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The A* algorithm is commonly used to solve NP-hard combinatorial optimization problems. When provided with a completely informed heuristic function, A* can solve such problems in time complexity that is polynomial in the solution cost and branching factor. In light of this fact, we examine a line of recent publications that propose fitting deep neural networks to the completely informed heuristic function. We assert that these works suffer from inherent scalability limitations since --- under the assumption of NP P/poly --- such approaches result in either (a) network sizes that scale super-polynomially in the instance sizes or (b) the accuracy of the fitted deep neural networks scales inversely with the instance sizes. Complementing our theoretical claims, we provide experimental results for three representative NP-hard search problems. The results suggest that fitting deep neural networks to informed heuristic functions requires network sizes that grow quickly with the problem instance size. We conclude by suggesting that the research community should focus on scalable methods for integrating heuristic search with machine learning, as opposed to methods relying on informed heuristic estimation.
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Relevant Region Exploration On General Cost-maps For Sampling-Based Motion Planning
Asymptotically optimal sampling-based planners require an intelligent exploration strategy to accelerate convergence. After an initial solution is found, a necessary condition for improvement is to generate new samples in the so-called “Informed Set”. However, Informed Sampling can be ineffective in focusing search if the chosen heuristic fails to provide a good estimate of the solution cost. This work proposes an algorithm to sample the “Relevant Region” instead, which is a subset of the Informed Set. The Relevant Region utilizes cost-to-come information from the planner’s tree structure, reduces dependence on the heuristic, and further focuses the search. Benchmarking tests in uniform and general cost-space settings demonstrate the efficacy of Relevant Region sampling.
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- Award ID(s):
- 2008686
- PAR ID:
- 10276013
- Date Published:
- Journal Name:
- International Conference on Intelligent Robots and Systems
- Page Range / eLocation ID:
- 6689 to 6695
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/IROS45743.2020.9340806
