Stochastic Gradient Descent (SGD) has played a central role in machine learning. However, it requires a carefully hand-picked stepsize for fast convergence, which is notoriously tedious and time-consuming to tune. Over the last several years, a plethora of adaptive gradient-based algorithms have emerged to ameliorate this problem. In this paper, we propose new surrogate losses to cast the problem of learning the optimal stepsizes for the stochastic optimization of a non-convex smooth objective function onto an online convex optimization problem. This allows the use of noregret online algorithms to compute optimal step-sizes on the fly. In turn, this results in a SGD algorithm with self-tuned stepsizes that guarantees convergence rates that are automatically adaptive to the level of noise.
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