A diameter criterion tied to a potential function certifies convergence of difference inclusions, enabling discrete proofs for first-order optimization methods with diminishing steps.
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Optimistic bilevel optimization with manifold lower-level minimizers is differentiable if the optimistic selection is unique, yielding a pseudoinverse hyper-gradient and a convergent HG-MS algorithm whose rate depends on intrinsic manifold dimension.
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Convergence of difference inclusions via a diameter criterion
A diameter criterion tied to a potential function certifies convergence of difference inclusions, enabling discrete proofs for first-order optimization methods with diminishing steps.
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Select-then-differentiate: Solving Bilevel Optimization with Manifold Lower-level Solution Sets
Optimistic bilevel optimization with manifold lower-level minimizers is differentiable if the optimistic selection is unique, yielding a pseudoinverse hyper-gradient and a convergent HG-MS algorithm whose rate depends on intrinsic manifold dimension.