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math.OC2024
Asymptotic regularity of a generalised stochastic Halpern scheme
Nicholas Pischke, Thomas Powell
We provide abstract, general and highly uniform rates of asymptotic regularity for a generalized stochastic Halpern-style iteration, which incorporates a second mapping in the styl…
math.OC2024
A quantitative Robbins-Siegmund theorem
Morenikeji Neri, Thomas Powell
The Robbins-Siegmund theorem is one of the most important results in stochastic optimization, where it is widely used to prove the convergence of stochastic algorithms. We provide…
math.PR2024
On quantitative convergence for stochastic processes: Crossings, fluctuations and martingales
Morenikeji Neri, Thomas Powell
We develop a general framework for extracting highly uniform bounds on local stability for stochastic processes in terms of information on fluctuations or crossings. This includes…