In view of a direct and simple improvement vanilla SGD, this paper presents fine-tuning its step-sizes in the mini-batch case. For doing so, one estimates curvature, based on local quadratic model using only noisy gradient approximations. One obtains new stochastic first-order method (Step-Tuned SGD), enhanced by second-order information, which can be seen as version classical Barzilai-Borwein ...