Positive Spectral Gap Condition
The positive spectral gap condition requires a positive gap between the nonzero and zero eigenvalues of a matrix, permitting the matrix to be singular while keeping its nonzero eigenvalues away from zero; it is weaker than strong convexity.
Timeline (last 90 days)
Under the positive spectral gap condition, Newton GALET uses the range-space structure to avoid the squared-Hessian multiplier system used in GALET.
The positive spectral gap condition requires a positive lower-bound gap between the nonzero and zero eigenvalues of the lower-level Hessian, which is weaker than strong convexity.
According to analysis by Bilibili uploaders and YouTube channels, this work is consistent with the recent trend in the bilevel optimization field toward non-strongly-convex lower-level problems, but views diverge on how well the positive spectral gap condition is satisfied in practical tasks.
All Facts (3)
Under the positive spectral gap condition, Newton GALET uses the range-space structure to avoid the squared-Hessian multiplier system used in GALET.
50%UnverifiedThe positive spectral gap condition requires a positive lower-bound gap between the nonzero and zero eigenvalues of the lower-level Hessian, which is weaker than strong convexity.
50%UnverifiedAccording to analysis by Bilibili uploaders and YouTube channels, this work is consistent with the recent trend in the bilevel optimization field toward non-strongly-convex lower-level problems, but views diverge on how well the positive spectral gap condition is satisfied in practical tasks.
50%