Input Examples $\{$x$1,...,$xN$\},$ loss function L$($$)=1$N$$iL$($$,$xi$).$

Parameters: learning rate t$,$ noise scale, $,$ group size L$,$ gradient norm bound C$.$

Initialize $0$ randomly

for t in $[$T$]$ do

Take a random sample Lt with sampling probability L$/$N

Compute gradient For each i in Lt$,$ compute gt$($xi$)$tL$($t$,$xi$)$

Clip gradient g$$t$($xi$)$gt$($xi$)/$max$(1,$gt$($xi$)2$C$)$

Add noise g~t$1$L$($ig$$t$($xi$)+$N$(0,$$2$C$2$I$))$

Descent t$+1$t$$tg~t

Output T and compute the overall privacy cost $($$,$$)$ using a privacy accounting method.

Task: Read the algorithm above. Write down, for each symbol$/$notation used in the algorithm, what it represents. Pay particular attention to the symbol gt$($xi$)$ and its various modifications.