Impact of fully interactive (blackboard) protocols on sample complexity

Determine whether fully interactive blackboard protocols in distributed simple binary hypothesis testing can significantly reduce the sample complexity required to achieve a target Bayes error compared to non-interactive or sequentially interactive settings.

Background

This paper establishes that sequential interaction does not provide more than a constant-factor reduction in sample complexity relative to identical-channel non-interactive schemes for distributed simple binary hypothesis testing under information constraints. While this resolves an earlier open question about sequential interactivity, the fully interactive multi-round model—often referred to as the blackboard protocol—allows richer forms of interaction among agents.

The conclusion highlights that it remains unknown whether such fully interactive protocols can lead to meaningful (i.e., more than constant-factor) reductions in sample complexity for this testing problem. Clarifying this would complete the landscape of how different interaction models impact sample complexity.