Learning in Prophet Inequalities with Noisy Observations | Signal Canvas | ScienceToStartup

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Learning in Prophet Inequalities with Noisy Observations

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Proof freshness: stale
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Display score: 4/10
Last proof check: 2026-04-03
Score updated: 2026-04-03
Score fresh until: 2026-05-03
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Coverage: 33%

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Learning in Prophet Inequalities with Noisy Observations

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Claim map

Strong 8Mixed 0Weak 0

Evidencepartial
In the i.i.d. setting, we establish that both an Explore-then-Decide strategy and an ε-Greedy variant achieve the sharp competitive ratio of 1 - 1/e, under a mild condition on the optimal value.
Implicationpartial
Directly stated in abstract with specific competitive ratio and condition
Verificationpartial
partial
Evidencepartial
In the i.i.d. setting, we establish that both an Explore-then-Decide strategy and an ε-Greedy variant achieve the sharp competitive ratio of 1 - 1/e, under a mild condition on the optimal value.
Implicationpartial
Directly stated in abstract alongside Explore-then-Decide strategy with same competitive ratio
Verificationpartial
partial
Evidencepartial
For non-identical distributions, we show that a competitive ratio of 1/2 can be guaranteed against a relaxed benchmark.
Implicationpartial
Directly stated in abstract with specific competitive ratio
Verificationpartial
partial
Evidencepartial
Moreover, with limited window access to past rewards, the tight ratio of 1/2 against the optimal benchmark is achieved.
Implicationpartial
Directly stated in abstract with specific competitive ratio and condition
Verificationpartial
partial
Evidencepartial
To address this challenge, we propose algorithms that integrate learning and decision-making via lower-confidence-bound (LCB) thresholding.
Implicationpartial
Directly stated in abstract as the core algorithmic approach
Verificationpartial
partial
Evidencepartial
We study the prophet inequality, a fundamental problem in online decision-making and optimal stopping, in a practical setting where rewards are observed only through noisy realizations and reward distributions are unknown.
Implicationpartial
Directly stated in abstract as the problem setting
Verificationpartial
partial
Evidencepartial
At each stage, the decision-maker receives a noisy reward whose true value follows a linear model with an unknown latent parameter, and observes a feature vector drawn from a distribution.
Implicationpartial
Directly stated in abstract describing the specific model
Verificationpartial
partial
Evidencepartial
under a mild condition on the optimal value
Implicationpartial
Explicitly mentioned as a condition for achieving the 1 - 1/e ratio
Verificationpartial
partial

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