Before a new policy replaces a deployed one, we often want a certificate, computed from logged episodes, that it is better. The central question is how many episodes such a certificate requires when the logging policy is known but history-dependent. A new arXiv paper addresses this by introducing the concept of a "certification exponent."
The paper asks for the minimal number of episodes needed to certify improvement, and it does so in an instance-optimal way—meaning the bound adapts to the specific structure of the problem rather than relying on a worst-case uniform bound. The setting is sequential, and the logging policy's history dependence is explicitly accounted for.
The abstract does not state the exact form of the exponent or the resulting bounds, but the contribution is framed as a general characterization. This work is likely to be of interest to researchers working on offline reinforcement learning and safe policy deployment, where data-efficient certification is critical.