Stochasticapproximationproblemistofindsomerootorextremumofanon-linearfunctionforwhichonlynoisymeasurementsofthefunctionareavailable.TheclassicalalgorithmforstochasticapproximationproblemistheRobbins-Monro(RM)algorithm,whichusesthenoisyevaluationofthenegativegradientdirectionastheiterativedirection.InordertoacceleratetheRMalgorithm,thispapergivesaflamealgorithmusingadaptiveiterativedirections.Ateachiteration,thenewalgorithmgoestowardseitherthenoisyevaluationofthenegativegradientdirectionorsomeotherdirectionsundersomeswitchcriterions.Twofeasiblechoicesofthecriterionsarepro-posedandtwocorrespondingflamealgorithmsareformed.Differentchoicesofthedirectionsunderthesamegivenswitchcriterionintheflamecanalsoformdifferentalgorithms.Wealsoproposedthesimultanousperturbationdifferenceformsforthetwoflamealgorithms.Thealmostsurelyconvergenceofthenewalgorithmsareallestablished.Thenumericalexperimentsshowthatthenewalgorithmsarepromising.
