A single random direction exploration step added to any base optimizer guarantees directional stationarity almost surely at accumulation points under local Lipschitz continuity and continuous directional derivatives.
Stochastic approximations and differential inclusions
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Achieving Directional-Stationarity from a Single Random Direction Step
A single random direction exploration step added to any base optimizer guarantees directional stationarity almost surely at accumulation points under local Lipschitz continuity and continuous directional derivatives.