optimization of rule-based model on discrete variables

[Elena]

Il Mon, 14 Jun 2021 19:39:17 +1200, Greg Ewing ha scritto:

> On 14/06/21 4:15 am, Elena wrote:
>> Given a dataset of X={(x1... x10)} I can calculate Y=f(X) where f is
>> this rule-based function.
>> 
>> I know an operator g that can calculate a real value from Y: e = g(Y)
>> g is too complex to be written analytically.
>> 
>> I would like to find a set of rules f able to minimize e on X.
> 
> There must be something missing from the problem description.
>  From what you've said here, it seems like you could simply find
> a value k for Y that minimises g, regardless of X, and then f would
> consist of a single rule: y = k.
> 
> Can you tell us in more concrete terms what X and g represent?

I see what you mean, so I try to explain it better: Y is a vector say [y1, 
y2, ... yn], with large (n>>10), where yi = f(Xi) with Xi = [x1i, x2i, ... 
x10i] 1<=i<=n. All yi and xji assume discrete values.

I already have a dataset of X={Xi} and would like to find the rules f able 
to minimize a complicated-undifferenciable Real function g(f(X)).
Hope this makes more sense.

x1...x10 are 10 chemical components that can be absent (0), present (1), 
modified (2). yi represent a quality index of the mixtures and g is a 
global quality of the whole process.

Thank you in advance

ele