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.
arXiv preprint arXiv:2406.01992 , year=
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Provides the first systematic generalization analysis via algorithmic stability for single-timescale and two-timescale stochastic gradient descent-ascent in bilevel minimax problems.
AGILS is an alternating gradient algorithm for bilevel optimization that uses Moreau envelope reformulation to handle inexact lower-level solves, with convergence to stationary points proven under stated assumptions.
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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.
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Provides the first systematic generalization analysis via algorithmic stability for single-timescale and two-timescale stochastic gradient descent-ascent in bilevel minimax problems.
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