Locally Optimal Descent for Dynamic Stepsize Scheduling

Abstract: We introduce a novel dynamic learning-rate scheduling scheme grounded in theory with the goal of simplifying the manual and time-consuming tuning of schedules in practice. Our approach is based on estimating the locally-optimal stepsize, guaranteeing maximal descent in the direction of the stochastic gradient of the current step. We first establish theoretical convergence bounds for our method within the context of smooth non-convex stochastic optimization, matching state-of-the-art bounds while only assuming knowledge of the smoothness parameter. We then present a practical implementation of our algorithm and conduct systematic experiments across diverse datasets and optimization algorithms, comparing our scheme with existing state-of-the-art learning-rate schedulers. Our findings indicate that our method needs minimal tuning when compared to existing approaches, removing the need for auxiliary manual schedules and warm-up phases and achieving comparable performance with drastically reduced parameter tuning.