通过双锚定分布鲁棒优化利用目标信息的域适应

中文摘要 AI 辅助

域适应（DA）通常缺乏最坏情况下的保证，而仅基于源数据的分布鲁棒优化（DRO）将其模糊集以源分布为中心，忽略了可用的目标结构。为弥合这一差距，我们提出了一种双锚定DRO框架，其模糊集是以源分布和源补全的目标参考分布为中心的φ-散度球的交集，后者将目标协变量分布与源条件分布配对。我们推导了对称和非对称散度配对的对偶诱导对抗桥几何，特别引入了Kullback-Leibler/平方Hellinger（KL/HD）桥。这种非对称公式产生了Lambert-W几何，其中源侧指数风险倾斜和目标侧Hellinger稳定通过不同的项进入，减弱但不限制大似然比的影响。此外，在不施加协变量偏移的情况下，我们在有界重叠条件下为结构性的、与损失无关的密度桥风险的最小化器建立了有限样本泛化界；这些界不直接适用于损失感知的DRO最小-最大估计器。我们将我们的框架转化为桥加权Nadaraya-Watson估计器，证明了源回归函数的一致性和逐点渐近正态性，当源和目标回归函数一致时（如在协变量偏移下），目标恢复得以实现。最后，在域偏移的Fashion-MNIST数据集上的实证评估说明了非对称KL/HD桥在严重合成目标协变量损坏下的有限样本稳定性。

英文摘要

Domain Adaptation (DA) often lacks worst-case guarantees, while Distributionally Robust Optimization (DRO) based only on source data centers its ambiguity set at the source law and ignores available target structure. To bridge this gap, we introduce a doubly-anchored DRO framework whose ambiguity set is the intersection of $ϕ$-divergence balls centered at the source law and a source-completed target reference law, the latter pairing the target covariate law with the source conditional law. We derive dual-induced adversarial bridge geometries for symmetric and asymmetric divergence pairings, notably introducing a Kullback--Leibler/squared-Hellinger (KL/HD) bridge. This asymmetric formulation yields a Lambert-$W$ geometry in which source-side exponential risk tilting and target-side Hellinger stabilization enter through distinct terms, attenuating, but not bounding, the effect of large likelihood ratios. Furthermore, without imposing covariate shift, we establish finite-sample generalization bounds for the minimizer of a structural, loss-agnostic density-bridge risk under bounded-overlap conditions; these bounds do not apply directly to the loss-aware DRO min--max estimator. We translate our framework into a bridge-weighted Nadaraya--Watson estimator, proving uniform consistency for the source regression function and pointwise asymptotic normality, with target recovery when the source and target regression functions coincide, as under covariate shift. Finally, an empirical evaluation on a domain-shifted Fashion-MNIST dataset illustrates the finite-sample stability of the asymmetric KL/HD bridge under severe synthetic target-covariate corruption.

发表机构

• George Mason University（乔治梅森大学）

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