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Differential Privacy Budget

(ε, δ)-differential privacy: ε bounds privacy loss; δ is probability of failure (typically 1/n²). Lower ε = stronger privacy. Apple uses ε≈8; medical/Census often ε<0.1–1. RDP gives tighter composition than basic.

Concept Fundamentals
Privacy budget
ε-Privacy
Information leakage bound
Failure probability
δ-Privacy
Relaxation parameter
σ ∝ sensitivity/ε
Gaussian Mech.
Noise calibration
Private ML training
Application
DP-SGD
CalculateUse the calculator below to run neural computations

Why This ML Metric Matters

Why: Differential privacy ensures ML models don't leak individual data. ε (epsilon) bounds the max privacy loss; δ is the failure probability. Production systems use RDP accounting for tight bounds.

How: Enter dataset size, batch size, epochs, noise multiplier σ, delta δ, clipping norm. Select mechanism (Gaussian/Laplace) and composition method (RDP recommended). Calculator computes ε and privacy level.

  • ●ε<0.1 for medical/Census
  • ●Apple uses ε≈8
  • ●RDP 2–10× tighter than basic
  • ●δ < 1/n² rule of thumb
Sources:Microsoft DP-SGD CalculatorAbadi et al. 2016 — Deep Learning with Differential Privacy
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Differential Privacy Budget Calculator

Calculate ε (epsilon) and δ (delta) via RDP accounting. Model Apple (ε≈8), Google Federated, US Census (ε<0.1), and medical standards.

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📊 Quick Examples — Click to Load

DP-SGD Parameters

number of training samples
samples per gradient step
full passes over dataset
Gaussian noise scale
privacy failure probability
gradient clip threshold
noise distribution
composition method
dp_budget.sh
CALCULATED
$ dp_budget --dataset=100000 --batch=256 --epochs=50 --sigma=1.2 --delta=1e-10
ε (epsilon)
74.9085
δ (delta)
1.00e-10
Sampling rate
0.2560%
Steps
19,532
Bayes β
1.0000
Privacy level
Low
Share:
Differential Privacy Budget
ε = 74.9085
Low
δ = 1e-10Steps: 19,532q = 0.2560%
numbervibe.com/calculators/machine-learning/differential-privacy-calculator

ε vs Epochs

Privacy–Utility Tradeoff (ε vs σ)

1. Sampling rate
q = batch/dataset = 256/100000 = 0.002560
2. Training steps
T = epochs × (dataset/batch) = 50 × 391 = 19532
3. Basic composition (simplified)
ε_basic ≈ (T·q·C)/σ = (19532·0.0026·1)/1.2 ≈ 41.6683
4. RDP bound (tighter)
ε_RDP ≤ ε_basic (RDP gives tighter accounting) ≈ 74.9085
5. Bayes security
β ≈ 1 - e^(-ε/4) = 1.0000

For educational and informational purposes only. Verify with a qualified professional.

🤖 AI & ML Facts

🍎

Apple uses ε≈8 for on-device learning (Learning with Privacy at Scale)

— Apple

📊

US Census Bureau uses ε≈0.1–1 for 2020 Census data release

— Census Bureau

🔬

Abadi et al. 2016 introduced DP-SGD with Gaussian noise and moment accounting

— Abadi 2016

🤖

Meta Opacus provides PyTorch primitives for DP training with RDP accounting

— Opacus

📋 Key Takeaways

  • • (ε, δ)-differential privacy: ε bounds privacy loss; δ is probability of failure (typically 1/n²)
  • • Lower ε = stronger privacy. Apple uses ε≈8; medical/Census often ε<0.1–1
  • • RDP (Rényi DP) gives tighter composition than basic composition — use for production
  • • Sampling rate q = batch/dataset affects privacy: smaller batches = more privacy per step
  • • Noise multiplier σ: higher σ = more privacy, lower utility. Typical range 0.5–4
  • • Gradient clipping (C) limits per-sample influence; essential for DP-SGD

💡 Did You Know

🍎Apple uses ε≈8 for on-device learning (Learning with Privacy at Scale). They report this balances utility and privacy for billions of devices.
📊US Census Bureau uses ε≈0.1–1 for 2020 Census data release. Medical/HIPAA contexts often require ε<0.1.
🔬Abadi et al. 2016 introduced DP-SGD with Gaussian noise and moment accounting — the foundation for Opacus and TensorFlow Privacy.
🤖Meta Opacus provides PyTorch primitives for DP training. It uses RDP accounting for tight epsilon bounds.
📱Google Federated Learning combines secure aggregation with DP. Client-level DP often uses ε=1–10.
⚖️Privacy-utility tradeoff: doubling σ roughly halves ε but can reduce model accuracy by several percent.
📐RDP (Rényi DP) composes additively in α, then converts to (ε,δ)-DP — much tighter than basic composition.
🛡️Bayes security β measures worst-case adversary success. β→0 means strong privacy; β→1 means weak.

📖 How It Works

1. DP-SGD Pipeline

Per batch: clip gradients to norm C, add Gaussian noise N(0, σ²C²), then update. Each step is (ε_step, δ)-DP.

2. Composition

Basic: ε_total ≈ T × ε_step. Advanced/RDP: use Rényi divergence for tighter bounds (Abadi 2016).

3. Sampling Amplification

Subsampling (q < 1) amplifies privacy. With Poisson sampling, privacy improves by ~1/√q.

4. Epsilon Interpretation

ε is the max log-ratio of output probabilities on neighboring datasets. ε=1 means ~2.7× difference; ε=0.1 means ~1.1×.

5. Delta

δ is the probability of a catastrophic privacy breach. Rule of thumb: δ < 1/n² where n = dataset size.

🎯 Expert Tips

Use RDP accounting

RDP gives 2–10× tighter epsilon than basic composition. Opacus and TF Privacy use it by default.

Set δ < 1/n²

For n=100k, δ=1e-10 is safe. For n=1M, use δ=1e-12.

Tune σ first

Start with σ=1–2, then adjust epochs/batch to hit target ε. Larger σ = more privacy, less accuracy.

Clip norm C

C=1 is common. For large gradients, try C=0.5–2. Too small = gradient starvation; too large = weak DP.

⚖️ Privacy Standards by Use Case

Use CaseTypical εδSource
Apple on-device ML~81e-10Apple Learning with Privacy
Google Federated1–101e-8Google FL papers
US Census0.1–11e-10Census Bureau
Medical / HIPAA<0.11e-6Healthcare DP guidelines
Strong privacy research0.01–0.11e-10Academic benchmarks

❓ Frequently Asked Questions

What is epsilon (ε) in differential privacy?

ε bounds the maximum log-ratio of output probabilities on neighboring datasets. Lower ε = stronger privacy. ε=1 means outputs can differ by at most e≈2.7×; ε=0.1 means ~1.1×.

What is delta (δ)?

δ is the probability of a catastrophic privacy breach. Rule of thumb: δ < 1/n² where n = dataset size. For n=100k, δ=1e-10 is common.

Why use RDP instead of basic composition?

RDP (Rényi DP) gives 2–10× tighter epsilon bounds. Basic composition is loose; RDP moment accounting (Abadi 2016) is the industry standard.

What noise multiplier (σ) should I use?

σ=1–2 is common for DP-SGD. Higher σ = more privacy, lower accuracy. Start with σ=1.2 (Apple-style) and tune.

How does gradient clipping help?

Clipping limits per-sample gradient norm to C. Without it, one sample could dominate and leak information. C=1 is typical.

Apple vs Census vs Medical — which ε?

Apple: ε≈8 (utility-focused). Census: ε≈0.1–1 (strong). Medical: ε<0.1 (strict). Choose by sensitivity of data.

What is Bayes security?

β measures worst-case adversary success at distinguishing outputs. β→0 = strong privacy; β→1 = weak. β ≈ 1 - exp(-ε/4) is a simplified bound.

Gaussian vs Laplace mechanism?

Gaussian is standard for DP-SGD (smooth, well-studied). Laplace is used for counting queries. This calculator focuses on Gaussian (DP-SGD).

📊 Differential Privacy by the Numbers

ε≈8
Apple Production
ε<0.1
Medical/Census
2016
Abadi DP-SGD
1/n²
δ Rule of Thumb

⚠️ Disclaimer: This calculator provides simplified DP budget estimates for educational and planning purposes. Production systems should use verified libraries (Opacus, TensorFlow Privacy) with proper RDP accounting. Epsilon bounds are approximations; actual privacy depends on implementation details. Consult privacy experts for compliance (HIPAA, GDPR, Census).

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