Surrogate Losses for Online Learning of Stepsizes in Stochastic Non-Convex Optimization
This addresses the tedious and time-consuming stepsize tuning in SGD for machine learning practitioners, offering a method with theoretical guarantees in non-convex settings.
The paper tackles the problem of manually tuning stepsizes in Stochastic Gradient Descent (SGD) for non-convex optimization by proposing surrogate losses to learn optimal stepsizes online, resulting in a self-tuned SGD algorithm with convergence rates adaptive to noise.
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. They have proved efficient in reducing the labor of tuning in practice, but many of them lack theoretic guarantees even in the convex setting. 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 no-regret online algorithms to compute optimal stepsizes 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.