Instructor: Pratik Jawanpuria and Pranay Sharma
TA: TBA
Time: Mondays and Thursdays, 5.30-7.00 pm
Room: TBA
Office Hours: TBA
Course Description
This course introduces an advanced set of topics at the intersection of optimization, sampling, and generative modeling, which are foundational to modern machine learning and artificial intelligence. It covers essential techniques such as mirror descent, natural gradient methods, and zeroth-order optimization, which are critical for scalable and efficient learning algorithms. The inclusion of optimal transport and sampling methods like Langevin dynamics and Hamiltonian Monte Carlo reflects their growing importance in probabilistic modeling and inference.
Pre-requisites
At least one graduate course in both optimization and probability-statistics.
Tentative Topics (evolving)
Mirror Descent (MD)
(Generalized) Bregman divergence; mirror descent; variants - Dual Averaging, Mirror Prox
Natural Gradient Method - relation to MD; applications to RL - natural actor-critic, TRPO, etc.
Optimal Transport
Generative AI and Inverse problems
Introduction to diffusion models; DDPMs; DDIMs; inverse problems
References
[B17] Amir Beck. "First-order Methods in Optimization." SIAM (2017).
[B15] Sébastien Bubeck. "Convex optimization: Algorithms and complexity." Foundations and Trends in Machine Learning 8.3-4 (2015).
[O19] Francesco Orabona. "A modern introduction to online learning." arXiv preprint arXiv:1912.13213 (2019).
[M23] Kevin Murphy, “Probabilistic Machine Learning: Advanced Topics.” MIT Press (2023).
[PC19] Peyre and Cuturi, “Computational Optimal Transport.” Now publishers (2019).
[LSK+25] Lai, Song, Kim, Mitsufuji, and Ermon. "The principles of diffusion models." arXiv preprint arXiv:2510.21890 (2025).
[C24] Stanley Chan. "Tutorial on diffusion models for imaging and vision." Foundations and Trends® in Computer Graphics and Vision 16.4: 322-471 (2024).
Some Related Courses
to be updated
Lecture Notes (will be posted here)