  Regret minimization is a powerful tool for solving large-scale problems; it
was recently used in breakthrough results for large-scale extensive-form game
solving. This was achieved by composing simplex regret minimizers into an
overall regret-minimization framework for extensive-form game strategy spaces.
In this paper we study the general composability of regret minimizers. We
derive a calculus for constructing regret minimizers for composite convex sets
that are obtained from convexity-preserving operations on simpler convex sets.
We show that local regret minimizers for the simpler sets can be combined with
additional regret minimizers into an aggregate regret minimizer for the
composite set. As one application, we show that the CFR framework can be
constructed easily from our framework. We also show ways to include curtailing
(constraining) operations into our framework. For one, they enables the
construction of CFR generalization for extensive-form games with general convex
strategy constraints that can cut across decision points.
