Enhancing Stochastic Gradient Descent: A Unified Framework and Novel Acceleration Methods for Faster Convergence

Understand

Based on SGD, previous works have proposed many algorithms that have improved convergence speed and generalization in stochastic optimization, such as SGDm, AdaGrad, Adam, etc.

• However, their convergence analysis under non-convex conditions is challenging.
• In this work, we propose a unified framework to address this issue.
• For any first-order methods, we interpret the updated direction $g_t$ as the sum of the stochastic subgradient $\nabla f_t(x_t)$ and an additional acceleration term $\frac{2|\langle v_t, \nabla f_t(x_t) \rangle|}{\|v_t\|_2^2} v_t$, thus we can discuss the convergence by analyzing $\langle v_t, \nabla f_t(x_t) \rangle$.