Requiring LICQ/SCS/SOSC everywhere in bilevel optimization is non-prevalent and rigid, while holding almost everywhere is prevalent, but the distinction introduces fundamental difficulties.
SIAM Journal on Optimization , volume=
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A barrier-smoothed first-order method achieves stationarity rates of tilde O(K to the -2/3) deterministic and tilde O(K to the -2/5) stochastic for linearly constrained bilevel optimization.
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.
Provides the first systematic generalization analysis via algorithmic stability for single-timescale and two-timescale stochastic gradient descent-ascent in bilevel minimax problems.
citing papers explorer
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On the Nature of Regularity Assumptions in Bilevel Optimization with Constrained Lower-level Problem
Requiring LICQ/SCS/SOSC everywhere in bilevel optimization is non-prevalent and rigid, while holding almost everywhere is prevalent, but the distinction introduces fundamental difficulties.
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A Barrier-Metric First-Order Method for Linearly Constrained Bilevel Optimization
A barrier-smoothed first-order method achieves stationarity rates of tilde O(K to the -2/3) deterministic and tilde O(K to the -2/5) stochastic for linearly constrained bilevel optimization.
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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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On the Stability and Generalization of First-order Bilevel Minimax Optimization
Provides the first systematic generalization analysis via algorithmic stability for single-timescale and two-timescale stochastic gradient descent-ascent in bilevel minimax problems.