Improving the approximation ratio through deferred-to-deadline commitment

Determine whether exploiting deferred-to-deadline commitment, which permits a policy to gather additional observations while retaining the option to select previously opened boxes that have not expired, can improve the approximation ratio beyond 1/2 for Pandora's problem with deadlines.

Background

The paper establishes a 1/2-approximation for a partially adaptive algorithm with immediate commitment, evaluated against a fully adaptive benchmark with deferred-until-stopping commitment. Deferred-to-deadline commitment is more permissive: an opened box remains available for selection until its deadline, allowing the policy to continue opening boxes while preserving earlier feasible options.

The authors explicitly note that neither their algorithm nor the prior algorithm of Berger et al. exploits this flexibility. The unresolved question is whether algorithms using deferred-to-deadline commitment can achieve an approximation ratio strictly greater than 1/2.

References

One direction is to exploit deferred-to-deadline commitment, which allows a policy to gather additional observations while retaining the option to select earlier boxes that have not expired. Neither our algorithm nor that of \citet{DBLP:conf/aaai/BergerEFF24} exploits this flexibility. Can it improve the approximation ratio beyond $1/2$?

— A $1/2$-Approximation for Pandora's Problem with Deadlines  (2610.13775 - Qin et al., 9 Oct 2026) in Section Conclusion

Under a common deferred commitment rule, can efficient fully adaptive algorithms achieve better approximation guarantees than partially adaptive algorithms?

— A $1/2$-Approximation for Pandora's Problem with Deadlines  (2610.13775 - Qin et al., 9 Oct 2026) in Section Conclusion