  In recent decades, a great variety of researches and applications concerning
Bell nonlocality have been developed with the advent of quantum information
science. Providing that Bell nonlocality can be revealed by the violation of a
family of Bell inequalities, finding maximal Bell violation (MBV) for unknown
quantum states becomes an important and inevitable task during Bell
experiments. In this paper we introduce a self-guide method to find MBVs for
unknown states using a stochastic gradient ascent algorithm (SGA), by
parameterizing the corresponding Bell operators. For all the investigated
systems (2-qubit, 3-qubit and 2-qutrit), this method can ascertain the MBV
accurately within 100 iterations. Moreover, SGA exhibits significant
superiority in efficiency, robustness and versatility compared to other
possible methods.
