Making SGD Parameter-Free
This work addresses the need for parameter-free optimization algorithms in machine learning, offering a more efficient solution for practitioners who want to avoid manual tuning, though it is incremental in improving convergence bounds.
The paper tackles the problem of parameter-free stochastic convex optimization by developing an algorithm that achieves a convergence rate only a double-logarithmic factor worse than the optimal known-parameter rate, improving upon previous methods with unavoidable excess logarithmic terms.
We develop an algorithm for parameter-free stochastic convex optimization (SCO) whose rate of convergence is only a double-logarithmic factor larger than the optimal rate for the corresponding known-parameter setting. In contrast, the best previously known rates for parameter-free SCO are based on online parameter-free regret bounds, which contain unavoidable excess logarithmic terms compared to their known-parameter counterparts. Our algorithm is conceptually simple, has high-probability guarantees, and is also partially adaptive to unknown gradient norms, smoothness, and strong convexity. At the heart of our results is a novel parameter-free certificate for SGD step size choice, and a time-uniform concentration result that assumes no a-priori bounds on SGD iterates.