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