Model adaptive queries in the low-degree framework

Develop a low-degree polynomial framework that captures adaptive query algorithms—where an algorithm chooses which input coordinates to observe based on prior observations—and prove corresponding lower and upper bounds for detection and recovery tasks under this adaptive query model.

Background

Non-adaptive query models have been used to paper finer-grained runtime tradeoffs and data collection constraints, but many practical procedures adaptively choose queries based on previously observed data.

The survey notes that incorporating adaptivity into the low-degree framework remains largely open, apart from limited forms of adaptivity handled in quantum learning contexts. Addressing adaptivity would broaden the applicability of low-degree complexity predictions.