Stochastic Optimization: Algorithms and Methods

This lecture covers stochastic optimization and adaptive gradient methods, examining algorithms like gradient descent, coordinate descent, subgradient, proximal gradient, projection gradient, and mirror descent. It explores the solution of convex optimization problems with and without constraints, for both smooth and nonsmooth risks. The lecture delves into exploiting the structure of the risk function and the challenges posed by large datasets and unknown statistics. Various stochastic algorithms are discussed, including stochastic gradient, subgradient, and proximal gradient methods, highlighting their convergence properties and the impact of step sizes on convergence.