In this article, we develop the method of continuous Pontryagin differentiable programming (Continuous PDP), which enables a robot to learn an objective function from few sparsely demonstrated keyframes. The keyframes, labeled with some time stamps, are desired task-space outputs, is expected follow sequentially. stamps keyframes can be different robot's actual execution. jointly finds and time...

We start from a simple asymptotic result for the problem of online regression with the quadratic loss function: the class of continuous limited-memory prediction strategies admits a “leading prediction strategy”, which not only asymptotically performs at least as well as any continuous limited-memory strategy but also satisfies the property that the excess loss of any continuous limited-memory ...

In this paper, we introduce the new definition of rough membership function using continuous and discuss several concepts properties set value functions as results on function. Moreover, extend to topology spaces by substituting an equivalence class prove some theorems certain types more general fundamental generalized sets. Our result concept valued theory.