2024/02/14 by Idan Attias, Gintare Karolina Dziugaite, Attias, Idan +7 · 1 citation
Computer Science · #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #Machine Learning (cs.LG) #Metaheuristic Optimization Algorithms Research #Neural Networks and Applications
paper · pdf · doi:10.48550/arxiv.2402.09327
openalex publication_date 2024/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we investigate the interplay between memorization and learning in the context of stochastic convex optimization (SCO). We define memorization via the information a learning algorithm reveals about its training data points. We then quantify this information using the framework of conditional mutual information (CMI) proposed by Steinke and Zakynthinou (2020). Our main result is a precise characterization of the tradeoff between the accuracy of a learning algorithm and its CMI, answering an open question posed by Livni (2023). We show that, in the L2 Lipschitz--bounded setting and under strong convexity, every learner with an excess error ε has CMI bounded below by Ω(1/ε2) and Ω(1/ε), respectively. We further demonstrate the essential role of memorization in learning problems in SCO by designing an adversary capable of accurately identifying a significant fraction of the training samples in specific SCO problems. Finally, we enumerate several implications of our results, such as a limitation of generalization bounds based on CMI and the incompressibility of samples in SCO problems.