We examine the relationship between the mutual information between the output model and the empirical sample and the generalization of the algorithm in the context of stochastic convex optimization. Despite increasing interest in information-theoretic generalization bounds, it is uncertain if these bounds can provide insight into the exceptional performance of various learning algorithms. Our study of stochastic convex optimization reveals that, for true risk minimization, dimension-dependent mutual information is necessary. This indicates that existing information-theoretic generalization bounds fall short in capturing the generalization capabilities of algorithms like SGD and regularized ERM, which have dimension-independent sample complexity.

翻译：我们研究了随机凸优化背景下输出模型与经验样本之间的互信息与算法泛化能力之间的关系。尽管信息论泛化界日益受到关注，但尚不确定这些界能否为各类学习算法的卓越性能提供洞见。通过对随机凸优化的研究发现，在真实风险最小化过程中，互信息必须依赖于维度。这表明现有信息论泛化界无法捕捉如SGD和正则化ERM等算法的泛化能力，而这些算法的样本复杂度与维度无关。