  We analyze the learning properties of the stochastic gradient method when
multiple passes over the data and mini-batches are allowed. We study how
regularization properties are controlled by the step-size, the number of passes
and the mini-batch size. In particular, we consider the square loss and show
that for a universal step-size choice, the number of passes acts as a
regularization parameter, and optimal finite sample bounds can be achieved by
early-stopping. Moreover, we show that larger step-sizes are allowed when
considering mini-batches. Our analysis is based on a unifying approach,
encompassing both batch and stochastic gradient methods as special cases. As a
byproduct, we derive optimal convergence results for batch gradient methods
(even in the non-attainable cases).
