Interactive Learning of Single-Index Models via Stochastic Gradient Descent

Researchers Nived Rajaraman and Yanjun Han have published significant theoretical work on arXiv analyzing Stochastic Gradient Descent (SGD) for interactive learning of single-index models, also known as generalized linear or ridge bandits. Their paper 'Interactive Learning of Single-Index Models via Stochastic Gradient Descent' provides the first comprehensive analysis of SGD's learning dynamics in sequential decision-making settings where data is collected adaptively.

The research reveals that SGD undergoes two distinct phases: an initial 'burn-in' phase followed by a 'learning' phase, mirroring the behavior of optimal interactive learners. Crucially, the authors prove that with properly scheduled learning rates, a single SGD procedure simultaneously achieves near-optimal (or best-known) guarantees for both sample complexity and regret across these phases. This holds for a broad class of link functions, making the results widely applicable to generalized linear models used in recommendation systems, personalized medicine, and online advertising.

This work bridges the gap between SGD's empirical success in high-dimensional optimization and theoretical understanding of its performance in interactive settings. By showing that the simple, widely-used SGD algorithm can match the performance of specialized optimal learners with proper tuning, the research provides practical guidance for implementing efficient sequential learning systems while maintaining theoretical guarantees. The 26-page paper includes mathematical proofs and analysis of SGD's convergence behavior under adaptive data collection, offering insights for both theoretical researchers and practitioners implementing bandit algorithms.