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arXiv 2007.12397cs.ROcs.AIcs.LG
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最优化问题解流形的学习及其在运动规划中的应用

Learning the Solution Manifold in Optimization and Its Application in Motion Planning

Kyushu Institute of Technology(九州工业大学);RIKEN Center for Advanced Intelligence Project(理化学研究所先进智能研究中心)

Takayuki Osa

摘要:

优化是解决广泛领域问题的重要组成部分。理想情况下,目标函数应设计为使得解是唯一的,并且优化问题可以稳定地求解。然而,在实际应用中所使用的目标函数通常是非凸的,有时甚至有无穷多个解。为了解决这个问题,我们建议在优化中学习解决方案流形。我们训练一个以潜变量为条件的模型,使该模型代表一组无限的解。在我们的框架中,我们减少了这个问题的密度估计,通过使用重要性采样,和潜在的代表性的解决方案是学习最大化的变分下界。我们将该算法应用于运动规划问题,其中涉及高维参数的优化。实验结果表明,该算法可以学习的解决方案的流形,和训练的模型表示一个无限集的同伦运动规划问题的解决方案。

英文摘要:

Optimization is an essential component for solving problems in wide-ranging fields. Ideally, the objective function should be designed such that the solution is unique and the optimization problem can be solved stably. However, the objective function used in a practical application is usually non-convex, and sometimes it even has an infinite set of solutions. To address this issue, we propose to learn the solution manifold in optimization. We train a model conditioned on the latent variable such that the model represents an infinite set of solutions. In our framework, we reduce this problem to density estimation by using importance sampling, and the latent representation of the solutions is learned by maximizing the variational lower bound. We apply the proposed algorithm to motion-planning problems, which involve the optimization of high-dimensional parameters. The experimental results indicate that the solution manifold can be learned with the proposed algorithm, and the trained model represents an infinite set of homotopic solutions for motion-planning problems.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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