Convergence Bound

Convergence bounds quantify the speed at which iterative algorithms, such as Markov Chain Monte Carlo methods and stochastic optimization algorithms, approach a solution. Current research focuses on developing tighter bounds for various algorithms, including those employing neural networks (e.g., for solving contractive drift equations) and diffusion models, often addressing challenges posed by high dimensionality and multimodality. These improved bounds are crucial for assessing algorithm efficiency, guiding algorithm design, and providing reliable performance guarantees in diverse applications like Bayesian inference, machine learning, and scientific computing. Furthermore, research explores the practical utility of convergence bounds beyond theoretical analysis, for example, in optimizing distributed learning strategies.