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On the Complexity of Differentially Private Best-Arm Identification with Fixed Confidence

NeurIPS 2023 · Federated learning and privacy › Differential privacy · approach: Privacy accounting and mechanisms · 2 citations (OpenAlex)

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Use Ada-TT instead of DP-SEFixed-confidence differentially private best-arm identification · Bernoulli instances testedstopping timeHelped
Increase privacy by reducing epsilonAda-TT · Bernoulli instances testedstopping timeHurt
Increase epsilon above 0.2Ada-TT · Bernoulli instances testedstopping timeNo clear effect
Use adaptive sampling rather than uniform sampling within phasesPrivate fixed-confidence best-arm identification · Bernoulli instances testedstopping timeHelped
Add per-arm doubling episodes and forget rewards from previous phases (ablation)Ada-TT · Asymptotic sample complexitysample complexity: 4 T_{\mathrm{KL},\beta}^\star(\boldsymbol{\mu})Hurt
Add Laplace noise to empirical means (ablation)Ada-TT · Asymptotic sample complexitysample complexity: 4 T_{\mathrm{KL},\beta}^\star(\boldsymbol{\mu}) \left( 1+ \sqrt{1 + \frac{\Delta^2_{\max}}{2\epsilon^2}} \right)Hurt
Use a private GLR threshold instead of the non-private threshold (ablation)Ada-TT stopping rule · Asymptotic sample complexitysample complexityHurt
Use privacy with sufficiently large epsilonFixed-confidence best-arm identification · Low-privacy regimesample complexity lower boundNo clear effect

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