  We introduce a modular framework for market making. It combines cost-function
based automated market makers with bandit algorithms. We obtain worst-case
profits guarantee's relative to the best in hindsight within a class of natural
"overround" cost functions . This combination allow us to have
distribution-free guarantees on the regret of profits while preserving the
bounded worst-case losses and computational tractability over combinatorial
spaces of the cost function based approach. We present simulation results to
better understand the practical behaviour of market makers from the framework.
