The equivalence of realizable and agnostic learnability is a fundamental phenomenon in learning theory. With variants ranging from classical settings like PAC learning and regression to recent trends such as adversarially robust learning, it's surprising that we still lack a unified theory; traditional proofs of the equivalence tend to be disparate, and rely on strong model-specific assumptions like uniform convergence and sample compression. In this work, we give the first model-independent framework explaining the equivalence of realizable and agnostic learnability: a three-line blackbox reduction that simplifies, unifies, and extends our understanding across a wide variety of settings. This includes models with no known characterization of learnability such as learning with arbitrary distributional assumptions and more general loss functions, as well as a host of other popular settings such as robust learning, partial learning, fair learning, and the statistical query model. More generally, we argue that the equivalence of realizable and agnostic learning is actually a special case of a broader phenomenon we call property generalization: any desirable property of a learning algorithm (e.g. noise tolerance, privacy, stability) that can be satisfied over finite hypothesis classes extends (possibly in some variation) to any learnable hypothesis class.

翻译：可实现学习与不可知学习之间的等价性是学习理论中的一个基本现象。从经典场景（如PAC学习和回归）到最新趋势（如对抗鲁棒学习），各种变体层出不穷，但令人惊讶的是，我们仍缺乏统一的理论；传统的等价性证明往往互不关联，且依赖于强模型特定假设（如一致收敛和样本压缩）。在本工作中，我们首次提出了一个与模型无关的框架来解释可实现学习与不可知学习之间的等价性：一个三行的黑盒化简方法，它简化、统一并扩展了我们在多种设置下的理解。这包括尚无学习性表征的模型（如具有任意分布假设和更一般损失函数的学习），以及诸多其他流行设置（如鲁棒学习、部分学习、公平学习和统计查询模型）。更一般地，我们认为可实现学习与不可知学习的等价性实际上是一个更广泛现象（我们称之为性质泛化）的特例：任何学习算法的理想性质（如噪声容忍性、隐私性、稳定性），只要能在有限假设类上满足，就能（可能以某种变体形式）推广到任何可学习的假设类。