 Solution

Choose $I_s$ independently and uniformly from $\{1,\dots ,n\}$. Starting from any ${\beta }_1\in C$, the projected stochastic gradient descent iteration isConditional on ${\beta }_s$, $\mathbb{E}[G_s\mid {\beta }_s]=\nabla f({\beta }_s)$, so $G_s$ is an unbiased stochastic gradient. The metric projection onto a closed convex set keeps every iterate in $C$. For a fixed step size, return the Cesaro average $\bar{\beta }=k^{-1}{\sum }_{s=1}^k{\beta }_s$.