MRO and SNR outperform DRO in robust linear regression
Original title: Regret-Optimal Wasserstein-Robust Linear Regression
MRO and SNR achieve minimax rates in Wasserstein-robust regression where DRO is provably suboptimal by dimension-dependent factors.
DRO minimizes worst-case risk under distributional uncertainty but can have high excess regret. In multivariate least-squares with 2-Wasserstein perturbation of size epsilon the asymptotic complexity depends on condition number kappa. DRO achieves instance-optimal rate O(kappa epsilon squared) as epsilon approaches 0 but fails for fixed epsilon. Two alternatives minimax regret optimization and spectral-norm regularization attain minimax rates with convex reformulations and guarantees.
- DRO achieves O(kappa epsilon squared) as epsilon to 0
- DRO suboptimal by dimension-dependent factors for fixed epsilon
- MRO and SNR attain minimax rates
- Exact convex reformulation for MRO
- Accelerated proximal algorithm for SNR
From the original article
1 min read at arxiv.orgDistributionally robust optimization (DRO) minimizes worst-case risk under distributional uncertainty, but its decisions can be suboptimal in terms of their excess risk, or regret. We study this gap for multivariate least-squares regression, assuming that the observed source law and unknown target law differ by an adversarial 2-Wasserstein perturbation of size $\varepsilon$.
By Sloan Nietert · arxiv.org
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