Inprior work, ithas been shown that, when the constraints on the factorized variable regularly define a smooth manifold, providedk is large enough, for almost all cost matrices, all second-order stationary points (SOSPs) are optimal. Importantly, in practice, one can only compute points which approximately satisfy necessary optimality conditions, leading tothequestion: aresuch points also approximately optimal?

We introduce in this paper a novel strategy for efficiently approximating the Sinkhorn distance between twodiscrete measures.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

We give a precise trade-off between the rank of the SVDs required and the radius of the ball in which we need to initialize the method.