Optimal transport (OT) has profoundly impacted machine learning by providing theoretical and computational tools to realign datasets. In this context, given two large point clouds of sizes nnn and mmm in Rdmathbb{R}^dRd, entropic OT (EOT) solvers have emerged as the most reliable tool to either solve the Kantorovich problem and output a n×mntimes mn×m coupling matrix, or to solve the Monge problem and learn a vector-valued push-forward map. While the robustness of EOT couplings/maps makes them a go-to choice in practical applications, EOT solvers remain difficult to tune because of a small…