  We introduce an optimal renormalization group analysis pertinent to the
analysis of polarization functions associated with the $s$-quark mass relevant
in $\tau$-decay. The technique is based on the renormalization group invariance
constraints which lead to closed form summation of all the leading and
next-to-leading logarithms at each order in perturbation theory. The new
perturbation series exhibits reduced sensitivity to the renormalization scale
and improved behavior in the complex plane along the integration contour. Using
improved experimental and theory inputs, we have extracted the value of the
strange quark mass $m_s(2{\rm GeV}) = 106.70 \pm 9.36~{\rm MeV}$ and $m_s(2{\rm
GeV}) = 74.47 \pm 7.77~{\rm MeV}$ from presently available ALEPH and OPAL data
respectively. These determinations are in agreement with the determinations in
other phenomenological methods and from the lattice.
