A Deep Dive into Recent Advances in Stochastic Approximation (video)

This mini-tutorial provides an introduction to the recent development of stochastic approximation (SA) scheme. The first part introduces the essential foundation of the SA scheme as a general device for locating the roots of mean field functions. The presenter then showcases how the SA scheme can be applied to examples in signal processing and machine learning, such as compressed training, online expectation maximization, reinforcement learning, performative prediction, etc., that go beyond the use of gradient updates. This demonstrates the versatility of SA in analyzing and understanding classical algorithms. The second part introduces a general theory for the convergence of SA scheme accommodating scenarios with non-gradient updates and biased oracles. He will emphasize on modern convergence analyses encompassing sample complexity and high-probability bounds. By incorporating these latest innovations, participants will be well equipped to explore emerging frontiers in applying SA in their research. This is an abridged version of a tutorial given at ICASSP 2025 which was jointly given with Eric Moulines (Ecole Polytechnique) and Gersende Fort (CNRS), and the materials are based upon the overview paper Stochastic Approximation beyond Gradient for Signal Processing and Machine Learning" published in IEEE TSP in 2023."