The idea is to separate the two effects of lasso

1. Variable selection (i.e., many, even most, $\beta$s are zero)
2. Variable shrinkage (i.e., even non-zero $\beta$s are smaller, in absolute value, than in unpenalised regression). This is often a good thing even without selection because you avoid over-fitting.

If you have many variables ($p >\!\!> n$), and are running lasso, then you want to have a large penalty to select a small number of variables. However, this penalty might shrink the selected variables too much (you are under-fitting).

The idea of relaxed lasso is that you separate the two effects: you use a high penalty on the first pass to select variables; and a smaller penalty on the second pass to shrink them by a smaller amount.

The original paper (as linked by Néstor) gives more detail.

The idea is to separate the two effects of lasso

1. Variable selection (i.e., many, even most, $\beta$s are zero)
2. Coefficient shrinkage (i.e., even non-zero $\beta$s are smaller, in absolute value, than in unpenalised regression). This is often a good thing even without selection because you avoid over-fitting.

If you have many variables ($p >\!\!> n$), and are running lasso, then you want to have a large penalty to select a small number of variables. However, this penalty might shrink the selected variables too much (you are under-fitting).

The idea of relaxed lasso is that you separate the two effects: you use a high penalty on the first pass to select variables; and a smaller penalty on the second pass to shrink them by a smaller amount.

The original paper (as linked by Néstor) gives more detail.

The idea is to separate the two effects of lasso

1. Variable selection (i.e., many $\beta$s are zero)
2. Variable shrinkage (i.e., even non-zero $\beta$s are smaller, in absolute value, than in unpenalised regression)

If you have many variables ($p >\!\!> n$), and are running lasso, then you want to have a large penalty to select a small number of variables. However, this penalty might shrink the selected variables too much.

The idea of relaxed lasso is that you separate the two effects: you use a high penalty on the first pass to select variables; and a smaller penalty on the second pass to shrink them by a smaller amount.

The original paper (as linked by Néstor) gives more detail.

The idea is to separate the two effects of lasso

1. Variable selection (i.e., many, even most, $\beta$s are zero)
2. Variable shrinkage (i.e., even non-zero $\beta$s are smaller, in absolute value, than in unpenalised regression). This is often a good thing even without selection because you avoid over-fitting.

If you have many variables ($p >\!\!> n$), and are running lasso, then you want to have a large penalty to select a small number of variables. However, this penalty might shrink the selected variables too much (you are under-fitting).

The idea of relaxed lasso is that you separate the two effects: you use a high penalty on the first pass to select variables; and a smaller penalty on the second pass to shrink them by a smaller amount.

The original paper (as linked by Néstor) gives more detail.