What the Noise Assumptions Actually Buy Us
Series: Stochastic Approximation from First Principles · Part 10 of 22 Preserving history helps only when the history contains enough signal to average out the noise. The usual noise assumptions explain when that hope is justified. In the river analogy, $\eta_k$ is not the wind or the echo itself. It is the location error produced after those physical disturbances affect your judgment: $$ \eta_k=\text{target}_k-w^*. $$The assumptions describe the errors in the inferred target. ...