MDPs of practical size from being solved exactly. One main focus of the thesis is on the development of a new family of algorithms for computing approximate solutions to large-scale MDPs. Our algorithms are similar in spirit to Bellman residual methods, which attempt to minimize the error incurred in solving Bellman's equation at a set of sample states. However, by exploiting kernel-based regression techniques (such as support vector regression and Gaussian process regression) with nondegenerate kernel functions as the underlying cost-to-go function approximation architecture, our algorithms are able to construct cost-to-go solutions for which the Bellman residuals are explicitly forced to zero at the sample states. For this reason, we have named our approach Bellman residual elimination (BRE). In addition to developing the basic ideas behind BRE, we present multi-stage and model-free extensions to the approach. The multistage extension allows for automatic selection of an appropriate kernel for the MDP at hand, while the model-free extension can use simulated or real state trajectory data to learn an approximate policy when a system model is unavailable.(cont.) We present theoretical analysis of all BRE algorithms proving convergence to the optimal policy in the limit of sampling the entire state space, and show computational results on several benchmark problems. Another challenge in implementing control policies based on MDPs is that there may be parameters of the system model that are poorly known and/or vary with time as the system operates. System performance can suer if the model used to compute the policy differs from the true model. To address this challenge, we develop an adaptive architecture that allows for online MDP model learning and simultaneous re-computation of the policy. As a result, the adaptive architecture allows the system to continuously re-tune its control policy to account for better model information 3 obtained through observations of the actual system in operation, and react to changes in the model as they occur. Planning in complex, large-scale multi-agent robotic systems is another focus of the thesis. In particular, we investigate the persistent surveillance problem, in which one or more unmanned aerial vehicles (UAVs) and/or unmanned ground vehicles (UGVs) must provide sensor coverage over a designated location on a continuous basis. This continuous coverage must be maintained even in the event that agents suer failures over the course of the mission. The persistent surveillance problem is pertinent to a number of applications, including search and rescue, natural disaster relief operations, urban traffic monitoring, etc.(cont.) Using both simulations and actual flight experiments conducted in the MIT RAVEN indoor flight facility, we demonstrate the successful application of the BRE algorithms and the adaptive MDP architecture in achieving high mission performance despite the random occurrence of failures. Furthermore, we demonstrate performance benefits of our approach over a deterministic planning approach that does not account for these failures.by Brett M. Bethke.Ph.D

Regularized approximate policy iteration using kernel for on-line reinforcement learning

By using Reinforcement Learning (RL), an autonomous agent interacting with the environment can learn how to take adequate actions for every situation in order to optimally achieve its own goal. RL provides a general methodology able to solve uncertain and complex decision problems which may be present in many real-world applications. RL problems are usually modeled as a Markov Decision Processes (MDPs) deeply studied in the literature. The main peculiarity of a RL algorithm is that the RL agent is assumed to learn the optimal policies from its experiences without knowing the parameters of the MDP. The key element in solving the MDP is learning a value function which gives the expectation of total reward an agent might expect at its current state taking a given action. This value function allows to obtain the optimal policy. In this thesis we study the capacity of SVR using kernel methods to adapt and solve complex RL problems in large or continuous state space. SVR can be studied using a geometrical interpretation in terms of optimal margin or can be seen as a regularization problem given in a Reproducing Kernel Hilbert Space (RKHS) SVR have good properties over the generalization ability and as they are based a on convex optimization problem, they do not suffer from sub-optimality. SVR are non-parametric showing the ability to automatically adapt to the complexity of the problem. Accordingly, applying SVR to approximate value functions sounds to be a good approach. SVR can be solved both in batch mode when the whole set of training sample are at disposal of the learning agents or incrementally which enables the addition or removal of training samples very effectively. Incremental SVR finds the appropriate KKT conditions for new or updated data by modifying their influences into the regression function maintaining consistence in the KKT conditions for the rest of data used for learning. In RL problems an incremental SVR should be able to approximate the action value function leading to the optimal policy. Accordingly, computation load should be lower, learning speed faster and generalization more effective than other existing method The overall contribution coming from of our work is to develop, formalize, implement and study a new RL technique for generalization in discrete and continuous state spaces with finite actions. Our method uses the Approximate Policy Iteration (API) framework with the BRM criterion which allows to represent the action value function using SVR. This approach for RL is the first one we know using SVR compatible to the agent interaction- with-the-environment framework of RL which shows his power by solving a large number of benchmark problems, including very difficult ones, like the bicycle driving and riding control problem. In addition, unlike most RL approaches to generalization, we develop a proof finding theoretical bounds for the convergence of the method to the optimal solution under given conditions.Mediante el uso de aprendizaje por refuerzo (RL), un agente autónomo interactuando con el medio ambiente puede aprender a tomar adecuada acciones para cada situación con el fin de lograr de manera óptima su propia meta. RL proporciona una metodología general capaz de resolver problemas de decisión complejos que pueden estar presentes en muchas aplicaciones del mundo real. Problemas RL usualmente se modelan como una Procesos de Decisión de Markov (MDP) estudiados profundamente en la literatura. La principal peculiaridad de un algoritmo de RL es que el agente es asumido para aprender las políticas óptimas de sus experiencias sin saber los parámetros de la MDP. El elemento clave en resolver el MDP está en el aprender una función de valor que da la expectativa de recompensa total que un agente puede esperar en su estado actual para tomar una acción determinada. Esta función de valor permite obtener la política óptima. En esta tesis se estudia la capacidad del SVR utilizando núcleo métodos para adaptarse y resolver problemas RL complejas en el espacio estado grande o continua. RVS puede ser estudiado mediante un interpretación geométrica en términos de margen óptimo o puede ser visto como un problema de regularización dado en un Reproducing Kernel Hilbert Space (RKHS). SVR tiene buenas propiedades sobre la capacidad de generalización y ya que se basan en una optimización convexa problema, ellos no sufren de sub-optimalidad. SVR son no paramétrico que muestra la capacidad de adaptarse automáticamente a la complejidad del problema. En consecuencia, la aplicación de RVS para aproximar funciones de valor suena para ser un buen enfoque. SVR puede resolver tanto en modo batch cuando todo el conjunto de muestra de entrenamiento están a disposición de los agentes de aprendizaje o incrementalmente que permite la adición o eliminación de muestras de entrenamiento muy eficaz. Incremental SVR encuentra las condiciones adecuadas para KKT nuevas o actualizadas de datos modificando sus influencias en la función de regresión mantener consistencia en las condiciones KKT para el resto de los datos utilizados para el aprendizaje. En los problemas de RL una RVS elemental será capaz de aproximar la función de valor de acción que conduce a la política óptima. En consecuencia, la carga de cálculo debería ser menor, la velocidad de aprendizaje más rápido y generalización más efectivo que el otro método existente La contribución general que viene de nuestro trabajo es desarrollar, formalizar, ejecutar y estudiar una nueva técnica de RL para la generalización en espacio de estados discretos y continuos con acciones finitas. Nuestro método utiliza el marco de la Approximate Policy Iteration (API) con el criterio de BRM que permite representar la función de valor de acción utilizando SVR. Este enfoque de RL es el primero que conocemos usando SVR compatible con el marco de RL con agentes interaccionado con el ambiente que muestra su poder mediante la resolución de un gran número de problemas de referencia, incluyendo los muy difíciles, como la conducción de bicicletas y problema de control de conducción. Además, a diferencia de la mayoría RL se acerca a la generalización, desarrollamos un hallazgo prueba límites teóricos para la convergencia del método a la solución óptima en condiciones dadas