Scalable Kernel Methods via Doubly Stochastic Gradients

The general perception is that kernel methods are not scalable, and neural nets are the methods of choice for nonlinear learning problems. Or have we simply not tried hard enough for kernel methods? Here we propose an approach that scales up kernel methods using a novel concept called "doubly stochastic functional gradients". Our approach relies on the fact that many kernel methods can be expressed as convex optimization problems, and we solve the problems by making two unbiased stochastic approximations to the functional gradient, one using random training points and another using random functions associated with the kernel, and then descending using this noisy functional gradient. We show that a function produced by this procedure after $t$ iterations converges to the optimal function in the reproducing kernel Hilbert space in rate $O(1/t)$, and achieves a generalization performance of $O(1/\sqrt{t})$. This doubly stochasticity also allows us to avoid keeping the support vectors and to implement the algorithm in a small memory footprint, which is linear in number of iterations and independent of data dimension. Our approach can readily scale kernel methods up to the regimes which are dominated by neural nets. We show that our method can achieve competitive performance to neural nets in datasets such as 8 million handwritten digits from MNIST, 2.3 million energy materials from MolecularSpace, and 1 million photos from ImageNet.Comment: 32 pages, 22 figure

Online Robot Introspection via Wrench-based Action Grammars

Robotic failure is all too common in unstructured robot tasks. Despite well-designed controllers, robots often fail due to unexpected events. How do robots measure unexpected events? Many do not. Most robots are driven by the sense-plan act paradigm, however more recently robots are undergoing a sense-plan-act-verify paradigm. In this work, we present a principled methodology to bootstrap online robot introspection for contact tasks. In effect, we are trying to enable the robot to answer the question: what did I do? Is my behavior as expected or not? To this end, we analyze noisy wrench data and postulate that the latter inherently contains patterns that can be effectively represented by a vocabulary. The vocabulary is generated by segmenting and encoding the data. When the wrench information represents a sequence of sub-tasks, we can think of the vocabulary forming a sentence (set of words with grammar rules) for a given sub-task; allowing the latter to be uniquely represented. The grammar, which can also include unexpected events, was classified in offline and online scenarios as well as for simulated and real robot experiments. Multiclass Support Vector Machines (SVMs) were used offline, while online probabilistic SVMs were are used to give temporal confidence to the introspection result. The contribution of our work is the presentation of a generalizable online semantic scheme that enables a robot to understand its high-level state whether nominal or abnormal. It is shown to work in offline and online scenarios for a particularly challenging contact task: snap assemblies. We perform the snap assembly in one-arm simulated and real one-arm experiments and a simulated two-arm experiment. This verification mechanism can be used by high-level planners or reasoning systems to enable intelligent failure recovery or determine the next most optima manipulation skill to be used.Comment: arXiv admin note: substantial text overlap with arXiv:1609.0494