SGD unbiasedness and variance

Tutor me on https://mlprep.iwase.dev/item/ml-screen-gradient-descent-advanced-sgd/. This is a screening item. If window.mlPrepAgent is available, read attempts for item ml-screen-gradient-descent-advanced-sgd before tutoring. Inspect my attempt, keep the item ID, and do not reveal the full answer first. After a real attempt, append its record with recorded_by agent, include agent_session_id when available, and read it back.

Problem

At $w=2$ , three examples have gradients $0$ , $4$ , and $-2$ . One example is sampled uniformly per SGD step. Compute the full gradient, the stochastic-gradient variance, all next iterates for $\eta=0.3$ , and the expected next iterate.

Reveal answer or reference solution

The full gradient is

\frac{0+4-2}{3}=\frac{2}{3}.

The variance is

\frac{0^2+4^2+(-2)^2}{3}-\left(\frac{2}{3}\right)^2=\frac{56}{9}.

The possible next iterates are $2$ , $0.8$ , and $2.6$ . Their expectation is

2-0.3\left(\frac{2}{3}\right)=1.8,

equal to the full-gradient update.

Previous attempts

Loading attempts saved in this browser…

Review Screening Results

SGD unbiasedness and variance

Problem

Previous attempts

Appears in