10201031
Kernel Predictive Linear Gaussian models for nonlinear stochastic dynamical systems
The recent Predictive Linear Gaussian model (or PLG) improves upon traditional linear dynamical system models by using a predictive representation of state, which makes consistent parameter estimation possible without any loss of modeling power and while using fewer parameters. In this paper we extend the PLG to model stochastic, nonlinear dynamical systems by using kernel methods. With a Gaussian kernel, the model admits closed form solutions to the state update equations due to conjugacy between the dynamics and the state representation. We also explore an efficient sigma-point approximation to the state updates, and show how all of the model parameters can be learned directly from data (and can be learned on-line with the Kernel Recursive Least-Squares algorithm). We empirically compare the model and its approximation to the original PLG and discuss their relative advantages.
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.
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.
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.
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.
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.
17852912
Lock Free Data Structures Using STM in Haskell
This paper explores the feasibility of re-expressing concurrent algorithms with explicit locks in terms of lock free code written using Haskell's implementation of software transactional memory. Experimental results are presented which show that for multi-processor systems the simpler lock free implementations offer superior performance when compared to their corresponding lock based implementations.
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.
1823400
Models for Automated Earthmoving
We present a composite forward model of the mechanics of an excavator backhoe digging in soil. This model is used to predict the trajectories developed by a closed-loop force based control scheme given initial conditions, some of which can be controlled (excavator control parameters), some directly measured (shape of the terrain), and some estimated (soil properties). Since soil conditions can vary significantly, it is necessary that soil properties be estimated online. Our models are used to both estimate soil properties and predict contact forces between the excavator and the terrain. In a large set of experiments we have conducted, we find that these models are accurate to within approximately 20% and run about 10 times faster than real-time. In this paper we motivate the development of these models and discuss experimental data from our testbed.
13328335
Multiparametric sensitivity analysis in programming problem with linear-plus-linear fractional objective function
Abstract In this paper, we study multiparametric sensitivity analysis for programming problems with linear-plus-linear fractional objective function using the concept of maximum volume in the tolerance region. We construct critical regions for simultaneous and independent perturbations in the objective function coefficients and in the right-hand-side vector of the given problem. Necessary and sufficient conditions are derived to classify perturbation parameters as `focal' and `non-focal'. Non-focal parameters can have unlimited variations, because of their low sensitivity in practice, these parameters can be deleted from the analysis. For focal parameters, a maximum volume tolerance region is characterized. Theoretical results are illustrated with the help of a numerical example.
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.