<h3 dir="auto">Describe the workflow you want to enable</h3>
<p dir="auto">Linear and logistic regression allow l1, l2, or elasticnet regularization. However, the Poisson regression class (which is amazing to have!) only allows L2 regularization.</p>
<h3 dir="auto">Describe your proposed solution</h3>
<p dir="auto">Enable flexible regularization choices for the Generalized Linear Models</p>
<h3 dir="auto">Describe alternatives you've considered, if relevant</h3>
<p dir="auto"><em>No response</em></p>
<h3 dir="auto">Additional context</h3>
<p dir="auto"><em>No response</em></p>
<p dir="auto">The L1 penalty with  coordinate descent solver for GLM was proposed in <a class="issue-link js-issue-link" data-error-text="Failed to load title" data-id="243835169" data-permission-text="Title is private" data-url="https://github.com/scikit-learn/scikit-learn/issues/9405" data-hovercard-type="pull_request" data-hovercard-url="/scikit-learn/scikit-learn/pull/9405/hovercard" href="https://github.com/scikit-learn/scikit-learn/pull/9405">#9405</a> and was not included in the minimal implementation merged in <a class="issue-link js-issue-link" data-error-text="Failed to load title" data-id="465886592" data-permission-text="Title is private" data-url="https://github.com/scikit-learn/scikit-learn/issues/14300" data-hovercard-type="pull_request" data-hovercard-url="/scikit-learn/scikit-learn/pull/14300/hovercard" href="https://github.com/scikit-learn/scikit-learn/pull/14300">#14300</a>.</p>
<p dir="auto">It would be be good to add it, however care must to taken to avoid redundancy with the existing coordinate descent solver in ElasticNet.</p>
<p dir="auto">Preliminary benchmarks were done in <a class="issue-link js-issue-link" data-error-text="Failed to load title" data-id="243835169" data-permission-text="Title is private" data-url="https://github.com/scikit-learn/scikit-learn/issues/9405" data-hovercard-type="pull_request" data-hovercard-url="/scikit-learn/scikit-learn/pull/9405/hovercard?comment_id=499578511&amp;comment_type=issue_comment" href="https://github.com/scikit-learn/scikit-learn/pull/9405#issuecomment-499578511">#9405 (comment)</a></p>
<p dir="auto">Also see: <a class="issue-link js-issue-link" data-error-text="Failed to load title" data-id="575407340" data-permission-text="Title is private" data-url="https://github.com/scikit-learn/scikit-learn/issues/16634" data-hovercard-type="issue" data-hovercard-url="/scikit-learn/scikit-learn/issues/16634/hovercard" href="https://github.com/scikit-learn/scikit-learn/issues/16634">#16634</a> <a class="issue-link js-issue-link" data-error-text="Failed to load title" data-id="575422429" data-permission-text="Title is private" data-url="https://github.com/scikit-learn/scikit-learn/issues/16635" data-hovercard-type="issue" data-hovercard-url="/scikit-learn/scikit-learn/issues/16635/hovercard" href="https://github.com/scikit-learn/scikit-learn/issues/16635">#16635</a></p>