| # Reproduction: Gradient Flow Sampler-based Distributionally Robust Optimization | |
| ## Pages | |
| | Page | | |
| | --- | | |
| | [Executive summary](#/executive-summary) | | |
| | [Claim 1: The paper introduces a unified PDE gradient flow framework for distributionally robust optimization (DRO) with six concrete algorithms, including Wasserstein Gradient Flow (Algorithm 3) and Wasserstein Fisher-Rao flow (Algorithm 4) variants for entropy-regularized Wasserstein DRO (Section 4, Algorithms 3-4).](#/claim-1-six-algorithms) | | |
| | [Claim 2: Proposition 1 shows the Wasserstein gradient flow sampler must run for time at least on the order of O((1/λ) log(L/√(λε))) to produce an ε-accurate gradient estimate (Section 4, Proposition 1).](#/claim-2-flow-time) | | |
| | [Claim 3: Theorem 1 proves the outer loop of the gradient-flow-sampler-based DRO algorithm requires O(1/ε²_opt) iterations to reach an ε-stationary point (Section 5, Theorem 1).](#/claim-3-outer-loop) | | |
| | [Claim 4: Theorem 2 bounds the total computational complexity of the WGF-based DRO algorithm (Algorithm 3) as Õ(L_Φ L²_U L²_f d² / (λ³_U ε⁴_opt)) (Section 5, Theorem 2).](#/claim-4-total-complexity) | | |
| | [Claim 5: On CIFAR-10 adversarial training under PGD attacks, the WFR- and WGF-based DRO methods achieve consistently higher robust accuracy across all perturbation settings compared to baseline DRO methods (Section 6.3).](#/claim-5-cifar-robustness) | | |
| | [Claim 6: Lemma 1 establishes that the entropy-regularized DRO problem is equivalent to a Schrödinger half-bridge problem, enabling sampling from the conditional worst-case distribution (Section 3.1, Lemma 1).](#/claim-6-half-bridge) | | |
| | [Conclusion](#/conclusion) | | |