Exponential Convergence of General Iterative Proportional Fitting Procedures
研究了用于求解一般信息投影问题的迭代比例拟合过程(IPFP)的收敛性质，建立了指数收敛保证，并揭示了约束子空间之间的几何关系对收敛速度的影响。
Motivated by the success of Sinkhorn's algorithm for entropic optimal transport, we study convergence properties of iterative proportional fitting procedures (IPFP) used to solve more general information projection problems. We establish exponential convergence guarantees for the IPFP whenever the set of probability measures which is projected onto is defined through constraints arising from linear function spaces. This unifies and extends recent results from multi-marginal, adapted and martingale optimal transport. The proofs are based on strong convexity arguments for the dual problem, and the key contribution is to illuminate the role of the geometric interplay between the subspaces defining the constraints. In this regard, we show that the larger the angle (in the sense of Friedrichs) between the linear function spaces, the better the rate of contraction of the IPFP.