Above are papers related to the following paper: [Paper_ID] Paper #1109581. 	[Title] Structured Reachability Analysis for Markov Decision Processes [Abstract] Recent research in decision theoretic planning has focussed on making the solution of Markov decision processes (MDPs) more feasible. We develop a family of algorithms for structured reachability analysis of MDPs that are suitable when an initial state (or set of states) is known. Using compact, structured representations of MDPs (e.g., Bayesian networks), our methods, which vary in the tradeoff between complexity and accuracy, produce structured descriptions of (estimated) reachable states that can be used to eliminate variables or variable values from the problem description, reducing the size of the MDP and making it easier to solve. One contribution of our work is the extension of ideas from GRAPHPLAN to deal with the distributed nature of action representations typically embodied within Bayes nets and the problem of correlated action effects. We also demonstrate that our algorithm can be made more complete by using k-ary constraints instead of binary constraints. Another contribution is the illustration of how the compact representation of reachability constraints can be exploited by several existing (exact and approximate) abstraction algorithms for MDPs. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #189708. 	[Title] A Model for Projection and Action [Abstract] In designing autonomous agents that deal competently with issues involving time and space, there is a tradeoff to be made between guaranteed response-time reactions on the one hand, and flexibility and expressiveness on the other. We propose a model of action with probabilistic reasoning and decision analytic evaluation for use in a layered control architecture. Our model is well suited to tasks that require reasoning about the interaction of behaviors and events in a fixed temporal horizon. Decisions are continuously reevaluated, so that there is no problem with plans becoming obsolete as new information becomes available. In this paper, we are particularly interested in the tradeoffs required to guarantee a fixed reponse time in reasoning about nondeterministic cause-and- effect relationships. By exploiting approximate decision making processes, we are able to trade accuracy in our predictions for speed in decision making in order to improve expected per Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6169. 	[Title] In  Improving Elevator Performance Using Reinforcement Learning [Abstract] This paper describes the application of reinforcement learning (RL) to the difficult real world problem of elevator dispatching. The elevator domain poses a combination of challenges not seen in most RL research to date. Elevator systems operate in continuous state spaces and in continuous time as discrete event dynamic systems. Their states are not fully observable and they are nonstationary due to changing passenger arrival rates. In addition, we use a team of RL agents, each of which is responsible for controlling one elevator car. The team receives a global reinforcement signal which appears noisy to each agent due to the effects of the actions of the other agents, the random nature of the arrivals and the incomplete observation of the state. In spite of these complications, we show results that in simulation surpass the best of the heuristic elevator control algorithms of which we are aware. These results demonstrate the power of RL on a very large scale stochastic dynamic optimization problem of practical utility. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6170. 	[Title] Improving Policies without Measuring Merits [Abstract] Performing policy iteration in dynamic programming should only require knowledge of relative rather than absolute measures of the utility of actions what Baird (1993) calls the advantages of actions at states. Nevertheless, existing methods in dynamic programming (including Baird's) compute some form of absolute utility function. For smooth problems, advantages satisfy two differential consistency conditions (including the requirement that they be free of curl), and we show that enforcing these can lead to appropriate policy improvement solely in terms of advantages. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #75674. 	[Title] Exploration Bonuses and Dual Control [Abstract] Finding the Bayesian balance between exploration and exploitation in adaptive optimal control is in general intractable. This paper shows how to compute suboptimal estimates based on a certainty equivalence approximation arising from a form of dual control. This systematizes and extends existing uses of exploration bonuses in reinforcement learning (Sutton, 1990). The approach has two components: a statistical model of uncertainty in the world and a way of turning this into exploratory behaviour. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1118245. 	[Title] Learning sorting and decision trees with POMDPs [Abstract] pomdps are general models of sequential decisions in which both actions and observations can be probabilistic. Many problems of interest can be formulated as pomdps, yet the use of pomdps has been limited by the lack of effective algorithms. Recently this has started to change and a number of problems such as robot navigation and planning are beginning to be formulated and solved as pomdps. The advantage of the pomdp approach is its clean semantics and its ability to produce principled solutions that integrate physical and information gathering actions. In this paper we pursue this approach in the context of two learning tasks: learning to sort a vector of numbers and learning decision trees from data. Both problems are formulated as pomdps and solved by a general pomdp algorithm. The main lessons and results are that 1) the use of suitable heuristics and representations allows for the solution of sorting and classification pomdps of non-trivial sizes, 2) the quality of the resulting solutions are competitive with the best algorithms, and 3) problematic aspects in decision tree learning such as test and mis-classification costs, noisy tests, and missing values are naturally accommodated. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #149669. 	[Title] Reasoning about Time and Probability [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1108389. 	[Title] Structured Arc Reversal and Simulation of Dynamic Probabilistic Networks [Abstract] We present an algorithm for arc reversal in Bayesian networks with tree-structured conditional probability tables, and consider some of its advantages, especially for the simulation of dynamic probabilistic networks. In particular, the method allows one to produce CPTs for nodes involved in the reversal that exploit regularities in the conditional distributions. We argue that this approach alleviates some of the overhead associated with arc reversal, plays an important role in evidence integration and can be used to restrict sampling of variables in DPNs. We also provide an algorithm that detects the dynamic irrelevance of state variables in forward simulation. This algorithm exploits the structured CPTs in a reversed network to determine, in a time-independent fashion, the conditions under which a variable does or does not need to be sampled. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #28202. 	[Title] MultiPlayer Residual Advantage Learning With General Function Approximation [Abstract] A new algorithm, advantage learning, is presented that improves on advantage updating by requiring that a single function be learned rather than two. Furthermore, advantage learning requires only a single type of update, the learning update, while advantage updating requires two different types of updates, a learning update and a normilization update. The reinforcement learning system uses the residual form of advantage learning. An application of reinforcement learning to a Markov game is presented. The testbed has continuous states and nonlinear dynamics. The game consists of two players, a missile and a plane; the missile pursues the plane and the plane evades the missile. On each time step , each player chooses one of two possible actions; turn left or turn right, resulting in a 90 degree instantaneous change in the aircraft s heading. Reinforcement is given only when the missile hits the plane or the plane reaches an escape distance from the missile. The advantage function is stored in a single-hidden-layer sigmoidal network. Speed of learning is increased by a new algorithm , Incremental Delta-Delta (IDD), which extends Jacobs (1988) Delta-Delta for use in incremental training, and differs from Suttons Incremental Delta-Bar-Delta (1992) in that it does not require the use of a trace and is amenable for use with general function approximation systems. The advantage learning algorithm for optimal control is modified for games in order to find the minimax point, rather than the maximum. Empirical results gathered using the missile/aircraft testbed validate theory that suggests residual forms of reinforcement learning algorithms converge to a local minimum of the mean squared Bellman residual when using general function approximation systems. Also, to our knowledge, this is the first time an approximate second order method has been used with residual algorithms. Empirical results are presented comparing convergence rates with and without the use of IDD for the reinforcement learning testbed described above and for a supervised learning testbed. The results of these experiments demonstrate IDD increased the rate of convergence and resulted in an order of magnitude lower total asymptotic error than when using backpropagation alone. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #206259. 	[Title] Asynchronous Modified Policy Iteration with Single-sided Updates [Abstract] We present a new algorithm for solving Markov decision problems that extends the modified policy iteration algorithm of Puterman and Shin [6] in two important ways: 1) The new algorithm is asynchronous in that it allows the values of states to be updated in arbitrary order, and it does not need to consider all actions in each state while updating the policy. 2) The new algorithm converges under more general initial conditions than those required by modified policy iteration. Specifically, the set of initial policy-value function pairs for which our algorithm guarantees convergence is a strict superset of the set for which modified policy iteration converges. This generalization was obtained by making a simple and easily implementable change to the policy evaluation operator used in updating the value function. Both the asynchronous nature of our algorithm and its convergence under more general conditions expand the range of problems to which our algorithm can be applied. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #20534. 	[Title] A Reinforcement Learning Approach to Job-shop Scheduling [Abstract] We apply reinforcement learning methods to learn domain-specific heuristics for job shop scheduling. A repair-based scheduler starts with a critical-path schedule and incrementally repairs constraint violations with the goal of finding a short conflict-free schedule. The temporal difference algorithm T D() is applied to train a neural network to learn a heuristic evaluation function over states. This evaluation function is used by a one-step looka-head search procedure to find good solutions to new scheduling problems. We evaluate this approach on synthetic problems and on problems from a NASA space shuttle payload processing task. The evaluation function is trained on problems involving a small number of jobs and then tested on larger problems. The TD sched-uler performs better than the best known existing algorithm for this task|Zweben's iterative repair method based on simulated annealing. The results suggest that reinforcement learning can provide a new method for constructing high-performance scheduling systems. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #28471. 	[Title] Markov Decision Processes in Large State Spaces [Abstract] In this paper we propose a new framework for studying Markov decision processes (MDPs), based on ideas from statistical mechanics. The goal of learning in MDPs is to find a policy that yields the maximum expected return over time. In choosing policies, agents must therefore weigh the prospects of short-term versus long-term gains. We study a simple MDP in which the agent must constantly decide between exploratory jumps and local reward mining in state space. The number of policies to choose from grows exponentially with the size of the state space, N . We view the expected returns as defining an energy landscape over policy space. Methods from statistical mechanics are used to analyze this landscape in the thermodynamic limit N ! 1. We calculate the overall distribution of expected returns, as well as the distribution of returns for policies at a fixed Hamming distance from the optimal one. We briefly discuss the problem of learning optimal policies from empirical estimates of the expected return. As a first step, we relate our findings for the entropy to the limit of high-temperature learning. Numerical simulations support the theoretical results. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1117760. 	[Title] KnightCap: A chess program that learns by combining TD() with minimax search [Abstract] In this paper we present TDLeaf(), a variation on the TD() algorithm that enables it to be used in conjunction with minimax search. We present some experiments in which our chess program, KnightCap, used TDLeaf() to learn its evaluation function while playing on the Free Ineternet Chess Server (FICS, fics.onenet.net). It improved from a 1650 rating to a 2100 rating in just 308 games and 3 days of play. We discuss some of the reasons for this success and also the relationship between our results and Tesauro's results in backgammon. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #35778. 	[Title] Context-Specific Independence in Bayesian Networks [Abstract] Bayesiannetworks provide a languagefor qualitatively representing the conditional independence properties of a distribution. This allows a natural and compact representation of the distribution, eases knowledge acquisition, and supports effective inference algorithms. It is well-known, however, that there are certain independencies that we cannot capture qualitatively within the Bayesian network structure: independencies that hold only in certain contexts, i.e., given a specific assignment of values to certain variables. In this paper, we propose a formal notion of context-specific independence (CSI), based on regularities in the conditional probability tables (CPTs) at a node. We present a technique, analogous to (and based on) d-separation, for determining when such independence holds in a given network. We then focus on a particular qualitative representation schemetree-structured CPTs for capturing CSI. We suggest ways in which this representation can be used to support effective inference algorithms. In particular, we present a structural decomposition of the resulting network which can improve the performance of clustering algorithms, and an alternative algorithm based on cutset conditioning. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #341188. 	[Title] A Unified Analysis of Value-Function-Based Reinforcement-Learning Algorithms [Abstract] Reinforcement learning is the problem of generating optimal behavior in a sequential decision-making environment given the opportunity of interacting with it. Many algorithms for solving reinforcement-learning problems work by computing improved estimates of the optimal value function. We extend prior analyses of reinforcement-learning algorithms and present a powerful new theorem that can provide a unified analysis of value-function-based reinforcement-learning algorithms. The usefulness of the theorem lies in how it allows the asynchronous convergence of a complex reinforcement-learning algorithm to be proven by verifying that a simpler synchronous algorithm converges. We illustrate the application of the theorem by analyzing the convergence of Q-learning, model-based reinforcement learning, Q-learning with multi-state updates, Q-learning for Markov games, and risk-sensitive reinforcement learning. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6213. 	[Title] Machine Learning Learning to Predict by the Methods of Temporal Differences Keywords: Incremental learning, prediction, [Abstract] This article introduces a class of incremental learning procedures specialized for prediction|that is, for using past experience with an incompletely known system to predict its future behavior. Whereas conventional prediction-learning methods assign credit by means of the difference between predicted and actual outcomes, the new methods assign credit by means of the difference between temporally successive predictions. Although such temporal-difference methods have been used in Samuel's checker player, Holland's bucket brigade, and the author's Adaptive Heuristic Critic, they have remained poorly understood. Here we prove their convergence and optimality for special cases and relate them to supervised-learning methods. For most real-world prediction problems, temporal-difference methods require less memory and less peak computation than conventional methods; and they produce more accurate predictions. We argue that most problems to which supervised learning is currently applied are really prediction problems of the sort to which temporal-difference methods can be applied to advantage. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6214. 	[Title] Integrated Architectures for Learning, Planning, and Reacting Based on Approximating Dynamic Programming [Abstract] This paper extends previous work with Dyna, a class of architectures for intelligent systems based on approximating dynamic programming methods. Dyna architectures integrate trial-and-error (reinforcement) learning and execution-time planning into a single process operating alternately on the world and on a learned model of the world. In this paper, I present and show results for two Dyna architectures. The Dyna-PI architecture is based on dynamic programming's policy iteration method and can be related to existing AI ideas such as evaluation functions and universal plans (reactive systems). Using a navigation task, results are shown for a simple Dyna-PI system that simultaneously learns by trial and error, learns a world model, and plans optimal routes using the evolving world model. The Dyna-Q architecture is based on Watkins's Q-learning, a new kind of reinforcement learning. Dyna-Q uses a less familiar set of data structures than does Dyna-PI, but is arguably simpler to implement and use. We show that Dyna-Q architectures are easy to adapt for use in changing environments. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #17476. 	[Title] Markov games as a framework for multi-agent reinforcement learning [Abstract] In the Markov decision process (MDP) formalization of reinforcement learning, a single adaptive agent interacts with an environment defined by a probabilistic transition function. In this solipsistic view, secondary agents can only be part of the environment and are therefore fixed in their behavior. The framework of Markov games allows us to widen this view to include multiple adaptive agents with interacting or competing goals. This paper considers a step in this direction in which exactly two agents with diametrically opposed goals share an environment. It describes a Q-learning-like algorithm for finding optimal policies and demonstrates its application to a simple two-player game in which the optimal policy is probabilistic. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #38480. 	[Title] Learning to Achieve Goals [Abstract] Temporal difference methods solve the temporal credit assignment problem for reinforcement learning. An important subproblem of general reinforcement learning is learning to achieve dynamic goals. Although existing temporal difference methods, such as Q learning, can be applied to this problem, they do not take advantage of its special structure. This paper presents the DG-learning algorithm, which learns efficiently to achieve dynamically changing goals and exhibits good knowledge transfer between goals. In addition, this paper shows how traditional relaxation techniques can be applied to the problem. Finally, experimental results are given that demonstrate the superiority of DG learning over Q learning in a moderately large, synthetic, non-deterministic domain. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #24530. 	[Title] Approximating Value Trees in Structured Dynamic Programming [Abstract] We propose and examine a method of approximate dynamic programming for Markov decision processes based on structured problem representations. We assume an MDP is represented using a dynamic Bayesian network, and construct value functions using decision trees as our function representation. The size of the representation is kept within acceptable limits by pruning these value trees so that leaves represent possible ranges of values, thus approximating the value functions produced during optimization. We propose a method for detecting convergence, prove errors bounds on the resulting approximately optimal value functions and policies, and describe some preliminary experi mental results. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1113182. 	[Title] TDLeaf(): Combining Temporal Difference learning with game-tree search. [Abstract] In this paper we present TDLeaf(), a variation on the TD() algorithm that enables it to be used in conjunction with minimax search. We present some experiments in both chess and backgammon which demonstrate its utility and provide comparisons with TD() and another less radical variant, TD-directed(). In particular, our chess program, KnightCap, used TDLeaf() to learn its evaluation function while playing on the Free Internet Chess Server (FICS, fics.onenet.net). It improved from a 1650 rating to a 2100 rating in just 308 games. We discuss some of the reasons for this success and the relationship between our results and Tesauro's results in backgammon. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #28387. 	[Title] On the Complexity of Solving Markov Decision Problems [Abstract] Markov decision problems (MDPs) provide the foundations for a number of problems of interest to AI researchers studying automated planning and reinforcement learning. In this paper, we summarize results regarding the complexity of solving MDPs and the running time of MDP solution algorithms. We argue that, although MDPs can be solved efficiently in theory, more study is needed to reveal practical algorithms for solving large problems quickly. To encourage future research, we sketch some alternative methods of analysis that rely on the struc ture of MDPs. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1105764. 	[Title] Least-Squares Temporal Difference Learning [Abstract] Submitted to NIPS-98 TD() is a popular family of algorithms for approximate policy evaluation in large MDPs. TD() works by incrementally updating the value function after each observed transition. It has two major drawbacks: it makes inefficient use of data, and it requires the user to manually tune a stepsize schedule for good performance. For the case of linear value function approximations and = 0, the Least-Squares TD (LSTD) algorithm of Bradtke and Barto [5] eliminates all stepsize parameters and improves data efficiency. This paper extends Bradtke and Barto's work in three significant ways. First, it presents a simpler derivation of the LSTD algorithm. Second, it generalizes from = 0 to arbitrary values of ; at the extreme of = 1, the resulting algorithm is shown to be a practical formulation of supervised linear regression. Third, it presents a novel, intuitive interpretation of LSTD as a model-based reinforcement learning technique. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #32872. 	[Title] Acting under Uncertainty: Discrete Bayesian Models for Mobile-Robot Navigation [Abstract] Discrete Bayesian models have been used to model uncertainty for mobile-robot navigation, but the question of how actions should be chosen remains largely unexplored. This paper presents the optimal solution to the problem, formulated as a partially observable Markov decision process. Since solving for the optimal control policy is intractable, in general, it goes on to explore a variety of heuristic control strategies. The control strategies are compared experimentally, both in simulation and in runs on a robot. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #39403. 	[Title] Auto-exploratory Average Reward Reinforcement Learning [Abstract] We introduce a model-based average reward Reinforcement Learning method called H-learning and compare it with its discounted counterpart, Adaptive Real-Time Dynamic Programming, in a simulated robot scheduling task. We also introduce an extension to H-learning, which automatically explores the unexplored parts of the state space, while always choosing greedy actions with respect to the current value function. We show that this "Auto-exploratory H-learning" performs better than the original H-learning under previously studied exploration methods such as random, recency-based, or counter-based exploration. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1107312. 	[Title] Optimal Navigation in a Probibalistic World [Abstract] In this paper, we define and examine two versions of the bridge problem. The first variant of the bridge problem is a determistic model where the agent knows a superset of the transitions and a priori probabilities that those transitions are intact. In the second variant, transitions can break or be fixed with some probability at each time step. These problems are applicable to planning in uncertain domains as well as packet routing in a computer network. We show how an agent can act optimally in these models by reduction to Markov decision processes. We describe methods of solving them but note that these methods are intractable for reasonably sized problems. Finally, we suggest neuro-dynamic programming as a method of value function approximation for these types of models. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #33013. 	[Title] Learning Conventions in Multiagent Stochastic Domains using Likelihood Estimates [Abstract] Fully cooperative multiagent systemsthose in which agents share a joint utility modelis of special interest in AI. A key problem is that of ensuring that the actions of individual agents are coordinated, especially in settings where the agents are autonomous decision makers. We investigate approaches to learning coordinated strategies in stochastic domains where an agent's actions are not directly observable by others. Much recent work in game theory has adopted a Bayesian learning perspective to the more general problem of equilibrium selection, but tends to assume that actions can be observed. We discuss the special problems that arise when actions are not observable, including effects on rates of convergence, and the effect of action failure probabilities and asymmetries. We also use likelihood estimates as a means of generalizing fictitious play learning models in our setting. Finally, we propose the use of maximum likelihood as a means of removing strategies from consideration, with the aim of convergence to a conventional equilibrium, at which point learning and deliberation can cease. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #117. 	[Title] Generalized Markov Decision Processes: Dynamic-programming and Reinforcement-learning Algorithms [Abstract] The problem of maximizing the expected total discounted reward in a completely observable Markovian environment, i.e., a Markov decision process (mdp), models a particular class of sequential decision problems. Algorithms have been developed for making optimal decisions in mdps given either an mdp specification or the opportunity to interact with the mdp over time. Recently, other sequential decision-making problems have been studied prompting the development of new algorithms and analyses. We describe a new generalized model that subsumes mdps as well as many of the recent variations. We prove some basic results concerning this model and develop generalizations of value iteration, policy iteration, model-based reinforcement-learning, and Q-learning that can be used to make optimal decisions in the generalized model under various assumptions. Applications of the theory to particular models are described, including risk-averse mdps, exploration-sensitive mdps, sarsa, Q-learning with spreading, two-player games, and approximate max picking via sampling. Central to the results are the contraction property of the value operator and a stochastic-approximation theorem that reduces asynchronous convergence to synchronous convergence. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #28278. 	[Title] Chapter 1 Reinforcement Learning for Planning and Control [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #156794. 	[Title] Correlated Action Effects in Decision Theoretic Regression [Abstract] Much recent research in decision theoretic planning has adopted Markov decision processes (MDPs) as the model of choice, and has attempted to make their solution more tractable by exploiting problem structure. One particular algorithm, structured policy construction achieves this by means of a decision theoretic analog of goal regression, using action descriptions based on Bayesian networks with tree-structured conditional probability tables. The algorithm as presented is not able to deal with actions with correlated effects. We describe a new decision theoretic regression operator that corrects this weakness. While conceptually straightforward, this extension requires a somewhat more complicated technical approach. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #7419. 	[Title] A Neuro-Dynamic Programming Approach to Retailer Inventory Management 1 [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1919. 	[Title] The Frame Problem and Bayesian Network Action Representations [Abstract] We examine a number of techniques for representing actions with stochastic effects using Bayesian networks and influence diagrams. We compare these techniques according to ease of specification and size of the representation required for the complete specification of the dynamics of a particular system, paying particular attention the role of persistence relationships. We precisely characterize two components of the frame problem for Bayes nets and stochastic actions, propose several ways to deal with these problems, and compare our solutions with Re-iter's solution to the frame problem for the situation calculus. The result is a set of techniques that permit both ease of specification and compact representation of probabilistic system dynamics that is of comparable size (and timbre) to Reiter's representation (i.e., with no explicit frame axioms). Please summarise all the given information.

Paper #1109581 has the title `Structured Reachability Analysis for Markov Decision Processes  
` and the abstract `Recent research in decision theoretic planning has focussed on making the solution of Markov decision processes (MDPs) more feasible. We develop a family of algorithms for structured reachability analysis of MDPs that are suitable when an initial state (or set of states) is known. Using compact, structured representations of MDPs (e.g., Bayesian networks), our methods, which vary in the tradeoff between complexity and accuracy, produce structured descriptions of (estimated) reachable states that can be used to eliminate variables or variable values from the problem description, reducing the size of the MDP and making it easier to solve. One contribution of our work is the extension of ideas from GRAPHPLAN to deal with the distributed nature of action representations typically embodied within Bayes nets and the problem of correlated action effects. We also demonstrate that our algorithm can be made more complete by using k-ary constraints instead of binary constraints. Another contribution is the illustration of how the compact representation of reachability constraints can be exploited by several existing (exact and approximate) abstraction algorithms for MDPs.
`.
Question: Which category should Paper #1109581 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1109581 has the title `Structured Reachability Analysis for Markov Decision Processes  
` and the abstract `Recent research in decision theoretic planning has focussed on making the solution of Markov decision processes (MDPs) more feasible. We develop a family of algorithms for structured reachability analysis of MDPs that are suitable when an initial state (or set of states) is known. Using compact, structured representations of MDPs (e.g., Bayesian networks), our methods, which vary in the tradeoff between complexity and accuracy, produce structured descriptions of (estimated) reachable states that can be used to eliminate variables or variable values from the problem description, reducing the size of the MDP and making it easier to solve. One contribution of our work is the extension of ideas from GRAPHPLAN to deal with the distributed nature of action representations typically embodied within Bayes nets and the problem of correlated action effects. We also demonstrate that our algorithm can be made more complete by using k-ary constraints instead of binary constraints. Another contribution is the illustration of how the compact representation of reachability constraints can be exploited by several existing (exact and approximate) abstraction algorithms for MDPs.
`.
Question: Which category should Paper #1109581 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Probabilistic_Methods