5 papers · 1 filter
An abstract effective convergence theorem for stochastic processes, with applications to stochastic approximation
Morenikeji Neri, Nicholas Pischke, Thomas Powell
We provide a general theorem on the asymptotic behavior of stochastic processes that conform to a relaxed supermartingale condition. The distinguishing feature of our result is tha…
Convergence guarantees for stochastic algorithms solving non-unique problems in metric spaces
Nicholas Pischke, Thomas Powell
We prove a general quantitative theorem on the asymptotic behavior of stochastic quasi-Fejér monotone sequences in a broad metric context. Concretely, our result explicitly constr…
Generalized fluctuation bounds for stochastic algorithms in the presence of compactness
Morenikeji Neri, Nicholas Pischke, Thomas Powell
We provide a convergence result for sequences of random variables taking values in a metric space that satisfy a stochastic quasi-Fejér monotonicity condition, in the context of a…
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…
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…