Personalized Privacy Budget Allocation

• PPBA is a framework of methods that allocate differential privacy budgets adaptively based on sensitivity, user preferences, and context.
• It integrates central, local, and streaming models with mechanisms like inverse-sensitivity budgeting and window-based allocation to control error.
• PPBA underpins applications in machine learning, trajectory protection, and privacy-aware data markets by balancing utility and privacy loss.

Personalized Privacy Budget Allocation Algorithm (PPBA) defines a class of methods for distributing privacy budgets in differentially private analysis such that parameters governing privacy guarantees (typically $\epsilon$ per record, feature, location, group, or time window) are adapted to underlying heterogeneity in sensitivity, user preference, data utility, temporal or spatial context, or trading constraints. PPBA is a central tool for personalized differential privacy, individual privacy accounting, privacy-aware data markets, trajectory protection in location-based services, adaptive stream analytics, and feature-aware privatization in synthetic data and text rewriting. Methods span central, local, and streaming models, often incorporating arbitrage-freeness, composition theorems, and mechanism-specific utility bounds. Contemporary variants integrate per-record, per-group, or per-location allocation with minimization of error, fairness constraints, or quality-of-service guarantees, frequently subject to privacy budget exhaustion, windowed constraints, or per-user parametrization.

1. Formal Models and Problem Statements

PPBA operates under several variants of differential privacy that relax the classical uniform-budget assumption. Common models include:

• Personalized Differential Privacy (PDP): Each data subject $i$ is assigned an individualized bound $\hat\epsilon_i$, and mechanisms $\mathcal{M}$ satisfy, for every output $o$ and neighboring data sets $D, D'$ differing only in record $i$,

$\Pr[\mathcal{M}(D)=o] \le e^{\epsilon_i} \Pr[\mathcal{M}(D')=o}$

(Zheng et al., 2019, Zheng et al., 2021).

• Per-record Differential Privacy (PrDP): Records $r$ carry privacy budgets $\mathcal{E}(r)$, with global lower and upper bounds, and mechanisms $\mathcal{M}$ satisfy,

$$\Pr[\mathcal{M}(D)\in S]\le e^{\mathcal{E}(r)}\Pr[\mathcal{M}(D^\prime)\in S]$$

where $D^\prime$ differs by record $r$ (Chen et al., 24 Nov 2025).

• Individualized DP in Learning: In DP-SGD, each user or group is assigned $\epsilon_i$, and the sampling/noising mechanism is tuned so that the cumulative privacy loss per individual is bounded by $\epsilon_i$ (Boenisch et al., 2023).
• Trajectory and Streaming Privacy: In spatiotemporal data or streaming settings, budgets are dynamically apportioned subject to windowed temporal constraints or spatial/semantic-sensitivity metrics, e.g., $(w,\epsilon)$-event PDP (Du et al., 10 Sep 2025, Min et al., 26 Nov 2025, Min et al., 27 Nov 2025).

The budget allocation problem seeks a vector $(\epsilon_1,\ldots,\epsilon_n)$, or higher-dimensional matrix/tensor in group, feature, or temporal settings, that (i) respects per-individual privacy preferences or global constraints, (ii) minimizes expected utility loss (variance, error), (iii) upholds arbitrage-freeness in market contexts, and (iv) satisfies the composition properties required for differential privacy guarantees.

2. Core Algorithms and Mathematical Formulation

Key PPBA methodologies fall into the following archetypes:

• Inverse-Sensitivity Budgeting: Allocate $\epsilon_i$ inversely proportional to sensitivity $S_i$ derived from stay-duration, frequency, semantic tags, or NLP-informed metrics, with normalization to satisfy $\sum_i \epsilon_i = \epsilon_s$ (Meisenbacher et al., 28 Mar 2025, Min et al., 26 Nov 2025):

$\epsilon_i = \frac{1/S_i}{\sum_j 1/S_j} \epsilon_s$

• Pattern-based Allocation for Markets: Data owners specify maximum tolerable loss; PPBA derives spending patterns $\rho$ that globally fit constraints and minimize deviation from normalized bounds, subject to arbitrage-freeness conditions (Zheng et al., 2021, Zheng et al., 2019):

$\epsilon_i = \rho_i \cdot \theta$

Offline, PPBA searches for optimal $\rho$, then inverts variance function $v(\theta)$ at query time.

• Optimal Budget Selection (Observation Thresholds): In stream analytics, OBS selects threshold by minimizing error components from sampling and Laplace noise:

$$\text{err}_s(\tilde{\epsilon}_k)+\text{err}_{dp}(\tilde{\epsilon}_k)$$

with per-slot and residual allocations managed by rules such as

$$\epsilon_{i,t}^{(2)} = \frac{1}{2} (\epsilon_i/2 - \sum_{\text{window}} \epsilon_{i, k}^{(2)})$$

• Window-based Adaptive Allocation: Spatiotemporal trajectory privacy uses sliding window constraints, location predictability, and sensitivity metrics to dynamically apportion per-location budgets so that total budget in any window remains within $\epsilon_w$ (Min et al., 27 Nov 2025):

$$\lambda_{i,t} = \alpha_1 LP_{i,t} + \alpha_2 LS_{i,t}$$

$$\epsilon_{i,t} = \max\{0, \epsilon_r - \lambda_{i,t} \Delta\epsilon\}$$

• Rényi Filter for Adaptive Accounting: PPBA in sequential adaptive analysis compressors privacy cost per individual $i$ as

$\rho_t^{(i)} = \text{cost at step } t$

and halts analysis for $i$ when $\sum_t \rho_t^{(i)} \geq B_i$ (Feldman et al., 2020).

3. Mechanism Integration and Workflow

PPBA forms a wrapper or modular layer over standard privacy mechanisms, altering batch composition, sampling probabilities, noise scale, or feature-wise allocation by inputting determined budget splits. Exemplary integrations include:

• IDP-SGD for ML Training: Personalized sampling and gradient clipping parameters, computed via RDP accounting, yield per-user privacy (Boenisch et al., 2023).
• Diffraction and DP-BART Mechanisms in Text Rewriting: Token-level budgets, derived from multi-feature sensitivity, guide geometric perturbations or latent representation noising per sentence (Meisenbacher et al., 28 Mar 2025).
• Permutation-and-Flip for Location Protection: Each region or neighbor receives tailor-made $\epsilon$ based on semantic and topological properties. Perturbed locations are sampled with density proportional to $\exp(-\epsilon_i d(x_i,x_j)/2D(PLS))$ (Min et al., 26 Nov 2025, Min et al., 27 Nov 2025).
• Stream Analytics with Windowed Constraints: Publishing is driven by private dissimilarity tests and error thresholds, with dynamic budget splitting and absorption across sliding windows (Du et al., 10 Sep 2025).
• Social Network Data Publication: Budget absorption (DEBA) and uniform ladder function schemes (DUBA-LF) concentrate budget on significant releases, tuning granularity and error versus utility (Li et al., 2017).
• Data Markets: Sample-based mechanisms for histogram queries incorporate N-grouping PPBA to maintain arbitrage-freeness and ensure owners’ cumulative privacy loss does not exceed their specified cap (Zheng et al., 2019, Zheng et al., 2021).

4. Theoretical Guarantees and Privacy Analysis

All PPBA variants retain strict privacy guarantees under their respective frameworks:

• Composition Theorems: Sequential composition of mechanisms with per-user allocated budgets aggregates to a maximum specified per-user loss, maintaining PDP or PrDP (Zheng et al., 2019, Chen et al., 24 Nov 2025, Zheng et al., 2021).
• Adaptive RDP Filtering: The sum of personalized Rényi costs for any user never exceeds $B_i$, and filtering mechanisms halt participation for any individual whose budget is exhausted (Feldman et al., 2020).
• Arbitrage-freeness: For market-oriented PPBA, specific conditions (e.g., monotonicity, convexity, harmonic equations on variance function derivatives) ensure no buyer can reconstruct answers cheaply by gaming the budget allocation (Zheng et al., 2021).
• Windowed Event Privacy: In stream analytics, analysis ensures every user’s windowed constraint on cumulative privacy allocation is respected at all times, with all published statistics certified to meet the personalized event-DP (Du et al., 10 Sep 2025).

5. Utility Bounds, Trade-offs, and Empirical Results

PPBA substantially improves utility and trade-offs compared to uniform budget splits:

• Machine Learning (IDP-SGD): Empirical boosts of 1–5 points in accuracy are observed over uniform-$\epsilon$ baselines, with tailored protection avoiding loss for most conservative participants (Boenisch et al., 2023).
• Text Privatization: Attribute and membership inference rates are reduced by up to 10–30% with PPBA-driven allocation, with modest drops in classification F1 but enhanced embedding similarity and BLEU scores (Meisenbacher et al., 28 Mar 2025).
• Spatiotemporal and Trajectory Privacy: Personalized allocation reduces QoS loss by up to 8% and raises adversarial inference error by up to 20%, maintaining theoretical guarantees (Min et al., 26 Nov 2025, Min et al., 27 Nov 2025).
• Streaming Analytics: Personalized budget distribution achieves up to 68% lower error (AMRE) than uniform baselines; budget absorption cuts error by over 24.9% in synthetic data streams (Du et al., 10 Sep 2025).
• Social Networks: Distance-based absorption schemes (DUBA-LF) reduce mean absolute error by up to 120% versus non-personalized allocation; DEBA offers similar but slightly less dramatic improvements (Li et al., 2017).
• Per-record DP: PPBA deployed as privacy-specified domain partitioning achieves near-minimal error $O(1/\varepsilon_{\min})$ on the subset of records actually present, never revealing the true minimal budget and outperforming naive baselines (Chen et al., 24 Nov 2025).

6. Implementation Considerations and Practical Aspects

PPBA implementations require attention to the following:

• Budget Specification: Owners or data subjects can select from categorical levels (“High/Medium/Low”), supply numerical bounds, or participate in surveys to assess risk tolerance (Boenisch et al., 2023, Zheng et al., 2021).
• Parameter Tuning: Sensitivity weights, adjustment steps, and window sizes require domain-specific or user-driven configuration for optimal privacy–utility balance (Min et al., 26 Nov 2025, Min et al., 27 Nov 2025).
• Complexity: Offline pattern fitting in market models is $O(n \log(1/\delta))$; window-based streaming and partitioned DP is $O(nL)$ for $n$ users/records and $L$ buckets. Per-query or per-release budgeting is linear in $n$ (Zheng et al., 2021, Chen et al., 24 Nov 2025, Du et al., 10 Sep 2025).
• Scalability: Algorithms are confirmed in experimental settings for $n$ up to $10^5$; complexity scales with data owner/user count and, for trajectory/location, with number of sensitive regions.
• Mechanism Integration: PPBA functions as a modular wrapper in central and local DP, easily plug-compatible with Laplace, Gaussian, Sample-based, Exponential, or PF mechanisms. No modification to underlying DP methods is usually required (Chen et al., 24 Nov 2025, Meisenbacher et al., 28 Mar 2025).

7. Extensions, Limitations, and Future Directions

Research continues on PPBA in several directions:

• Learned Budget Functions: Instead of hand-tuned or analytic inverse-sensitivity, PPBA may employ neural-net-based allocation over feature vectors (Meisenbacher et al., 28 Mar 2025).
• Hierarchical and Context-aware Allocation: Budget can be stratified across semantic units, network topologies, or hierarchical groups (Min et al., 26 Nov 2025, Meisenbacher et al., 28 Mar 2025).
• Human-in-the-loop and Adaptive Feedback: User-driven sensitivity assessment and ongoing adjustment may yield improved privacy satisfaction and utility (Meisenbacher et al., 28 Mar 2025).
• Advanced Composition Techniques: Adoption of sophisticated composition rules (moment accountant, RDP) can further reduce privacy-loss or minimize accumulated $\delta$ over records and time.
• Market Dynamics and Pricing: Ongoing refinement of arbitrage-freeness, compensation functions, and utility models for large-scale data trading platforms (Zheng et al., 2021, Zheng et al., 2019).
• Empirical Analysis: Most early works provide only theoretical or simulation results. Further benchmarking on real-world deployments and cross-modal applications is ongoing (Boenisch et al., 2023, Min et al., 26 Nov 2025).

PPBA, as a flexible family of privacy budget allocation schemes, is central to modern privacy engineering in personalized, adaptive, and heterogeneous settings. The approach underpins state-of-the-art trade-offs in privacy-preserving analytics, data-driven markets, and resilient location-based and streaming services.