Stochastic optimization for Machine Learning for finance

Stochastic algorithms

• Robbins-Monro algorithms, stochastic approximation.
• Stochastic gradient and pseudo-gradients.
• A.s. and L2 convergence using martingale methods.
• L2 speed, TCL and Ruppert and Polyak averaging principle.

Learning applications

• Penalized and non-penalized multi-arm bandit algorithms, and application to optimal financial asset allocation.
• Adaptive variance reduction and implicit correlation search.
• Elements of optimal quantization and distortion theory. Curse of dimension.
• Applications to numerical probabilities (expectations and conditional expectations by cubature, optimal stopping and American options, etc.).
• Lloyd’s algorithm (k-means) and Competitive Learning Vector Quantization.
• Application to artificial neural networks and automatic classification.
• Dimension reduction, Kohonen self-organizing maps.