Hello,

For sake of simplicity let:

e = \epslion(u) of your notation

H= H(u) //

T =t //

In my understanding, the expected feasibility could be written as:

EF = E[ (e - | H - T|) * 1[T-e,T+e]]

- The term 1[T-e,T+e] indicates that we integrate only close to T (in the interval I = [ T-e,T+e])

- The term H - T is a difference between T and the "values" of H . Let d = H-T. Since we integrate in I, then d is in [-e, e]

and finally e- |d| is just a triangular function of d in [-e, e].

The max being at d= 0 (i.e H = T) and decreases as the difference d increases and vanishes at |d| = e.

Roughly,

EF = E[ (e - |d|) * 1[-e, e]]

It is probably late but anyway, I hope this will help.

Best regards

----------

PS (With regard to the second equation): In Gausssian Process regression framework, the posterior distribution follows a Gaussian distribution H ~ N(mu, sigma^2). Then, the second equation is "just" the result after some Gaussian computation.

Hello,

Thank you so much for your answer,

I am still working on this so you still on time :-)

Best regards