Exponential Concentration in Stochastic Approximation

arXiv:2208.07243v4 Announce Type: replace-cross
Abstract: We analyze the behavior of stochastic approximation algorithms where iterates, in expectation, progress towards an objective at each step. When progress is proportional to the step size of the algorithm, we prove exponential concentration bounds. These tail-bounds contrast asymptotic normality results, which are more frequently associated with stochastic approximation. The methods that we develop rely on a geometric ergodicity proof. This extends a result on Markov chains due to Hajek (1982) to the area of …

abstract algorithm algorithms analyze approximation arxiv behavior contrast cs.lg math.oc normality progress prove results stat.ml stochastic the algorithm type