Suppose $f : ℝ^{d} \to ℝ$ 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 \geq 0,

(1)

where

G_{k + 1} {(X}_{k}) ≔ \nabla f (X_{k}) + ε_{k + 1} (X_{k})

and

{(ε_{k})}_{k \geq 1}

is a sequence of independent and identically distributed random fields defined on some filtered probability space

(Ω, ℱ, {(ℱ_{K})}_{k \geq 1}, ℙ)

such that

E [ɛ_{k + 1} (x) | ℱ_{k}] = 0

almost surely (a.s.) for all

x ε ℝ^{d}

Volume 9, Issue 3

September 2019

Pages 183-317

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Published Online:October 02, 2019

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Raghu Pasupathy, Harsha Honnappa, Susan R. Hunter (2019) Open Problem—Adaptive Constant-Step Stochastic Approximation. Stochastic Systems 9(3):307-310.

https://doi.org/10.1287/stsy.2019.0046

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Open Problem—Adaptive Constant-Step Stochastic Approximation

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Volume 9, Issue 3

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