Erwin Schrödinger International Institute for Mathematics and Physics (ESI) Courses

The First Optimal Distributed SGD in the Presence of Data, Compute and Communication Heterogeneity

Explore optimal time complexities for parallel optimization methods with heterogeneous data, compute, and communication. Gain insights into efficient distributed SGD algorithms.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Optimization of Functions with Low Effective Dimensionality

Explore optimization techniques for functions with low effective dimensionality, focusing on random and deterministic subspace methods for nonconvex problems and efficient subspace learning.

• YouTube
• 28 minutes
• Self-Paced
• Free Video

Bilevel Optimization Problems: Algorithms and Theory

Explore recent developments in bilevel optimization algorithms, their theoretical analysis, and challenges in machine learning and data science applications.

• YouTube
• 25 minutes
• Self-Paced
• Free Video

Hessian-Aware Stochastic Differential Equation Modeling of SGD

Explore a novel SDE model for SGD that incorporates Hessian information, improving accuracy in capturing escaping behaviors and achieving exact recovery for quadratic objectives.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Stochastic Algorithms for Constrained Continuous Optimization

Explore stochastic-gradient-based algorithms for constrained continuous optimization, focusing on interior-point and sequential-quadratic-programming methods with convergence guarantees and practical applications.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Sample Size Estimates for Risk-Neutral Semilinear PDE-Constrained Optimization

Explore sample size estimates for risk-neutral semilinear PDE-constrained optimization using SAA approach, covering nonasymptotic analysis and numerical illustrations.

• YouTube
• 30 minutes
• Self-Paced
• Free Video

Nonmonotone Forward-Backward Splitting Method for Infinite-Dimensional Optimization Problems

Explore nonmonotone forward-backward splitting for nonsmooth composite problems in Hilbert spaces, covering convergence analysis, complexity, and numerical experiments.

• YouTube
• 23 minutes
• Self-Paced
• Free Video

A New Derivative-Free Method Using an Improved Under-Determined Quadratic Interpolation Model

Explore a novel derivative-free optimization method using improved under-determined quadratic interpolation, considering trust-region iteration properties and model optimality.

• YouTube
• 23 minutes
• Self-Paced
• Free Video

Iterative Regularization of the Deep Inverse Prior via Inertial Gradient Flow

Explore neural networks for inverse problems, examining theoretical guarantees and overparametrization. Analyze convergence and recovery using inertial gradient flow in deterministic and random settings.

• YouTube
• 28 minutes
• Self-Paced
• Free Video

Nonconvex Optimization and the Curse of Local Minima - Lessons Learned from Orbital Tomography

Explore nonconvex optimization algorithms, focusing on quality of fixed points in orbital tomography. Gain insights into evaluating algorithm effectiveness beyond convergence speed.

• YouTube
• 24 minutes
• Self-Paced
• Free Video

Proximal Gradient Methods for Nonsmooth Nonconvex Minimax - A Unified Convergence Analysis

Explore proximal gradient methods for nonsmooth nonconvex minimax problems, analyzing convergence and complexity through a unified framework for parallel and alternating schemes.

• YouTube
• 26 minutes
• Self-Paced
• Free Video

How to Optimize a Schrödinger Bridge

Explore optimization techniques for Schrödinger Bridge problems, focusing on a novel geometric framework and Sinkhorn algorithm variants for efficient solutions in AI and diffusion models.

• YouTube
• 28 minutes
• Self-Paced
• Free Video

Computer-Aided Lyapunov Analyses and Counter-Examples to the Convergence of First-Order Optimization Methods

Explore computer-aided Lyapunov analyses and counter-examples for first-order optimization methods, focusing on constructive approaches and structural properties.

• YouTube
• 33 minutes
• Self-Paced
• Free Video

CCCP is Frank-Wolfe in Disguise - Connecting Optimization Methods

Uncover the surprising connection between CCCP and Frank-Wolfe methods, gaining insights and transferring convergence theory for nonconvex optimization problems.

• YouTube
• 24 minutes
• Self-Paced
• Free Video

Error Bounds for Mean-Payoff Markov Decision Processes

Explore optimal transport techniques for error bounds in reinforcement learning, focusing on mean-payoff Markov decision processes and stochastic fixed point iterations.

• YouTube
• 29 minutes
• Self-Paced
• Free Video