Fall 2026

This first-year graduate course offers a rigorous yet accessible introduction to the algorithmic foundations of optimization, emphasizing both theory and applications in computer science and engineering. Topics include convex sets and functions, necessary and sufficient conditions for optimality, unconstrained and constrained optimization (gradient descent, Newton’s method, projection methods, Lagrange multipliers, KKT conditions), duality theory, and augmented Lagrangian methods.

This course will examine graphs and graph neural networks from the specific aspects of representation, reasoning, robustness, and symmetry.

Lean is both a purely functional, dependently-typed programming language and a "proof assistant". Using Lean has been described as "programming proofs". It has been used to: formalize and verify mathematical theorems, distributed computing and cryptographic protocols, hardware models, neural networks, and many other kinds of abstractions; to implement and prove properties of software applications and concrete hardware designs; to model and verify properties of systems built in other languages; and much more. 

This graduate course gives an overview of machine learning for planning and control of complex dynamical systems. The central topic is the mathematical foundations of reinforcement learning in continuous state and action spaces. Supplementary topics include data-driven dynamics models, imitation learning, and robustness/adaptivity to environment shifts. Students will develop a thorough understanding of fundamental algorithms and learn to select appropriate methods based on the problem's interaction and information protocols.

This course covers advanced topics on neural information retrieval and search engines. The content to be focused includes indexing, retrieval, ranking, and system optimization for large-scale search services with deep machine learning and NLP models. Recent papers in top conferences on neural information retrieval will be reviewed, and issues in relevance, efficiency, and scalability will be studied.

This course provides a rigorous yet accessible introduction to the algorithmic foundations of optimization, with a focus on problems and applications in computer science and engineering. Topics include convex sets and functions; unconstrained methods such as gradient descent and Newton’s method; projection and gradient‐projection; equality and inequality constrained optimization via Lagrange multipliers and KKT conditions; duality theory; stochastic gradient techniques; and subgradient methods for nondifferentiable problems.