  We study unbiased $(1+1)$ evolutionary algorithms on linear functions with an
unknown number $n$ of bits with non-zero weight. Static algorithms achieve an
optimal runtime of $O(n (\ln n)^{2+\epsilon})$, however, it remained unclear
whether more dynamic parameter policies could yield better runtime guarantees.
We consider two setups: one where the mutation rate follows a fixed schedule,
and one where it may be adapted depending on the history of the run. For the
first setup, we give a schedule that achieves a runtime of $(1\pm o(1))\beta n
\ln n$, where $\beta \approx 3.552$, which is an asymptotic improvement over
the runtime of the static setup. Moreover, we show that no schedule admits a
better runtime guarantee and that the optimal schedule is essentially unique.
For the second setup, we show that the runtime can be further improved to
$(1\pm o(1)) e n \ln n$, which matches the performance of algorithms that know
$n$ in advance.
  Finally, we study the related model of initial segment uncertainty with
static position-dependent mutation rates, and derive asymptotically optimal
lower bounds. This answers a question by Doerr, Doerr, and K\"otzing.
