Domain generalization aims at performing well on unseen test environments with data from a limited number of training environments. Despite a proliferation of proposal algorithms for this task, assessing their performance, both theoretically and empirically is still very challenging. Moreover, recent approaches such as Invariant Risk Minimization (IRM) require a prohibitively large number of training environments - linear in the dimension of the spurious feature space $d_s$ - even on simple data models like the one proposed by [Rosenfeld et al., 2021]. Under a variant of this model, we show that both ERM and IRM cannot generalize with $o(d_s)$ environments. We then present a new algorithm based on performing iterative feature matching that is guaranteed with high probability to yield a predictor that generalizes after seeing only $O(\log{d_s})$ environments.
翻译:广域化的目的是利用来自有限培训环境的数据,在无形的测试环境中很好地发挥作用。尽管对这项任务的建议算法激增,但从理论上和从经验上评估其绩效仍然非常具有挑战性。此外,最近的一些方法,如 " 易变风险最小化 " (IRM),要求大量的培训环境 -- -- 虚假地物空间层面的线性化($d_s) -- -- 甚至使用像[Rosenfeld 等人, 2021]提议的那种简单数据模型。在这个模型的一个变式下,我们证明机构风险管理和IMM都无法以$(d_s)环境为通用。我们随后提出了一种新的算法,其基础是进行迭代特征匹配,保证极有可能产生预测,或者在只看到$($(log{d_s})环境之后,一般化。