Theoretical analysis of UCB-type sampling with e-process rewards

Analyze theoretically UCB-type sampling algorithms that use e-process-based reward processes within the adaptive multiple-testing framework, including corresponding sample-complexity guarantees.

Background

The paper proposes e-value-based posterior sampling (e-PS) and notes that the same e-value-based reward processes can also be used with UCB-type algorithms. UCB-type sampling is evaluated empirically in the appendix, but its theoretical properties are not established in the paper. The unresolved task is therefore to develop a rigorous analysis of these UCB-based adaptive sampling procedures.

References

Our e-value-based reward processes can also be combined with UCB-type algorithms: we evaluate the empirical performance of such methods in Section~\ref{app:sim-ucb} while leaving the theoretical analysis to future work.

— Sample-Efficient Multiple Testing with Adaptive Data Collection  (2609.26651 - Lin et al., 22 Sep 2026) in Section 6, Discussion