Q1: Table 1 looks strange to me. It might better to give more intuitions and explanations.

Contract theory studies the setting where a principal seeks to design a contract for rewarding an agent on the basis of the uncertain outcomes caused by the agent's private actions [

We present an efficient algorithm for regularized optimal transport.

Let x be a root ofG(,θ), i.e., G(x,θ) = 0. Frank-Wolfeimplementations typically maintain theconvexweights ofthe vertices, which we use to get an approximation ofp?(θ). As a more advanced example, we now describe how to implement the KKT conditions(6). In all experiments, we only show how to compute gradients with the outer objective. There areseveral ways to differentiate this projection. The first is to use the KKT conditions as detailed in 2.2.