5860317
Reinforcement Learning with Replacing Eligibility Traces
The eligibility trace is one of the basic mechanisms used in reinforcement learning to handle delayed reward. In this paper we introduce a new kind of eligibility trace, the replacing trace, analyze it theoretically, and show that it results in faster, more reliable learning than the conventional trace. Both kinds of trace assign credit to prior events according to how recently they occurred, but only the conventional trace gives greater credit to repeated events. Our analysis is for conventional and replace-trace versions of the offline TD(1) algorithm applied to undiscounted absorbing Markov chains. First, we show that these methods converge under repeated presentations of the training set to the same predictions as two well known Monte Carlo methods. We then analyze the relative efficiency of the two Monte Carlo methods. We show that the method corresponding to conventional TD is biased, whereas the method corresponding to replace-trace TD is unbiased. In addition, we show that the method corresponding to replacing traces is closely related to the maximum likelihood solution for these tasks, and that its mean squared error is always lower in the long run. Computational results confirm these analyses and show that they are applicable more generally. In particular, we show that replacing traces significantly improve performance and reduce parameter sensitivity on the "Mountain-Car" task, a full reinforcement-learning problem with a continuous state space, when using a feature-based function approximator.
5053575
Bias-Variance Error Bounds for Temporal Difference Updates
Temporal difference (td) algorithms are used in reinforcement learning to compute estimates of the value of a given policy in an unknown Markov decision process (policy evaluation). We give rigorous upper bounds on the error of the closely related phased td algorithms (which differ from the standard updates in their treatment of the learning rate) as a function of the amount of experience. These upper bounds prove exponentially fast convergence, with both the rate of convergence and the asymptote strongly dependent on the length of the backups k or the parameter . Our bounds give formal verification to the well-known intuition that td methods are subject to a bias-variance tradeoff, and they lead to schedules for k and that are predicted to be better than any fixed values for these parameters. We give preliminary experimental confirmation of our theory for a version of the random walk problem.
7241207
Intrinsically Motivated Reinforcement Learning
Psychologists call behavior intrinsically motivated when it is engaged in for its own sake rather than as a step toward solving a specific problem of clear practical value. But what we learn during intrinsically motivated behavior is essential for our development as competent autonomous entities able to efficiently solve a wide range of practical problems as they arise. In this paper we present initial results from a computational study of intrinsically motivated reinforcement learning aimed at allowing artificial agents to construct and extend hierarchies of reusable skills that are needed for competent autonomy.
2661414
Graphical Models for Game Theory
We introduce a compact graph-theoretic representation for multi-party game theory. Our main result is a provably correct and efficient algorithm for computing approximate Nash equilibria in one-stage games represented by trees or sparse graphs.
2624439
Learning Predictive State Representations
We introduce the first algorithm for learning predictive state representations (PSRs), which are a way of representing the state of a controlled dynamical system. The state representation in a PSR is a vector of predictions of tests, where tests are sequences of actions and observations said to be true if and only if all the observations occur given that all the actions are taken. The problem of finding a good PSR. one that is a sufficient statistic for the dynamical system--can be divided into two parts: 1) discovery of a good set of tests, and 2) learning to make accurate predictions for those tests. In this paper, we present detailed empirical results using a gradient-based algorithm for addressing the second problem. Our results demonstrate several sample systems in which the algorithm learns to make correct predictions and several situations in which the algorithm is less successful. Our analysis reveals challenges that will need to be addressed in future PSR learning algorithms.
2695116
Near-Optimal Reinforcement Learning in Polynomial Time
We present new algorithms for reinforcement learning and prove that they have polynomial bounds on the resources required to achieve near-optimal return in general Markov decision processes. After observing that the number of actions required to approach the optimal return is lower bounded by the mixing time T of the optimal policy (in the undiscounted case) or by the horizon time T (in the discounted case), we then give algorithms requiring a number of actions and total computation time that are only polynomial in T and the number of states and actions, for both the undiscounted and discounted cases. An interesting aspect of our algorithms is their explicit handling of the Exploration-Exploitation trade-off.
2178559
Efficient join processing over uncertain data
In many applications data values are inherently uncertain. This includes moving-objects, sensors and biological databases. There has been recent interest in the development of database management systems that can handle uncertain data. Some proposals for such systems include attribute values that are uncertain. In particular, an attribute value can be modeled as a range of possible values, associated with a probability density function. Previous efforts for this type of data have only addressed simple queries such as range and nearest-neighbor queries. Queries that join multiple relations have not been addressed in earlier work despite the significance of joins in databases. In this paper we address join queries over uncertain data. We propose a semantics for the join operation, define probabilistic operators over uncertain data, and propose join algorithms that provide efficient execution of probabilistic joins. The paper focuses on an important class of joins termed probabilistic threshold joins that avoid some of the semantic complexities of dealing with uncertain data. For this class of joins we develop three sets of optimization techniques: item-level, page-level, and index-level pruning. These techniques facilitate pruning with little space and time overhead, and are easily adapted to most join algorithms. We verify the performance of these techniques experimentally.
1844435
Neural network analysis of MINERVA scene analysis benchmark
Scene analysis is an important area of research with the aim of identifying objects and their relationships in natural scenes. The MINERVA benchmark has recently been introduced in this area for testing different image processing and classification schemes. We present results on the classification of eight natural objects in the complete set of 448 natural images using neural networks. An exhaustive set of experiments with this benchmark has been conducted using four different segmentation methods and five texture-based feature extraction methods. The results in this paper show the performance of a neural network classifier on a ten fold cross-validation task. On the basis of the results produced, we are able to rank how well different image segmentation algorithms are suited to the task of region of interest identification in these images, and we also see how well texture extraction algorithms rank on the basis of classification results.
1603562
Probabilistic Strategies for Pursuit in Cluttered Environments with Multiple Robots
In this paper, we describe a method for coordinating multiple robots in a pursuit-evasion domain. We examine the problem of multiple robotic pursuers attempting to locate a non-adversarial mobile evader in an indoor environment. Unlike many other approaches to this problem, our method seeks to minimize expected time of capture rather than guaranteeing capture. This allows us to examine the performance of our algorithm in complex and cluttered environments where guaranteed capture is difficult or impossible with limited pursuers. We present a probabilistic formulation of the problem, discretize the environment, and define cost heuristics for use in planning. We then propose a scalable algorithm using an entropy cost heuristic that searches possible movement paths to determine coordination strategies for the robotic pursuers. We present simulated results describing the performance of our algorithm against state of the art alternatives in a complex office environment. Our algorithm successfully reduces capture time with limited pursuers in an environment beyond the scope of many other approaches.
2391025
Preliminary results in range-only localization and mapping
This paper presents methods of localization using cooperating landmarks (beacons) that provide the ability to measure range only. Recent advances in radio frequency technology make it possible to measure range between inexpensive beacons and a transponder Such a method has tremendous benefit since line of sight is not required between the beacons and the transponder and because the data association problem can be completely avoided. If the positions of the beacons are known, measurements from multiple beacons can be combined using probability grids to provide an accurate estimate of robot location. This estimate can be improved by using Monte Carlo techniques and Kalman filters to incorporate odometry data. Similar methods can be used to solve the simultaneous localization and mapping problem (SLAM) when beacon locations are uncertain. Experimental results are presented for robot localization. Tracking and SLAM algorithms are demonstrated in simulation.
853906
Analytical Mean Squared Error Curves for Temporal Difference Learning
We provide analytical expressions governing changes to the bias and variance of the lookup table estimators provided by various Monte Carlo and temporal difference value estimation algorithms with offline updates over trials in absorbing Markov reward processes. We have used these expressions to develop software that serves as an analysis tool: given a complete description of a Markov reward process, it rapidly yields an exact mean-square-error curve, the curve one would get from averaging together sample mean-square-error curves from an infinite number of learning trials on the given problem. We use our analysis tool to illustrate classes of mean-square-error curve behavior in a variety of example reward processes, and we show that although the various temporal difference algorithms are quite sensitive to the choice of step-size and eligibility-trace parameters, there are values of these parameters that make them similarly competent, and generally good.