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Result · GENERAL-REFINEMENT-BB

Refinement bounds hold for every monotone criterion

Derived from the literaturepublication: derived from published

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Meaning

A refinement upper-bounds coarser assignments for any criterion monotone in the information matrix.

Statement

Any Loewner-monotone criterion can use information from a refinement as an upper bound on any coarser completion.

Relationships

Rests on

The full chain beneath it

Enables

Open next door

Local graph
Local map of Refinement upper bounds for Loewner-monotone criteria1 prerequisites to the left, 1 results it enables or questions it raises to the right, 0 boundary cases below.Refinement monotonicityRefinement monotonici…Refinement branch-and-bound applies to ERefinement branch-and…Refinement upper bounds for Loewner-monotone criteriaRefinement upper boun…
Prerequisites to the left, what it enables or raises to the right, boundary cases below. Open in the map.

Proof

U5. Refinement monotonicity

If P′\mathcal P' refines P\mathcal P, then

IP′⪰IP.I_{\mathcal P'}\succeq I_{\mathcal P}.

This powers branch-and-bound upper bounds for every Loewner-monotone criterion.

From Universal information structure · chapter contents