Locally Optimal Descent for Dynamic Stepsize Scheduling

Stochastic gradient-based optimization methods such as SGD and Adam (Kingma & Ba, 2014) are the main workhorse behind modern machine learning. Such methods sequentially apply stochastic gradient steps to update the trained model and their performance crucially depends on the choice of a learning rate sequence, or schedule, used throughout this process to determine the magnitude of the sequential updates. All in all, effectively tuning the learning rate schedule is widely considered a tedious task requiring extensive, sometimes prohibitive, hyper-parameter search, resulting in a significant excess of engineering time and compute resources usage in ML training. A prominent approach to address this issue gave rise to a plethora of adaptive optimization methods (most notably Duchi et al., 2011 and Kingma & Ba, 2014), where the learning rate parameter is automatically tuned during the optimization process based on previously received stochastic gradients. In some important applications these methods provide superior convergence performance, while their theoretical guarantees match the state-of-the-art in the stochastic convex and (smooth) non-convex optimization settings (Li & Orabona, 2019; Ward et al., 2020; Attia & Koren, 2023). However, despite the adaptivity incorporated into these methods, auxiliary learning rate schedules are often still required to actually attain their optimal performance (e.g., Loshchilov & Hutter, 2016), and the nuisance of laborious and extensive manual tuning still remain relevant for these methods as well.