Relaxing the requirement to know the prediction accuracy

Determine whether learning-augmented streaming algorithms for Boolean Max-CSPs can achieve comparable approximation and space guarantees without requiring the prediction-accuracy parameter to be known with high accuracy, including under only a constant-factor approximation to that parameter, or prove lower bounds showing that such relaxation is impossible.

Background

The paper studies streaming algorithms for Boolean Max-CSPs equipped with an oracle whose predictions independently agree with a fixed optimal assignment with probability 1/2+ε. The proposed algorithms achieve near-optimal value estimation using small space, but their estimators and degree thresholds depend on knowing ε accurately. The paper shows that a highly accurate estimate ε′ satisfying ε′=(1±O(η))ε is sufficient, while noting that the algorithm of Dong, Peng, and Vakilian for Max-Cut requires only a constant-factor estimate.

The authors explicitly leave unresolved whether the dependence on highly accurate knowledge of ε can be removed or weakened. The open problem therefore concerns either designing comparable algorithms using only a constant-factor estimate of ε or establishing impossibility results demonstrating that such limited parameter knowledge cannot suffice.