Triply Stochastic Gradients on Multiple Kernel Learning

Multiple Kernel Learning (MKL) is highly useful for learning complex data with multiple cues or representations. However, MKL is known to have poor scalability because of the expensive kernel computation. Dai et al (2014) proposed to use a doubly Stochastic Gradient Descent algorithm (doubly SGD) to greatly improve the scalability of kernel methods. However, the algorithm is not suitable for MKL because it cannot learn the kernel weights. In this paper, we provide a novel extension to doubly SGD for MKL so that both the decision functions and the kernel weights can be learned simultaneously. To achieve this, we develop the triply Stochastic Gradient Descent (triply SGD) algorithm which involves three sources of randomness – the data points, the random features, and the kernels, which was not considered in previous work. We prove that our algorithm enjoys similar convergence rate as that of doubly SGD. Comparing to several traditional MKL solutions, we show that our method has faster convergence speed and achieved better accuracy. Most importantly, our method makes it possible to learn MKL problems with millions of data points on a normal desktop PC.