  The problem of handling adaptivity in data analysis, intentional or not,
permeates a variety of fields, including test-set overfitting in ML challenges
and the accumulation of invalid scientific discoveries. We propose a mechanism
for answering an arbitrarily long sequence of potentially adaptive statistical
queries, by charging a price for each query and using the proceeds to collect
additional samples. Crucially, we guarantee statistical validity without any
assumptions on how the queries are generated. We also ensure with high
probability that the cost for $M$ non-adaptive queries is $O(\log M)$, while
the cost to a potentially adaptive user who makes $M$ queries that do not
depend on any others is $O(\sqrt{M})$.
