Under LDP, optimal online stopping uses binary reports and achieves competitive ratio e^ε/(n-1+e^ε) vs the non-private online optimum and (1+e^{-ε})/2 vs the LDP prophet.
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Prophet Inequalities under Local Differential Privacy
Under LDP, optimal online stopping uses binary reports and achieves competitive ratio e^ε/(n-1+e^ε) vs the non-private online optimum and (1+e^{-ε})/2 vs the LDP prophet.