The Robbins-Monro stochastic approximation procedure as a model for sequential estimation in learning and measurement¶

Theory · All theories
Evidence · no claims cited

Description¶

The article treats the Robbins-Monro stochastic approximation procedure as an iterative method for finding the root of a regression equation when observations are contaminated by random error. Each step adjusts an estimate in the direction suggested by the latest noisy observation, scaled by a sequence of iteration coefficients. The article analyzes the conditions under which this sequence converges, framing the procedure as relevant to sequential problems in psychological measurement and learning.

Design Implications¶

Context¶

Requirements¶

• A sequence of iteration coefficients satisfying the convergence condition proved in the article

Constraints¶

• Convergence guarantees are mathematical properties of the procedure, demonstrated analytically rather than through instructional experiments

Target Learners¶

• learners in adaptive measurement and instructional settings

Target Learning Objectives¶

• sequential estimation of ability or learning parameters

Claims¶

• Convergence Condition Stochastic Approximation [+M]

Related Theories¶

Examples¶

• Use stochastic approximation for sequential parameter estimation when observations are noisy and each observation is costly
• Iteration-coefficient sequences as the controllable design element of stochastic approximation
• 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