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About this paper
Guillaume Lauga
A generalized block-coordinate descent framework is introduced for non-convex composite optimization, offering robust theoretical convergence guarantees for a broad class of algorithms. Applying this framework to sparse precision matrix estimation with non-convex penalties yielded an 8-to-10-fold reduction in total iterations for specific solvers, maintaining or improving estimation quality.
Key insights
- The Kurdyka-Łojasiewicz (KŁ) property is central to establishing global convergence guarantees for block-coordinate descent algorithms in non-convex settings.
- Majorization of non-convex composite penalties allows complex problems to be broken down into simpler subproblems solvable by proximity operators with reweighting.
- Relaxing the full minimization requirement during iterative reweighting through the BCD framework drastically improves computational efficiency for non-convex regularized problems.
Summary by alphaXiv.
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