Stochastic optimization for Machine Learning for finance

G. Pagès

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.