Algorithm 1 IMTL-G algorithm with random-weighted multi-task losses

Input: Initialized task-shared/specific parameters ${\theta }_{sh}$/$\left\{{\theta }_t\right\}$ and learning rate $\eta$ Output: 1. for t = 1 to T do 2.   compute task scaled loss: $L_1$,…$L_t$ 3.   compute weight: $w_t$~Dirichlet 4.   compute total loss: $L_{total}$ = ${\sum }_{t=1}^T{w}_t{L}_t$ 5.   compute gradient of shared feature: $g_t$ = $\nabla L_{total}$ 6.   compute unit-norm gradient $u_t$ = $\frac{g_t}{\left|\right|g_t\left|\right|}$ 7. end for 8. $\tilde{\beta }$ = (1−I$\beta$,$\beta$), where I = (1,…,1), $\beta \in$ IMTL-G 9. update task-shared parameters ${\theta }_{sh}$ = ${\theta }_{sh}$ − $\eta {\nabla }_{ {\theta }_{sh}}$(${\sum }_{t=1}^T{\tilde{\beta }}_t{L}_t$) 10. for t = 1 to T do 11.   update task-specific parameters ${\theta }_t$ = ${\theta }_t-$ $\eta {\nabla }_{ \theta }{L}_t$ 12. end for