Expected complexity analysis of stochastic direct-search

This work presents the convergence rate analysis of stochastic variants broad class direct-search methods directional type. It introduces an algorithm designed to optimize differentiable objective functions f whose values can only be computed through a stochastically noisy blackbox. The proposed (SDDS) accepts new iterates by imposing sufficient decrease condition on so called probabilistic estimates corresponding unavailable function values. accuracy such is required hold with sufficiently large but fixed probability $$\beta$$ . this method utilizes existing supermartingale-based framework for rates optimization that use adaptive step sizes. aims show expected number iterations drive norm gradient below given threshold $$\epsilon$$ bounded in $${\mathcal {O}}\left( \epsilon ^{\frac{-p}{\min (p-1,1)}}/(2\beta -1)\right)$$ $$p>1$$ Unlike prior using same aforementioned as those trust-region and line search methods, SDDS does not any information find descent directions. However, its similar both latter dependence also matches deterministic which accept condition.