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New research establishes tight lower bounds for multi-secretary problem regret

By PulseAugur Editorial · [2 sources] ·

This paper investigates the multi-secretary problem, focusing on additive regret which measures the difference between optimal offline rewards and online policy rewards. Researchers have established logarithmic regret bounds for certain distributions and quadratic bounds for others. The study proves that a quadratic lower bound is necessary for mixtures of two separated uniform distributions, indicating that existing upper bounds for gapped distributions are tight. The proofs utilize Bellman certificates, which help construct explicit certificates and explain why support gaps lead to larger regret. AI

RANK_REASON Academic paper published on arXiv detailing theoretical computer science research. [lever_c_demoted from research: ic=1 ai=0.1]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

New research establishes tight lower bounds for multi-secretary problem regret

COVERAGE [2]

  1. arXiv cs.LG TIER_1 English(EN) · Jiawei Zhang ·

    Tight Lower Bounds for the Multi-Secretary Problem via Bellman Certificates

    arXiv:2607.02150v1 Announce Type: cross Abstract: This paper studies additive regret in the multi-secretary problem, defined as the gap between the expected offline prophet reward and the reward of the best online policy. Prior work established \(O(\log T)\) regret for bounded-de…

  2. arXiv cs.LG TIER_1 English(EN) · Jiawei Zhang ·

    Tight Lower Bounds for the Multi-Secretary Problem via Bellman Certificates

    This paper studies additive regret in the multi-secretary problem, defined as the gap between the expected offline prophet reward and the reward of the best online policy. Prior work established \(O(\log T)\) regret for bounded-density distributions with connected support and \(O…

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