We discuss these works in more detail in Section 5. Authors are listed in alphabetical order.

Two-sided matching markets have long existed to pair agents in the absence of regulated exchanges.

To reduce the computation burden, regularizing the OT problem with e.g. an entropic term

In this paper we revisit the fixed-confidence identification of the Pareto optimal set in a multi-objective multi-armed bandit model.

Unfortunately, this measure of similarity requires solving a nonconvex optimization problem. All elements of O (n) /SO ( n) are bijective maps between itself and SO (n) . Then we can show by the same logic that PD O (n) /SO ( n). According to Williams et al. [2021], only two things are needed. Then we must show that the similarity transform is an isometry: g (T (A), T(B)) = g ( A, B) (17) where T ( A) is a map that in our case is the similarity transform. Here we demonstrate how V ector Fields transform.

This arrangement is particularly important in scenarios with high sampling costs and potential dangers, such as autonomous driving and robotics.

These problems share a common nested optimization structure, and have inspired intensive study on the theory and algorithmic development of bilevel optimization. Prior efforts have been taken mainly on the single-machine scenario.

This allows us to include clustering in end-to-end trainable pipelines, with efficient gradients.