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Privacy Preserving Adaptive Experiment Design
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Proposes DP-ConSE, a differentially private contextual bandit experiment algorithm for CATE estimation that trades off regret and estimation error, matching a lower bound (regret × MSE = O(M)) while being (ε, 1/n)-anticipating-private.
Problem
Adaptive experiments estimating conditional average treatment effects (CATE) must balance regret (patient welfare) against estimation accuracy, while protecting privacy of patient data under differential privacy.
Approach
Extends a regret-vs-ATE tradeoff framework to contextual bandits with per-feature successive elimination in the first half, randomized-length RCTs in the second half, and Laplace noise on rewards and batch lengths for anticipating differential privacy; shows privacy comes at no asymptotic cost in the regret-estimation Pareto curve.
Key results
- DP-ConSE is (ε, 1/n)-private and attains regret O(M max{f_min(n)^(1-α), log n/ε}) with estimation error O(1/max{f_min(n)^(1-α), log n/ε}).
- The product of regret and CATE MSE is O(M) under DP, matching the non-private lower bound Ω(M), so privacy is 'almost free' in the Pareto trade-off.
- DP-ConSE estimator is asymptotically normal with the same asymptotic variance as non-private ConSE.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ConSE to balance regret and CATE estimation error | Contextual bandit experiment · Contextual bandit experiment (CATE) | regret × estimation error: \mathcal{O}(M) versus lower bound \Omega(M) | Helped |
| Add differential privacy using DP-ConSE | ConSE · Contextual bandit experiment (CATE) | regret × estimation error: \mathcal{O}(M) | No clear effect |
| Vary α toward 1 (ablation) | ConSE · Contextual bandit experiment (CATE) | regret | Helped |
| Vary α toward 1 (ablation) | ConSE · Contextual bandit experiment (CATE) | estimation error (MSE) | Hurt |
| Vary α toward 0 (ablation) | ConSE · Contextual bandit experiment (CATE) | estimation error (MSE) | Helped |
| Vary α toward 0 (ablation) | ConSE · Contextual bandit experiment (CATE) | regret | Hurt |
| Add differential privacy | ConSE · Contextual bandit experiment (CATE) | asymptotic variance | No clear effect |
| Use UCB or Thompson sampling instead of an exploration-heavy experiment design | Contextual bandit experiment · Contextual bandit experiment (CATE) | estimation error (MSE): \Omega\left(\frac{M}{\log (n)}\right) | Hurt |
Surprising findings
- Privacy adds no asymptotic cost to the regret-estimation Pareto frontier; only the attainable minimum (log n/ε) shifts, shrinking the curve for stronger privacy.
Limitations
- Results are asymptotic and rely on seasonal non-stationarity and assumed constant CATE magnitude Δ=Θ(1).
- Analysis restricted to binary treatment arms and finite feature sets.
- Uses anticipating DP rather than classical DP, which protects only outputs after time t.
Experimental setup
Metrics: regret mean squared error of CATE estimate asymptotic normality
Baselines: ConSE (non-private) random controlled trials (RCT) UCB Thompson sampling
Builds on: ConSE (Bandit experiment regret-ATE tradeoff) anticipating differential privacy DP successive elimination tree mechanism
Closest papers by meaning
- Differentially private learners for heterogeneous treatment effects (ICLR 2025 · similarity 0.88)
- Shuffle and Joint Differential Privacy for Generalized Linear Contextual Bandits (NeurIPS 2026 · similarity 0.84)
- Improving the Variance of Differentially Private Randomized Experiments through Clustering (ICML 2025 · similarity 0.83)
- Towards Safe Policy Learning under Partial Identifiability: A Causal Approach (AAAI 2024 · similarity 0.83)
- Connecting Thompson Sampling and UCB: Towards More Efficient Trade-offs Between Privacy and Regret (ICML 2025 · similarity 0.83)
- Efficient Adaptive Experimentation with Noncompliance (NeurIPS 2025 · similarity 0.83)
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