At the midpoint of the project, we have made substantial progress toward understanding one of the most fundamental questions in modern machine learning and AI: why do learning algorithms that are trained on limited data perform so well on new, unseen examples? Our research explores this question through the lens of optimization: the mathematical process by which machine learning models are trained, and has led to several important and sometimes surprising discoveries.
A central achievement is a new theoretical understanding of how stochastic (randomized) training methods generalize. We discovered that stochastic gradient descent, the algorithmic paradigm that drives modern machine learning, performs well not because it finds the simplest model or explicitly avoids overfitting, but because of intrinsic algorithmic properties that cause it to generalize reliably even in very high-dimensional settings. This insight reshapes long-held assumptions about how learning works and represents a major advance in the theoretical understanding of generalization. We also showed that while a single pass of stochastic training achieves robust performance, repeating passes over the same data can quickly lead to overfitting, revealing a delicate balance between optimization and generalization even in fundamental, extensively studied learning scenarios.
We have also made notable progress in understanding learning under limited feedback and uncertainty, including in reinforcement learning (RL), where an agent learns through interaction with its environment. Our work developed efficient algorithms that generalize across dynamic settings, even when the model of the environment is inaccurate or misspecified, advancing the theoretical understanding of agnostic RL as a robust framework for learning from imperfect models. In parallel, we achieved breakthrough results in multiclass classification with limited feedback, proving for the first time that optimal, fast learning rates are achievable even in the so-called “bandit setting,” where only partial outcome information is revealed. These advances resolve long-standing open questions and provide a rigorous foundation for learning and decision-making algorithms that generalize reliably under uncertainty.
In terms of methodologies and algorithms for reliable generalization, we advanced the study of parameter-free and tuning-robust optimization: methods that can automatically adapt to the learning problem without requiring manual adjustment of hyperparameters such as the learning rate. These algorithms simplify the practical use of machine learning systems while maintaining optimal generalization, making them both efficient and reliable in real-world applications. Taken together, these achievements mark a significant step forward in understanding how optimization drives generalization and in developing more adaptive, principled, and robust approaches to generalization in modern machine learning and AI.
