论文标题
线性回归游戏：融合保证可近似分布解决方案
Linear Regression Games: Convergence Guarantees to Approximate Out-of-Distribution Solutions
论文作者
论文摘要
最近，提出了不变的风险最小化（IRM）（Arjovsky等人）作为解决分布外（OOD）概括的有前途的解决方案。在Ahuja等人中，可以证明，解决新类“合奏游戏”的NASH均衡等同于解决IRM。在这项工作中，我们扩展了Ahuja等人的框架。对于线性回归，通过在$ \ ell _ {\ infty} $ ball上投影集合游戏。我们表明，尽管没有达到完美的不变性，但这种预测有助于实现非平凡的OOD保证。对于具有混杂因素的线性模型，我们证明，与标准的经验风险最小化（ERM）相比，这些游戏的NASH平衡更接近理想的OOD解决方案，并且我们还提供了学习算法，这些算法可证明与这些NASH均衡。该方法与最先进的方法的经验比较表明，在涉及反毒物变量和混杂因素的几种环境中实现OOD解决方案方面的一致性。
Recently, invariant risk minimization (IRM) (Arjovsky et al.) was proposed as a promising solution to address out-of-distribution (OOD) generalization. In Ahuja et al., it was shown that solving for the Nash equilibria of a new class of "ensemble-games" is equivalent to solving IRM. In this work, we extend the framework in Ahuja et al. for linear regressions by projecting the ensemble-game on an $\ell_{\infty}$ ball. We show that such projections help achieve non-trivial OOD guarantees despite not achieving perfect invariance. For linear models with confounders, we prove that Nash equilibria of these games are closer to the ideal OOD solutions than the standard empirical risk minimization (ERM) and we also provide learning algorithms that provably converge to these Nash Equilibria. Empirical comparisons of the proposed approach with the state-of-the-art show consistent gains in achieving OOD solutions in several settings involving anti-causal variables and confounders.
