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Tuning the step size of stochastic gradient descent is tedious and errorprone. This has motivated the development of methods that automatically adaptthe step size using readily available information. In this paper, we considerthe family of SPS (Stochastic gradient with a Polyak Stepsize) adaptivemethods. These are methods that make use of gradient and loss value at thesampled points to adaptively adjust the step size. We first show that SPS andits recent variants can all be seen as extensions of the Passive-Aggressivemethods applied to nonlinear problems. We use this insight to develop newvariants of the SPS method that are better suited to nonlinear models. Our newvariants are based on introducing a slack variable into the interpolationequations. This single slack variable tracks the loss function acrossiterations and is used in setting a stable step size. We provide extensivenumerical results supporting our new methods and a convergence theory.

Cutting Some Slack for SGD with Adaptive Polyak Stepsizes