Gradient Momentum

Gradient momentum methods enhance the convergence speed of optimization algorithms by incorporating past gradient information into current updates. Current research focuses on analyzing and improving momentum's effectiveness in various contexts, including stochastic settings, zeroth-order optimization (relevant for memory-constrained large language models), and bilevel optimization problems. These advancements are significant for improving the efficiency and stability of training complex models in machine learning and for solving challenging optimization problems in other scientific domains, such as those involving partial differential equations. The development of scale-invariant and adaptive momentum techniques further contributes to robust and efficient optimization across diverse applications.