Stochastic Polyak Stepsize with a Moving Target
This is an incremental improvement for stochastic gradient optimization in machine learning, addressing a specific convergence issue.
The authors tackled the limitation of the Stochastic Polyak method, which only converges under the interpolation condition, by proposing MOTAPS, a variant that uses past loss values and auxiliary variables to remove this reliance, and demonstrated its competitiveness in convex learning and deep learning tasks.
We propose a new stochastic gradient method called MOTAPS (Moving Targetted Polyak Stepsize) that uses recorded past loss values to compute adaptive stepsizes. MOTAPS can be seen as a variant of the Stochastic Polyak (SP) which is also a method that also uses loss values to adjust the stepsize. The downside to the SP method is that it only converges when the interpolation condition holds. MOTAPS is an extension of SP that does not rely on the interpolation condition. The MOTAPS method uses $n$ auxiliary variables, one for each data point, that track the loss value for each data point. We provide a global convergence theory for SP, an intermediary method TAPS, and MOTAPS by showing that they all can be interpreted as a special variant of online SGD. We also perform several numerical experiments on convex learning problems, and deep learning models for image classification and language translation. In all of our tasks we show that MOTAPS is competitive with the relevant baseline method.