Differentiable Cost-Parameterized Monge Map Estimators

• URL: http://arxiv.org/abs/2406.08399v1
• Date: Wed, 12 Jun 2024 16:47:54 GMT
• Title: Differentiable Cost-Parameterized Monge Map Estimators
• Authors: Samuel Howard, George Deligiannidis, Patrick Rebeschini, James Thornton,
• Abstract summary: It is desirable to use known information to tailor cost functions and hence learn OT maps which are adapted to the problem at hand. We construct a differentiable Monge map estimator which can be optimized to be consistent with known information about an OT map. Our method provides a general approach for incorporating prior information about the Monge map itself when learning adapted OT maps and cost functions.
• Score: 19.015367254988448
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Within the field of optimal transport (OT), the choice of ground cost is crucial to ensuring that the optimality of a transport map corresponds to usefulness in real-world applications. It is therefore desirable to use known information to tailor cost functions and hence learn OT maps which are adapted to the problem at hand. By considering a class of neural ground costs whose Monge maps have a known form, we construct a differentiable Monge map estimator which can be optimized to be consistent with known information about an OT map. In doing so, we simultaneously learn both an OT map estimator and a corresponding adapted cost function. Through suitable choices of loss function, our method provides a general approach for incorporating prior information about the Monge map itself when learning adapted OT maps and cost functions.

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