https://dudusoar.github.io/tags/expectation/Recent content in Expectation on Yuchen DuHugo -- 0.164.0en-usFri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/09-expectation-and-variance-of-two-updates/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/09-expectation-and-variance-of-two-updates/A direct derivation compares memoryless and history-preserving updates under zero-mean finite-variance noise.https://dudusoar.github.io/posts/stochastic-approximation/17-expectation-variance-proof-route/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/17-expectation-variance-proof-route/Expanding the recursion explains how initial error and historical noise decay, but usually yields convergence in probability rather than almost-sure convergence.https://dudusoar.github.io/posts/stochastic-approximation/19-how-initial-error-disappears-in-expectation/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/19-how-initial-error-disappears-in-expectation/Zero-mean noise removes the disturbance terms from the expectation, leaving a product that vanishes when the step sizes sum to infinity.