C.40:5.8 - Combine processing rules, expose an interaction and revise the policy

A constructed document-processing service chooses between two optional operations: a preflight check P and an alternate parser R. Context S denotes a standard template; F denotes a fragile template. The template type is known before processing. Each row below describes a 100-document test batch with reference answers. Time includes the selected operations; errors are remaining incorrect records. The two context types have equal weight in this illustrative comparison. The numbers are stipulated test results, not measured production performance.

The receiver seeks mean time at most 20 minutes and mean errors at most 5 for the two test contexts. These are conjunctive requirements, not weights in one score. Expert A recommends P in either context; expert B recommends R in either context. Query both at S and F and represent each as a two-row action table. Here that translation is exact for the entire declared finite context set. A real expert’s behavior outside that set has not been captured.

The first model keeps the measured times and estimates the missing F interaction by adding the separate error reductions. P reduces F errors by 5 and R by 12, so the additive prediction for both is 20−5−12=3. The same construction gives 8−4−3=1 for S, agreeing with its observed joint case. Agreement at S motivates a candidate assumption for F; it does not establish it.

A policy chooses one action at S and one at F. There are only 16 such policies, so enumerate them; an evolutionary algorithm would add needless overhead here. The enumeration expresses the same representational choices a larger search must make: combine specialists across contexts, combine operations within a context, and compare the resulting whole. Five useful candidates are:

C improves both measures relative to B by combining the experts across contexts. Neither selection of A nor selection of B as one unchanged whole obtains C. D adds an untested within-context combination. Under the first model D meets both requirements and dominates E, so it is the tempting selection. The useful next inquiry is the missing F joint response; more precise arithmetic on the additive model cannot settle it.

Suppose the permitted test of P and R on the F batch returns 13 errors. Inspection shows that preflight’s rewrites disrupt this alternate parser’s handling of the fragile template. The additive prediction missed an interaction of 13−3=10 errors. Add that interaction for F while retaining the already established S responses. D now has (4+13)/2=8.5 mean errors at 19.5 minutes and is dominated by C’s 6 at 17 minutes. E, whose two component responses were already tested, meets the requirements at 20 minutes and 4.5 errors. Re-enumeration of the 16 policies shows E is the only one meeting both stated limits. Return E for these batches, with the type-dependent rule and the source test; do not call this production effectiveness or a learned general law of parser interaction.

A direct test of all eight context/action combinations would also have been inexpensive in this toy setting. The surrogate is useful here for exposing where prediction-guided selection needs a return, not for claiming an economic saving. In a large processing family, test cost, the number of context/action combinations and the consequences of a miss can favor different mixtures of modeling and direct trials.

Now suppose template type will not be observable until after the action has been selected. E cannot be applied as written. If the available policy must choose one fixed action for both contexts, neither P, R, both nor neither meets both limits: their respective mean pairs are (15.5,9.5), (18,6.5), (22.5,7) and (11,14). With no permitted extra observation or changed processing operation, return the unmet requirement. The change invalidates the policy’s information condition, not the earlier batch measurements. MMP.8 supplies the information-dependent choice; obtaining a timely type check is a new practical contribution to compare with relaxing a limit or changing the service.