Analogue of "to the best of our knowledge"
Solution 1:
When you say "to the best of my/our knowledge," you're saying that "you think your statement is true, because it is based on what you know/believe, but you are not completely sure" [Macmillan].
So any phrase that expresses that lack of complete certainty that fits the context will do. In the context of an academic paper, you might say:
We believe that this is the first work that shows how to optimize a non-submodular function...
Solution 2:
What about "As far as I/we know" or "As far as I/we can tell"
Solution 3:
You may use as far as we know.