The convergence of many numerical optimization techniques is highly sensitive to the initial guess provided to the solver. We propose an approach based on tensor methods to initialize the existing optimization solvers close to global optima. The approach uses only the definition of the cost function and does not need access to any database of good solutions. We first transform the cost function, which is a function of task parameters and optimization variables, into a probability density function. Unlike existing approaches that set the task parameters as constant, we consider them as another set of random variables and approximate the joint probability distribution of the task parameters and the optimization variables using a surrogate probability model. For a given task, we then generate samples from the conditional distribution with respect to the given task parameter and use them as initialization for the optimization solver. As conditioning and sampling from an arbitrary density function are challenging, we use Tensor Train decomposition to obtain a surrogate probability model from which we can efficiently obtain the conditional model and the samples. The method can produce multiple solutions coming from different modes (when they exist) for a given task. We first evaluate the approach by applying it to various challenging benchmark functions for numerical optimization that are difficult to solve using gradient-based optimization solvers with a naive initialization, showing that the proposed method can produce samples close to the global optima and coming from multiple modes. We then demonstrate the generality of the framework and its relevance to robotics by applying the proposed method to inverse kinematics and motion planning problems with a 7-DoF manipulator.
翻译:许多数字优化技术的趋同性对于向求解者提供的最初猜想非常敏感。 我们提出一种基于强效方法的方法,在接近全球opima的地方初始化现有优化求解器。 这种方法只使用成本功能的定义, 不需要访问任何好解决方案的数据库。 我们首先将成本功能( 任务参数和优化变量的函数) 转换为概率密度函数。 与将任务参数设定为常数的现有方法不同, 我们把它们视为另一套随机变量, 并用一种代金概率模型来比较任务参数和优化变量的联合概率分布。 对于一项特定任务, 我们随后从有条件的分配中提取样本样本样本样本, 并使用与特定任务参数相关的样本。 当任意密度函数的调节和取样具有挑战性时, 我们使用Tensor 火车解压缩功能, 以获得一种代金概率模型和样本的替代模型。 这种方法可以产生来自不同模式( 当存在时)的多重解决方案。 我们首先通过应用该方法来评估该方法, 将一些具有挑战性的基准功能用于对特定任务参数的分布,, 并且将它作为优化工具, 我们用一个难以选择一个通用的模型来演示方法,, 并且用一个难以以精确的模型来演示方法 。