Reinforcement learning offers to robotics a framework and set of tools for the design of sophisticated and hard-to-engineer behaviors. Conversely, the challenges of robotic problems provide both inspiration, impact, and validation for developments in reinforcement learning. The relationship between disciplines has sufficient promise to be likened to that between physics and mathematics. In this article, we attempt to strengthen the links between the two research communities by providing a survey of work in reinforcement learning for behavior generation in robots. We highlight both key challenges in robot reinforcement learning as well as notable successes. We discuss how contributions tamed the complexity of the domain and study the role of algorithms, representations, and prior knowledge in achieving these successes. As a result, a particular focus of our paper lies on the choice between model-based and model-free as well as between value-function-based and policy-search methods. By analyzing a simple problem in some detail we demonstrate how reinforcement learning approaches may be profitably applied, and we note throughout open questions and the tremendous potential for future research.

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Reinforcement learning in robotics: A survey

The cross-entropy (CE) method is a new generic approach to combinatorial and multi-extremal optimization and rare event simulation. The purpose of this tutorial is to give a gentle introduction to the CE method. We present the CE methodology, the basic algorithm and its modiﬁcations, and discuss applications in combinatorial optimization and machine learning.

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A Tutorial on the Cross-Entropy Method

This report presents a unified approach for the study of constrained Markov decision processes with a countable state space and unbounded costs. We consider a single controller having several objectives; it is desirable to design a controller that minimize one of cost objective, subject to inequality constraints on other cost objectives. The objectives that we study are both the expected average cost, as well as the expected total cost (of which the discounted cost is a special case). We provide two frameworks: the case were costs are bounded below, as well as the contracting framework. We characterize the set of achievable expected occupation measures as well as performance vectors. This allows us to reduce the original control dynamic problem into an infinite Linear Programming. We present a Lagrangian approach that enables us to obtain sensitivity analysis. In particular, we obtain asymptotical results for the constrained control problem: convergence of both the value and the policies in the time horizon and in the discount factor. Finally, we present and several state truncation algorithms that enable to approximate the solution of the original control problem via finite linear programs.

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Constrained Markov Decision Processes

An integral part of modeling the global view of network security is constructing attack graphs. Manual attack graph construction is tedious, error-prone, and impractical for attack graphs larger than a hundred nodes. In this paper we present an automated technique for generating and analyzing attack graphs. We base our technique on symbolic model checking algorithms, letting us construct attack graphs automatically and efficiently. We also describe two analyses to help decide which attacks would be most cost-effective to guard against. We implemented our technique in a tool suite and tested it on a small network example, which includes models of a firewall and an intrusion detection system.

Automated generation and analysis of attack graphs

Planning under uncertainty is a central problem in the study of automated sequential decision making, and has been addressed by researchers in many different fields, including AI planning, decision analysis, operations research, control theory and economics. While the assumptions and perspectives adopted in these areas often differ in substantial ways, many planning problems of interest to researchers in these fields can be modeled as Markov decision processes (MDPs) and analyzed using the techniques of decision theory.

This paper presents an overview and synthesis of MDP-related methods, showing how they provide a unifying framework for modeling many classes of planning problems studied in AI. It also describes structural properties of MDPs that, when exhibited by particular classes of problems, can be exploited in the construction of optimal or approximately optimal policies or plans. Planning problems commonly possess structure in the reward and value functions used to describe performance criteria, in the functions used to describe state transitions and observations, and in the relationships among features used to describe states, actions, rewards, and observations.

Specialized representations, and algorithms employing these representations, can achieve computational leverage by exploiting these various forms of structure. Certain AI techniques-- in particular those based on the use of structured, intensional representations--can be viewed in this way. This paper surveys several types of representations for both classical and decision-theoretic planning problems, and planning algorithms that exploit these representations in a number of different ways to ease the computational burden of constructing policies or plans. It focuses primarily on abstraction, aggregation and decomposition techniques based on AI-style representations.

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Decision-theoretic planning: structural assumptions and computational leverage

From the Publisher: \nThe past decade has seen considerable theoretical and applied research on Markov decision processes, as well as the growing use of these models in ecology, economics, communications engineering, and other fields where outcomes are uncertain and sequential decision-making processes are needed. A timely response to this increased activity, Martin L. Puterman's new work provides a uniquely up-to-date, unified, and rigorous treatment of the theoretical, computational, and applied research on Markov decision process models. It discusses all major research directions in the field, highlights many significant applications of Markov decision processes models, and explores numerous important topics that have previously been neglected or given cursory coverage in the literature. Markov Decision Processes focuses primarily on infinite horizon discrete time models and models with discrete time spaces while also examining models with arbitrary state spaces, finite horizon models, and continuous-time discrete state models. The book is organized around optimality criteria, using a common framework centered on the optimality (Bellman) equation for presenting results. The results are presented in a \"theorem-proof\" format and elaborated on through both discussion and examples, including results that are not available in any other book. A two-state Markov decision process model, presented in Chapter 3, is analyzed repeatedly throughout the book and demonstrates many results and algorithms. Markov Decision Processes covers recent research advances in such areas as countable state space models with average reward criterion, constrained models, and models with risk sensitive optimality criteria. It also explores several topics that have received little or no attention in other books, including modified policy iteration, multichain models with average reward criterion, and sensitive optimality. In addition, a Bibliographic Remarks section in each chapter comments on relevant historic

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M. L. Puterman

Papers

Markov Decision Processes