We present a new framework for deriving bounds on the generalization bound of statistical learning algorithms from the perspective of online learning. Specifically, we construct an online learning game called the "generalization game", where an online learner is trying to compete with a fixed statistical learning algorithm in predicting the sequence of generalization gaps on a training set of i.i.d. data points. We establish a connection between the online and statistical learning setting by showing that the existence of an online learning algorithm with bounded regret in this game implies a bound on the generalization error of the statistical learning algorithm, up to a martingale concentration term that is independent of the complexity of the statistical learning method. This technique allows us to recover several standard generalization bounds including a range of PAC-Bayesian and information-theoretic guarantees, as well as generalizations thereof.

翻译：我们提出一个新框架，用于从在线学习的角度推导统计学习算法泛化界的界限。具体而言，我们构建了一个名为“泛化博弈”的在线学习游戏，其中在线学习器试图与一个固定的统计学习算法竞争，预测独立同分布数据点训练集上泛化差距的序列。我们通过证明该博弈中存在一个具有有界遗憾的在线学习算法，意味着统计学习算法的泛化误差存在一个界限（该界限上界由独立于统计学习方法复杂度的鞅集中项给出），从而建立了在线学习与统计学习环境之间的联系。该技术使我们能够恢复包括一系列PAC-贝叶斯和信息论保证在内的若干标准泛化界，以及这些界的一般化形式。