Algorithm 3.

Sparse Private Distributed Online Learning

1:	Input: $f_t^i(w):=\mathcal{l}\left(w,x_t^i,y_t^i\right),i\in [1,m]$ and $t\in [1,T]$; doubly stochastic matrix $A_t=\left(a_{ij}(t)\right)\in R^{m\times m}$.
2:	Initiaization: ${\vartheta }_1^i=0,i\in [1,m]$;
3:	for t = 1,...,T do
4:	for each node i = 1,...,m do
5:	receive $x_t^i\in {ℝ}^n$;
6:	$p_t^i=\nabla {\phi }_t^{*}\left({\vartheta }_t^j\right)$;
7:	$w_t^i={\text{arg min}}_w\frac{1}{2}{\Vert p_t^i-w\Vert }_2^2+\rho \Vert w{\Vert }_1$;
8:	predict ${\widehat{y}}_t^i$;
9:	receive $y_t^i$ and obtain $f_t^i\left(w_i^i\right):=\mathcal{l}\left(w_t^i,x_t^i,y_t^i\right)$;
10:	broadcast to neighbors: ${\tilde{\vartheta }}_{t+1}^i={\vartheta }_{t+1}^i+{\delta }_t^i$;
11:	end for
12:	end for