Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

Robust tuning with anti-optimization (Equation 4.12) is run on the model over
the reduced uncertainty space(s), and the resulting tuning parameters are applied to
the hardware to obtain new performance data, σHWk . The subscript k indicates the
iteration number. If the hardware performance, Jk, is within requirement then the
tuning is successful and the algorithm ends. Otherwise, the uncertainty space is still
too large to tune robustly, and the new performance data is used to reduce the space
further by searching for intersections in the uncertainty parameter space between the
original isoperformance line and that defined by the newly acquired data. Although
the tuning parameters, and consequently, the hardware performance, have changed,
the values of the uncertainty parameters have not. Therefore, it is guaranteed that the
iso-lines intersect somewhere in the uncertainty space. Conceptually, it is convenient
to think of two iso-contours crossing, but in the implementation it is not necessary to
trace out the second curve. Instead, it is sufficient to evaluate the model prediction
at each uncertainty point in Piso0 with the new tuning parameters and to retain those
points for which the predicted performance is equal to the new hardware performance
within a set tolerance, ɛ:
Pisok = � �p ∈ Pisok−1 ||σ (˜x, �yk,�p) − σHWk |≤ɛ�
(4.18)
The new isoperformance set, Pisok is a subset of Piso0 and allows a further reduction
of the uncertainty bounds. This new uncertainty set replaces Piso0 and the algorithm
begins another iteration. This process of robust tuning and uncertainty reduction
continues until the uncertainty space is small enough that robust tuning is successful.
It is possible that the tuning configuration resulting from the robust model tuning
does not successfully tune the hardware or produce a new iso-contour that significantly
reduces the uncertainty space. For example, the new iso-line may only be slightly
different from the previous one, so that all the points in Pisok−1 evaluate to the new
performance within the given tolerance, ɛ. This situation is handled in the algorithm
by evaluating the norm of the difference between the new tuning configuration and the
previous one before performing the hardware test. If this value is small indicating that
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