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The question is: what is the difference between multi-task lasso regression and ridge regression? The optimization function of multi-task lasso regression is $$ min_w \sum_{l=1}^L1/N_t\sum_{i=1}^{N_t} J^l(w,x,y) + \gamma\sum_{l=1}^L{||w^l||_2} $$ while ridge regression is $$ min_w \sum_{l=1}^L1/N_t J^l(w,x,y) + \gamma{||w^l||_2} $$

which looks the same as the ridge regression. As for me, the problem of multi-task lasso regression is equivalent to solve global ridge regression. So what is the difference between these two regression methods? Both of them use L2 function. Or does it mean that in multi-task lasso regression, the shape of W is (1,n)?

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LASSO (Least Absolute Shrinkage and Selection Operator) uses $L^1$ regularization $$\min_x f(x) + \lambda \|x\|_1.$$

See, for instance this presentation.

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