  Recent works showed that simple success-based rules for self-adjusting
parameters in evolutionary algorithms (EAs) can match or outperform the best
fixed parameters on discrete problems. Non-elitism in a (1,$\lambda$) EA
combined with a self-adjusting offspring population size $\lambda$ outperforms
common EAs on the multimodal Cliff problem. However, it was shown that this
only holds if the success rate $s$ that governs self-adjustment is small
enough. Otherwise, even on OneMax, the self-adjusting (1,$\lambda$) EA
stagnates on an easy slope, where frequent successes drive down the offspring
population size. We show that self-adjustment works as intended in the absence
of easy slopes. We define everywhere hard functions, for which successes are
never easy to find and show that the self-adjusting (1,$\lambda$) EA is robust
with respect to the choice of success rates $s$. We give a general
fitness-level upper bound on the number of evaluations and show that the
expected number of generations is at most $O(d + \log(1/p_{\min}))$ where $d$
is the number of non-optimal fitness values and $p_{\min}$ is the smallest
probability of finding an improvement from a non-optimal search point. We
discuss implications for the everywhere hard function LeadingOnes and a new
class OneMaxBlocks of everywhere hard functions with tunable difficulty.
