Research map / Learning theory and algorithms / Optimal transport
MinMax Methods for Optimal Transport and Beyond: Regularization, Approximation and Numerics
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a fixed mixture of 5 generators (ablation) | MOT base method · MOT | Error marginals: 0.126 -> 0.062 | Helped |
| Use 5 discriminator unrolling steps (ablation) | MOT base method · MOT | Error marginals: 0.126 -> 0.016 | Helped |
| Combine a fixed mixture of 5 generators with 5 discriminator unrolling steps (ablation) | MOT base method · MOT | Std dev iterations: 0.267 -> 0.015 | Helped |
| Use a mixture of 5 generators and 5 unrolling steps instead of the base optimization procedure (ablation) | 2-Wasserstein distance computation · 2-Wasserstein distance in R^d (m=64) | Objective value: 1.055 -> 0.998; 3.810 -> 2.001; 4.346 -> 3.004; 8.007 -> 5.292; 19.371 -> 10.061 | Helped |
| Use divergence regularization with ψ*_j(x) = x^2/150 instead of the base optimization procedure (ablation) | 2-Wasserstein distance computation · 2-Wasserstein distance in R^d (m=64) | Objective value: 1.055 -> 0.972; 3.810 -> 1.927; 4.346 -> 2.901; 8.007 -> 4.922; 19.371 -> 10.070 | Helped |
| Use divergence regularization with ψ*_j(x) = x^2/150 rather than the mixture-and-unrolling method (ablation) | 2-Wasserstein distance computation · 2-Wasserstein distance in R^d (m=64) | Std dev iterations: 0.004 vs 0.003; 0.004 vs 0.003; 0.010 vs 0.009; 0.020 vs 0.201; 0.067 vs 0.654 | Mixed |
| Increase hidden dimension from 64 to 256 in the base procedure (ablation) | 2-Wasserstein distance computation · 2-Wasserstein distance in R^d | Objective value: 1.055 -> 1.110; 3.810 -> 2.048; 4.346 -> 4.346; 8.007 -> 5.359; 19.371 -> 16.396 | Mixed |
| Use 10 discriminator updates per generator update instead of one in the DCOT experiment (ablation) | Unregularized (P^m) · DCOT | Training stability | Hurt |
| Use 10 discriminator updates per generator update with Lipschitz regularization (ablation) | (P^m_L) · DCOT | Training stability | Helped |
| Use 10 discriminator updates per generator update with divergence regularization (ablation) | (P^m_ψ) · DCOT | Training stability | Helped |
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