This paper addresses distributed learning of a complex object for multiple networked robots based on distributed optimization and kernel-based support vector machine. In order to overcome a fundamental limitation of polynomial kernels assumed in our antecessor, we employ Gaussian kernel as a kernel function for classification. The Gaussian kernel prohibits the robots to share the function through a finite number of equality constraints due to its infinite dimensionality of the function space. We thus reformulate the optimization problem assuming that the target function space is identified with the space spanned by the bases associated with not the data but a finite number of grid points. The above relaxation is shown to allow the robots to share the function by a finite number of equality constraints. We finally demonstrate the present approach through numerical simulations.

翻译：本文针对基于分布式优化与核支持向量机的多网络机器人复杂物体分布式学习问题展开研究。为克服先前工作中采用多项式核函数存在的根本性局限性，我们采用高斯核作为分类核函数。由于高斯核函数空间的无限维特性，机器人无法通过有限数量的等式约束共享函数。为此，我们通过假设目标函数空间由有限网格点（而非数据点）关联的基函数张成，重新构建了优化问题。研究表明上述松弛方法可使机器人通过有限数量的等式约束实现函数共享。最后通过数值仿真验证了本方法的有效性。