论文标题
学习优化中的解决方案歧管及其在运动计划中的应用
Learning the Solution Manifold in Optimization and Its Application in Motion Planning
论文作者
论文摘要
优化是解决广泛领域中问题的重要组成部分。理想情况下，应该设计目标函数，以使解决方案是唯一的，并且可以稳定地解决优化问题。但是，实际应用中使用的目标函数通常是非凸，有时甚至具有无限的解决方案。为了解决这个问题，我们建议学习优化中的解决方案歧管。我们训练一个以潜在变量为条件的模型，以使模型代表无限的解决方案。在我们的框架中，我们通过使用重要性采样将该问题减少到密度估计，并且通过最大化变异下限来学习解决方案的潜在表示。我们将提出的算法应用于运动规划问题，该问题涉及高维参数的优化。实验结果表明，可以使用所提出的算法来学习溶液歧管，并且训练有素的模型代表了一组无限的同型解决方案，用于运动规划问题。
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.
