Convergence Guarantee

Convergence guarantees in optimization algorithms are crucial for ensuring reliable and efficient solutions to complex problems across various fields, including machine learning and robotics. Current research focuses on establishing these guarantees for diverse settings, encompassing stochastic and deterministic optimization, convex and non-convex functions, and distributed or federated learning scenarios; algorithms under investigation include gradient descent variants (with momentum, adaptive step sizes, and variance reduction), proximal point methods, and Hamiltonian Monte Carlo. These advancements are vital for improving the robustness and predictability of machine learning models and enabling the development of provably efficient algorithms for challenging optimization tasks.