Open Problem—Adaptive Constant-Step Stochastic Approximation.

Pasupathy, Raghu; Honnappa, Harsha; Hunter, Susan R.

Suppose f:ℝd→ℝ is a smooth function that is bounded from below. The classic stochastic approximation (SA) recursion used to identify a stationary point of f is given by X k 1 = X k – η k G k 1 (X k) , k ≥ 0 , (1) where Gk 1(Xk)≔∇f(Xk) εk 1(Xk) and (εk)k≥1 is a sequence of independent and identically distributed random fields defined on some filtered probability space (Ω,ℱ,(ℱK)k≥1,ℙ) such that E[ɛk 1(x)|ℱk]=0 almost surely (a.s.) for all x ε ℝd.

STOCHASTIC approximation; SMOOTHNESS of functions; RANDOM fields; MACHINE learning; PROBABILITY theory

Stochastic Systems, 2019, Vol 9, Issue 3, p307

1946-5238

Academic Journal

10.1287/stsy.2019.0046