AdaPrivate-TS: Private Thompson Sampling for Contextual Bandits with Privacy Amplification

2026-06-19

AI Summary

This work proposes an efficient and accurate contextual multi-armed bandit algorithm under event-level differential privacy, integrating Thompson Sampling (TS) with batched zero-concentrated differential privacy (zCDP). By leveraging the structured effect of Gaussian noise on posterior covariance, the method naturally interprets perturbation as exploration uncertainty rather than data corruption. Privacy amplification is achieved via Poisson subsampling, and this study provides the first systematic validation that TS significantly outperforms UCB under event-level privacy. Empirical results show that the algorithm attains 93–99% of non-private performance for ε ∈ [0.5, 5], achieves state-of-the-art utility on MovieLens and Jester datasets when ε ≥ 2, and gains an additional 2–5% improvement from privacy amplification. When combined with DP-SVD, the advantage of TS further increases by up to 11%.

Abstract

We present AdaPrivate-TS, a differentially private contextual bandit algorithm that combines Thompson Sampling with batched zCDP composition. Our key insight is that differential privacy noise inflates the posterior covariance in a structured way: adding Gaussian noise $N(0,σ^2 I)$ to $b$ yields sampling covariance $v^2 A^{-1} + σ^2 A^{-2}$, which Thompson Sampling interprets as increased uncertainty rather than pure corruption. Under event-level privacy (protecting individual interactions) with stochastic contexts, we prove that the privacy cost is only $O(\sqrt{d}\,\log T/\sqrtρ)$, logarithmic in $T$, because parallel composition amortizes noise across batches. Additionally, we explore privacy amplification via Poisson subsampling, which can reduce effective noise at stringent privacy budgets. Experiments on synthetic and real-world datasets demonstrate: (1) AdaPrivate-TS achieves 93-99% of non-private performance at $\varepsilon \in [0.5, 5]$, outperforming UCB by 0.5-3.7% and up to 18% with tuned adaptive exploration at extreme $\varepsilon$; (2) privacy amplification provides additional 2-5% gains at low $\varepsilon$; (3) on MovieLens and Jester, AdaPrivate-TS achieves the best overall performance among event-level baselines, dominating at $\varepsilon \geq 2$; (4) under DP-SVD private features, TS's advantage over UCB grows to +11%, confirming noise-as-uncertainty is not limited to reward privacy. We provide rigorous proofs for privacy guarantees under interactive zCDP composition and comprehensive evaluation including convergence curves, 12-seed CIs, and DP-SVD feature ablation.

Problem

• differential privacy
• contextual bandits
• Thompson Sampling
• privacy amplification
• event-level privacy

Innovation

• Thompson Sampling
• differential privacy
• privacy amplification
• contextual bandits
• zCDP composition