Iteration-coefficient sequences as the controllable design element of stochastic approximation¶

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Evidence · no claims cited

Description¶

In the procedure analyzed by the article, the iteration coefficients are the designable component: they scale each update of the estimate, and their properties determine whether the sequence converges. The article's central result is "a necessary and sufficient condition on the iteration coefficients for convergence with probability one and in the quadratic mean," making coefficient selection the practical design decision for any application.

Design Implications¶

Context¶

Requirements¶

• Coefficients must satisfy the article's necessary and sufficient convergence condition

Constraints¶

Target Learners¶

• learners in sequentially administered measurement or instruction

Target Learning Goals¶

• convergent sequential estimation of a regression root

Affordances¶

• Robbins Monro Stochastic Approximation

Claims¶

Related Elements¶

Examples¶

• Select iteration coefficients according to the proved convergence condition when implementing stochastic approximation

Key Sources¶

• Wolff, Hans. (1970). On Stochastic Approximation. https://eric.ed.gov/?id=ED051258