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-density distributions with connected support and \(O((\log T)^2)\) upper bounds for bounded-density distributions with support gaps. It was unknown whether the extra logarithmic factor is necessary even in the one-resource model. We prove that it is necessary. For a mixture of two separated uniform distributions at the c
This research provides a fundamental theoretical advancement in understanding the limitations and performance of online algorithms for optimal selection problems, specifically in the multi-secretary problem context.
It refines our understanding of regret bounds in sequential decision-making, which is critical for developing more efficient and robust AI agents and online algorithms in various applications.
The established necessity of an extra logarithmic factor for certain conditions changes previous assumptions about the achievable regret, guiding future algorithm design and theoretical research in selection problems.
- · AI researchers
- · Algorithm designers
- · Online marketplaces
- · Developers of overly simplistic online selection algorithms
- · Theorists relying on prior, less precise regret bounds
Improved theoretical understanding of online decision-making under uncertainty.
More precisely calibrated expectations for the performance limits of agentic systems.
Potential for new algorithmic breakthroughs informed by these tighter bounds, improving efficiency in areas like resource allocation or dynamic pricing.
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Read at arXiv cs.LG