Optimum transport (OT) has profoundly impacted machine studying by offering theoretical and computational instruments to realign datasets. On this context, given two giant level clouds of sizes nn and mm in Rdmathbb{R}^d, entropic OT (EOT) solvers have emerged as probably the most dependable device to both remedy the Kantorovich downside and output a n×mntimes m coupling matrix, or to unravel the Monge downside and study a vector-valued push-forward map. Whereas the robustness of EOT couplings/maps makes them a go-to alternative in sensible functions, EOT solvers stay troublesome to tune due to a small however influential set of hyperparameters, notably the omnipresent entropic regularization power εvarepsilon. Setting εvarepsilon will be troublesome, because it concurrently impacts numerous efficiency metrics, equivalent to compute pace, statistical efficiency, generalization, and bias. On this work, we suggest a brand new class of EOT solvers (ProgOT),
that may estimate each plans and transport maps.
We reap the benefits of a number of alternatives to optimize the computation of EOT options by dividing mass displacement utilizing a time discretization, borrowing inspiration from dynamic OT formulations (McCann 1997), and conquering every of those steps utilizing EOT with correctly scheduled parameters. We offer experimental proof demonstrating that ProgOT is a sooner and extra strong different to EOT solvers when computing couplings and maps at giant scales, even outperforming neural network-based approaches. We additionally show the statistical consistency of ProgOT when estimating OT maps.