The Everlasting Database: Statistical Validity at a Fair Price

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(p M).