  Recent progress in optical lattice clocks requires unprecedented precision in
controlling systematic uncertainties at $10^{-18}$ level. Tuning of nonlinear
light shifts is shown to reduce lattice-induced clock shift for wide range of
lattice intensity. Based on theoretical multipolar, nonlinear, anharmonic and
higher-order light shifts, we numerically demonstrate possible strategies for
Sr, Yb, and Hg clocks to achieve lattice-induced systematic uncertainty below
$1\times 10^{-18}$.
