My research group develops the mathematical foundations and algorithms for learning, reasoning, and decision making. Working at the intersection of Machine Learning, Statistics, and Optimization, we study how learning systems can make effective use of data, feedback, and computation. Our current work spans reinforcement learning for language models, diffusion models and sampling, and learning in complex, changing environments. We are also interested in applications of AI to science, particularly where new modeling approaches and computational methods can lead to deeper scientific understanding.

Current research directions:

1. Reinforcement Learning, Reasoning, and Language Models: We develop algorithms and theory for improving language models through interaction and feedback. Recent work explores value-based RL for LLM reasoning, exploration in learning from human feedback, and the role of process versus outcome supervision. We connect practical methods for model training with fundamental questions about exploration, credit assignment, and the amount of feedback needed to learn.
2. Diffusion Models and Efficient Sampling: We study the foundations of generative modeling and design algorithms for sampling accurately with less computation. Our recent work develops high-accuracy sampling methods for diffusion models and new algorithms based on exact simulation of diffusions. These advances connect generative modeling with probability and optimization, and clarify how sampling complexity depends on accuracy and the structure of the data.
3. Foundations of Interactive and Online Learning: We study how to learn when data are dependent, environments change, and decisions shape future observations. Our work on the Decision-Estimation Coefficient (DEC) provides a unifying framework for the statistical complexity of decision making and reinforcement learning (see our course notes). Current directions include smoothed online learning, which bridges statistical and adversarial models, and learning with simulators.