Showing papers on "Admissible heuristic published in 2017"

A Framework For Optimal Grasp Contact Planning

Abstract: We consider the problem of finding grasp contacts that are optimal under a given grasp quality function on arbitrary objects. Our approach formulates a framework for contact-level grasping as a path finding problem in the space of supercontact grasps. The initial supercontact grasp contains all grasps and in each step along a path grasps are removed. For this, we introduce and formally characterize search space structure and cost functions under which minimal cost paths correspond to optimal grasps. Our formulation avoids expensive exhaustive search and reduces computational cost by several orders of magnitude. We present admissible heuristic functions and exploit approximate heuristic search to further reduce the computational cost while maintaining bounded suboptimality for resulting grasps. We exemplify our formulation with point-contact grasping for which we define domain specific heuristics and demonstrate optimality and bounded suboptimality by comparing against exhaustive and uniform cost search on example objects. Furthermore, we explain how to restrict the search graph to satisfy grasp constraints for modeling hand kinematics. We also analyze our algorithm empirically in terms of created and visited search states and resultant effective branching factor.

Verification and Synthesis of Admissible Heuristics for Kinodynamic Motion Planning

Abstract: How does one obtain an admissible heuristic for a kinodynamic motion planning problem? This letter develops the analytical tools and techniques to answer this question. A sufficient condition for the admissibility of a heuristic is presented, which can be checked directly from problem data. This condition is also used to formulate an infinite-dimensional linear program to optimize an admissible heuristic. We then investigate the use of sum-of-squares programming techniques to obtain an approximate solution to this linear program. A number of examples are provided to demonstrate these new concepts.

A family of admissible heuristics for A* to perform inference in probabilistic classifier chains

Abstract: Probabilistic classifier chains have recently gained interest in multi-label classification, due to their ability to optimally estimate the joint probability of a set of labels. The main hindrance is the excessive computational cost of performing inference in the prediction stage. This pitfall has opened the door to propose efficient inference alternatives that avoid exploring all the possible solutions. The $$\epsilon $$∈-approximate algorithm, beam search and Monte Carlo sampling are appropriate techniques, but only $$\epsilon $$∈-approximate algorithm with $$\epsilon =0$$∈=0 theoretically guarantees reaching an optimal solution in terms of subset 0/1 loss. This paper offers another alternative based on heuristic search that keeps such optimality. It consists of applying the A* algorithm providing an admissible heuristic able to explore fewer nodes than the $$\epsilon $$∈-approximate algorithm with $$\epsilon =0$$∈=0. A preliminary study has already coped with this goal, but at the expense of the high computational time of evaluating the heuristic and only for linear models. In this paper, we propose a family of heuristics defined by a parameter that controls the trade-off between the number of nodes explored and the cost of computing the heuristic. Besides, a certain value of the parameter provides a method that is also suitable for the non-linear case. The experiments reported over several benchmark datasets show that the number of nodes explored remains quite steady for different values of the parameter, although the time considerably increases for high values. Hence, low values of the parameter give heuristics that theoretically guarantee exploring fewer nodes than the $$\epsilon $$∈-approximate algorithm with $$\epsilon =0$$∈=0 and show competitive computational time. Finally, the results exhibit the good behavior of the A* algorithm using these heuristics in complex situations such as the presence of noise.

Merge-and-shrink abstractions for classical planning : theory, strategies, and implementation

Abstract: Classical planning is the problem of finding a sequence of deterministic actions in a state space that lead from an initial state to a state satisfying some goal condition. The dominant approach to optimally solve planning tasks is heuristic search, in particular A* search combined with an admissible heuristic. While there exist many different admissible heuristics, we focus on abstraction heuristics in this thesis, and in particular, on the well-established merge-and-shrink heuristics. Our main theoretical contribution is to provide a comprehensive description of the merge-and-shrink framework in terms of transformations of transition systems. Unlike previous accounts, our description is fully compositional, i.e. can be understood by understanding each transformation in isolation. In particular, in addition to the name-giving merge and shrink transformations, we also describe pruning and label reduction as such transformations. The latter is based on generalized label reduction, a new theory that removes all of the restrictions of the previous definition of label reduction. We study the four types of transformations in terms of desirable formal properties and explain how these properties transfer to heuristics being admissible and consistent or even perfect. We also describe an optimized implementation of the merge-and-shrink framework that substantially improves the efficiency compared to previous implementations. Furthermore, we investigate the expressive power of merge-and-shrink abstractions by analyzing factored mappings, the data structure they use for representing functions. In particular, we show that there exist certain families of functions that can be compactly represented by so-called non-linear factored mappings but not by linear ones. On the practical side, we contribute several non-linear merge strategies to the merge-and-shrink toolbox. In particular, we adapt a merge strategy from model checking to planning, provide a framework to enhance existing merge strategies based on symmetries, devise a simple score-based merge strategy that minimizes the maximum size of transition systems of the merge-and-shrink computation, and describe another framework to enhance merge strategies based on an analysis of causal dependencies of the planning task. In a large experimental study, we show the evolution of the performance of merge-and-shrink heuristics on planning benchmarks. Starting with the state of the art before the contributions of this thesis, we subsequently evaluate all of our techniques and show that state-of-the-art non-linear merge-and-shrink heuristics improve significantly over the previous state of the art.

A heuristic in A* for inference in nonlinear Probabilistic Classifier Chains

Abstract: Probabilistic Classifier Chains (PCC) is a very interesting method to cope with multi-label classification, since it is able to obtain the entire joint probability distribution of the labels. However, such probability distribution is obtained at the expense of a high computational cost. Several efforts have been made to overcome this pitfall, proposing different inference methods for estimating the probability distribution. Beam search and the - approximate algorithms are two methods of this kind. A more recently approach is based on the A* algorithm with an admissible heuristic, but it is limited to be used just for linear classifiers as base methods for PCC. This paper goes in that direction presenting an alternative admissible heuristic for the A* algorithm with two promising advantages in comparison to the above-mentioned heuristic, namely, i) it is more dominant for the same depth and, hence, it explores fewer nodes and ii) it is suitable for nonlinear classifiers. Additionally, the paper proposes an efficient implementation for the computation of the heuristic that reduces the number of models that must be evaluated by half. The experiments show, as theoretically expected, that this new algorithm reaches Bayes-optimal predictions in terms of subset 0/1 loss and explores fewer nodes than other state-of-the-art methods that also provide optimal predictions. In spite of exploring fewer nodes, this new algorithm is not as fast as the -approximate algorithm with =0 when the search for an optimal solution is highly directed. However, it shows its strengths when the datasets present more uncertainty, making faster predictions than other state-of-the-art approaches.

New perspectives on cost partitioning for optimal classical planning

Abstract: Admissible heuristics are the main ingredient when solving classical planning tasks optimally with heuristic search. There are many such heuristics, and each has its own strengths and weaknesses. As higher admissible heuristic values are more accurate, the maximum over several admissible heuristics dominates each individual one. Operator cost partitioning is a well-known technique to combine admissible heuristics in a way that dominates their maximum and remains admissible. But are there better options to combine the heuristics? We make three main contributions towards this question: Extensions to the cost partitioning framework can produce higher estimates from the same set of heuristics. Cost partitioning traditionally uses non-negative cost functions. We prove that this restriction is not necessary, and that allowing negative values as well makes the framework more powerful: the resulting heuristic values can be exponentially higher, and unsolvability can be detected even if all component heuristics have a finite value. We also generalize operator cost partitioning to transition cost partitioning, which can differentiate between different contexts in which an operator is used. Operator-counting heuristics reason about the number of times each operator is used in a plan. Many existing heuristics can be expressed in this framework, which gives new theoretical insight into their relationship. Different operator-counting heuristics can be easily combined within the framework in a way that dominates their maximum. Potential heuristics compute a heuristic value as a weighted sum over state features and are a fast alternative to operator-counting heuristics. Admissible and consistent potential heuristics for certain feature sets can be described in a compact way which means that the best heuristic from this class can be extracted in polynomial time. Both operator-counting and potential heuristics are closely related to cost partitioning. They offer a new look on cost-partitioned heuristics and already sparked research beyond their use as classical planning heuristics.