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Hidde Lycklama
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Adversary_view

Adversary View — What does each sampler reveal?

An adversary watches noisy gradients from all 5 batches and tries to locate canary ★. The critical question: can the adversary eliminate batches as the canary's possible location?

Poisson

Each step is an independent coin flip. Batch sizes vary. Observing one batch gives no structural information about others.

Privacy leakage (relative) Moderate — bounded by noise σ only.

Shuffle (WOR)

Fixed batch size lets the adversary detect canary absence per batch. After T−1 empty batches, the last is certain.

Privacy leakage (relative) High — empirically up to 4× Poisson ε.

Balls-and-Bins ✦

Variable batch size blocks elimination. The adversary cannot tell "canary absent" from "canary hidden in noise." p stays fixed.

Privacy leakage (relative) Low — similar or better than Poisson.
Balls-and-Bins: Each batch has a random number of balls (Binomial). The adversary cannot reliably distinguish an empty canary slot from one masked by noise. p = 0.20 for every batch, at every step — no elimination applies. Even seeing all 5 batches is only a guess, not a confirmation.
Shuffle WOR: Every batch has exactly 2 balls — fixed. The adversary knows this, so canary absence is detectable. Each empty batch rules out a location: 0.20 → 0.25 → 0.33 → 0.50 → certain! — already certain before Batch 5 is revealed.
Batch-by-batch reveal — adversary's view
Dataset: 10 samples, 5 batches. Canary = ★. Canary is in Batch 5 for both samplers. Drag the slider and watch how adversary certainty evolves differently.

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Balls-and-Bins variable batch size — no elimination — p fixed at 0.20

Shuffle Without Replacement fixed batch size — elimination applies — p updates

Sampling comparsion

DP-SGD Sampling Methods — Interactive Comparison

10 samples (balls) placed into 5 mini-batches (bins) under three sampling strategies. Ball ★ is the canary. Click Step to place one ball at a time across all three samplers simultaneously. Reset generates a fresh random draw.

Poisson Subsampling q = 0.4 Each ball enters each bin independently with probability q = 0.4. A ball may appear in multiple bins — or none.

Shuffle Without Replacement 2 per bin Balls shuffled once then sliced into fixed bins of 2. Every ball appears exactly once, but positions are correlated.

Balls-and-Bins ✦ Best of both Each ball independently picks one of the 5 bins uniformly at random. Exactly once per ball; placements are independent.

Samples
★ = canary
adversary's target
Ready — Step places one ball across all three samplers simultaneously.
Hidde Lycklama
Published on 

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