Batch Informed Trees (BIT*): Informed Asymptotically Optimal Anytime Search

Path planning in robotics often requires finding high-quality solutions to continuously valued and/or high-dimensional problems. These problems are challenging and most planning algorithms instead solve simplified approximations. Popular approximations include graphs and random samples, as respectively used by informed graph-based searches and anytime sampling-based planners. Informed graph-based searches, such as A*, traditionally use heuristics to search a priori graphs in order of potential solution quality. This makes their search efficient but leaves their performance dependent on the chosen approximation. If its resolution is too low then they may not find a (suitable) solution but if it is too high then they may take a prohibitively long time to do so. Anytime sampling-based planners, such as RRT*, traditionally use random sampling to approximate the problem domain incrementally. This allows them to increase resolution until a suitable solution is found but makes their search dependent on the order of approximation. Arbitrary sequences of random samples approximate the problem domain in every direction simultaneously and but may be prohibitively inefficient at containing a solution. This paper unifies and extends these two approaches to develop Batch Informed Trees (BIT*), an informed, anytime sampling-based planner. BIT* solves continuous path planning problems efficiently by using sampling and heuristics to alternately approximate and search the problem domain. Its search is ordered by potential solution quality, as in A*, and its approximation improves indefinitely with additional computational time, as in RRT*. It is shown analytically to be almost-surely asymptotically optimal and experimentally to outperform existing sampling-based planners, especially on high-dimensional planning problems.Comment: International Journal of Robotics Research (IJRR). 32 Pages. 16 Figure

Batch Informed Trees (BIT*): Sampling-based Optimal Planning via the Heuristically Guided Search of Implicit Random Geometric Graphs

In this paper, we present Batch Informed Trees (BIT*), a planning algorithm based on unifying graph- and sampling-based planning techniques. By recognizing that a set of samples describes an implicit random geometric graph (RGG), we are able to combine the efficient ordered nature of graph-based techniques, such as A*, with the anytime scalability of sampling-based algorithms, such as Rapidly-exploring Random Trees (RRT). BIT* uses a heuristic to efficiently search a series of increasingly dense implicit RGGs while reusing previous information. It can be viewed as an extension of incremental graph-search techniques, such as Lifelong Planning A* (LPA*), to continuous problem domains as well as a generalization of existing sampling-based optimal planners. It is shown that it is probabilistically complete and asymptotically optimal. We demonstrate the utility of BIT* on simulated random worlds in $\mathbb{R}^2$ and $\mathbb{R}^8$ and manipulation problems on CMU's HERB, a 14-DOF two-armed robot. On these problems, BIT* finds better solutions faster than RRT, RRT*, Informed RRT*, and Fast Marching Trees (FMT*) with faster anytime convergence towards the optimum, especially in high dimensions.Comment: 8 Pages. 6 Figures. Video available at http://www.youtube.com/watch?v=TQIoCC48gp

The induced 2-tuple linguistic generalized OWA operator and its application in linguistic decision making

We present the induced 2-tuple linguistic generalized ordered weighted averaging (2-TILGOWA) operator. This new aggregation operator extends previous approaches by using generalized means, order-inducing variables in the reordering of the arguments and linguistic information represented with the 2-tuple linguistic approach. Its main advantage is that it includes a wide range of linguistic aggregation operators. Thus, its analyses can be seen from different perspectives and we obtain a much more complete picture of the situation considered and are able to select the alternative that best fits with with our interests or beliefs. We further generalize the operator by using quasi-arithmetic means, and obtain the Quasi-2-TILOWA operator. We conclude this paper by analysing the applicability of this new approach in a decision-making problem concerning product management.linguistic decision making, linguistic generalized mean, 2-tuple linguistic owa operator, 2-tuple linguistic aggregation operator

Fast MCMC sampling for Markov jump processes and extensions

Markov jump processes (or continuous-time Markov chains) are a simple and important class of continuous-time dynamical systems. In this paper, we tackle the problem of simulating from the posterior distribution over paths in these models, given partial and noisy observations. Our approach is an auxiliary variable Gibbs sampler, and is based on the idea of uniformization. This sets up a Markov chain over paths by alternately sampling a finite set of virtual jump times given the current path and then sampling a new path given the set of extant and virtual jump times using a standard hidden Markov model forward filtering-backward sampling algorithm. Our method is exact and does not involve approximations like time-discretization. We demonstrate how our sampler extends naturally to MJP-based models like Markov-modulated Poisson processes and continuous-time Bayesian networks and show significant computational benefits over state-of-the-art MCMC samplers for these models.Comment: Accepted at the Journal of Machine Learning Research (JMLR

Dynamic Enfrachisement

Why would a political elite voluntarily dilute its political power by extending the franchise? This paper develops a dynamic recursive framework for studying voter enfranchisement. We study properties of dynamic enfranchisement games, dynamic games in which political rights evolve over time. Each period, private decisions of citizens co-mingle with government policies to act upon a state variable such as capital stock, a public good, or the likelihood of an insurrection. Policies are determined by the median voter of a potentially restricted franchise. The enfranchised group can choose, through its median voter, to expand the set of citizens with voting rights. In this way, each period's median voter can e.ectively delegate decision authority to a new median in the next period. We characterize the equilibria of a dynamic enfranchisement game by its Euler equations. In certain games, the equilibria generate paths that display a gradual, sometimes uneven history of enfranchisement that is roughly consistent with observed patterns of extensions. Our main result shows that extensions of the franchise occur in a given period if and only if the private decisions of the citizenry have a net positive spillover to the dynamic payo. of the current median voter. The size of the extension depends on the size of the spillover. Since the class of games we study can accommodate a number of proposed explanations for franchise extension (e.g., the threat of insurrection, or ideological or class conflict within the elite, etc), the result suggests a common causal mechanism for these seemingly di.erent explanations. We describe a number of parametric environments that correspond to the various explanations, and show how the mechanism works in each.Dynamic games, voter enfranchisement, franchise extension equilibria

Rule-based Machine Learning Methods for Functional Prediction

We describe a machine learning method for predicting the value of a real-valued function, given the values of multiple input variables. The method induces solutions from samples in the form of ordered disjunctive normal form (DNF) decision rules. A central objective of the method and representation is the induction of compact, easily interpretable solutions. This rule-based decision model can be extended to search efficiently for similar cases prior to approximating function values. Experimental results on real-world data demonstrate that the new techniques are competitive with existing machine learning and statistical methods and can sometimes yield superior regression performance.Comment: See http://www.jair.org/ for any accompanying file