Research map / Learning theory and algorithms / Optimal transport
Computational Guarantees for Doubly Entropic Wasserstein Barycenters
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add damping factor eta = min(1, tau/lambda) to Sinkhorn updates (ablation) | Iterative Bregman projections for (lambda,tau)-barycenters · Gaussian simulation, k=1, nu=N(0,1) | log KL(mu*||mu_t) | Helped |
| use the suggested damping factor versus four other damping choices (eta = 1.0, 0.85, 0.7, 0.5, 0.25) (ablation) | Algorithm 1 · Gaussian simulation, lambda/tau = 2.0 | convergence speed of log KL | Helped |
| add damping to the inexact (noisy) oracle algorithm at the critical case tau about lambda/2 (ablation) | Algorithm 2 · Gaussian simulation, k=3, nu=N(0,I10) | log KL(mu*||mu_t) | Helped |
| overdamp (eta smaller than min(1,tau/lambda)) the exact scheme (ablation) | Algorithm 2 · Gaussian simulation, k=3 | convergence speed | Hurt |
| increase damping strength in the noisy setup (ablation) | Algorithm 2 · Gaussian simulation, noisy oracle | accuracy at convergence | Hurt |
| decrease tau relative to lambda (lambda/tau from 0.5 to 2.1) without damping | Undamped Algorithm 1 · Gaussian simulation, k=1 | convergence of log KL: lambda/tau = 2.1 | Hurt |
| vary the noise level epsilon of the approximate Sinkhorn oracle | Algorithm 2 · Gaussian simulation, epsilon = 0.001, 0.0001, 0.00001 | log KL plateau | Mixed |
| add noise to the undamped scheme at tau = lambda/2 | Undamped Algorithm 2 · Gaussian simulation | stability | Hurt |
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