Intiution Behind Robbins–Siegmund Lemma

Introduction

so you may encounter Robbins-Siegmund Lemma in proof of Stochastic gradient descent which is really bizzare, so before that lets dive into something more basic before reaching to that one, and that is the defnition of martingle process:

so you might heard this in stock and crypto market about Martingale strategye¹, the question is why and how it works? or is it recipe for disaster?

Robbins-Monro conditions

Martingle Condition

SubMartingle and SuperMartingle

Martingale difference sequence

SGD

• https://en.wikipedia.org/wiki/Stochastic_approximation
• https://www.di.ens.fr/~fbach/orsay2016/lecture3.pdf
• https://www.princeton.edu/~kulkarni/Papers/Journals/j013_1996_kh_transac.pdf

Reverse Footnote

1. It involves doubling up on losing bets and reducing winning bets by half. ↩︎