  This paper studies the problem of maximizing a monotone submodular function
under an unknown knapsack constraint. A solution to this problem is a policy
that decides which item to pack next based on the past packing history. The
robustness factor of a policy is the worst case ratio of the solution obtained
by following the policy and an optimal solution that knows the knapsack
capacity. We develop an algorithm with a robustness factor that is decreasing
in the curvature $B$ of the submodular function. For the extreme cases $c=0$
corresponding to a modular objective, it matches a previously known and best
possible robustness factor of $1/2$. For the other extreme case of $c=1$ it
yields a robustness factor of $\approx 0.35$ improving over the best previously
known robustness factor of $\approx 0.06$.
