  We use the off-shell string effective action method developed by E.S. Fradkin
and A.A. Tseytlin to obtain the formula for all-genus string effective action
with and without compactification at the low-energy approximation in the
massless background fields. We find that for the bosonic string, one can
determine the dilaton vacuum expectation value from the all-genus effective
action because of the nontrivial dependence of potential energy on dilaton. For
compactified four-dimensional string models, if one requires that the
target-space dilaton field lie on a K\"ahler manifold, we obtain a constraint
which will specify the worldsheet dilaton in terms of the constant background
fields. We also show that under this constraint, the tree-level k\"ahlar
potential and superpotential are not changed by the higher-genus effect. This
proves again the non-renormalization theorem for a string moving in massless
background fields in the low-energy approximation.
