Research map / Learning theory and algorithms / Optimal transport
Adversarial Risk via Optimal Transport and Optimal Couplings
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Express binary 0-1 optimal adversarial risk through the D_epsilon transport cost between class distributions | Binary classification · Binary classification, 0-1 loss | optimal adversarial risk | Mixed |
| Replace the data-perturbing adversary with a W_1 distribution-perturbing adversary at the same budget | Binary classification with Uniform[0,1] and a point mass at 0 · Uniform[0,1] versus point mass at 0; epsilon = 3/4 | optimal adversarial risk: 3/8 -> 1/2 | Hurt |
| Increase the adversary budget to at least half the distance between equal-variance Gaussian means | Equal-prior Gaussian classification · Gaussian classes with identical variance | optimal adversarial risk: 1/2 | Hurt |
| Use the midpoint-threshold classifier for equal-variance Gaussian classes below the budget threshold | Equal-prior Gaussian classification · Gaussian classes with identical variance; epsilon < |mu_0 - mu_1|/2 | optimal adversarial risk | Helped |
| Use the optimal robust classifier rather than the MLE classifier when the Gaussian adversary budget is large | Equal-prior Gaussian classification · Gaussian classes with identical variance; epsilon >= |mu_0 - mu_1|/2 | adversarial risk | Helped |
| Use a classifier region equal to the epsilon-expansion of the shorter uniform interval | Uniform-distribution classification · Uniform distributions on closed intervals I and J, |I| <= |J| | optimal adversarial risk | Helped |
Closest papers by meaning
- Lower Bounds on Adversarial Robustness from Optimal Transport (NeurIPS 2019 · similarity 0.93)
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- Theoretical Analysis of Adversarial Learning: A Minimax Approach (NeurIPS 2019 · similarity 0.89)
- On Achieving Optimal Adversarial Test Error (ICLR 2023 · similarity 0.88)
- Analyzing and Improving Optimal-Transport-based Adversarial Networks (ICLR 2024 · similarity 0.88)
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