Newton BAMM
Newton BAMM is a bilevel optimization algorithm that uses a strongly convex aggregation model to ensure well-defined multiplier updates, applicable to settings where the lower level is convex and the upper level is strongly convex with respect to the lower-level variables.
Timeline (last 90 days)
A recent paper proposes two Newton methods that go beyond lower-level strong convexity: Newton GALET and Newton BAMM, and introduces a unified framework, GNBO.
Newton BAMM applies to settings where the lower-level objective is convex and the upper-level objective is strongly convex in the lower-level variables, using a strongly convex aggregation model to ensure the multiplier updates are well-defined.
Compared with sl-BAMM, Newton BAMM has improved complexity bounds under the corresponding assumptions.
The authors establish convergence guarantees for Newton GALET and Newton BAMM, and give complexity bounds improved relative to GALET and sl-BAMM under the corresponding assumptions.
All Facts (4)
A recent paper proposes two Newton methods that go beyond lower-level strong convexity: Newton GALET and Newton BAMM, and introduces a unified framework, GNBO.
50%UnverifiedNewton BAMM applies to settings where the lower-level objective is convex and the upper-level objective is strongly convex in the lower-level variables, using a strongly convex aggregation model to ensure the multiplier updates are well-defined.
50%UnverifiedCompared with sl-BAMM, Newton BAMM has improved complexity bounds under the corresponding assumptions.
50%UnverifiedThe authors establish convergence guarantees for Newton GALET and Newton BAMM, and give complexity bounds improved relative to GALET and sl-BAMM under the corresponding assumptions.
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