  We show that if the base frequency is Diophantine, then the Lyapunov exponent
of a $C^{k}$ quasi-periodic $SL(2,\mathbb{R})$ cocycle is $1/2$-H\"older
continuous in the almost reducible regime, if $k$ is large enough. As a
consequence, we show that if the frequency is Diophantine, $k$ is large enough,
and the potential is $C^k$ small, then the integrated density of states of the
corresponding quasi-periodic Schr\"odinger operator is $1/2$-H\"older
continuous.
