Personalized Budget Distribution (PBD)

• Personalized Budget Distribution (PBD) is a framework that allocates scarce resources non-uniformly across heterogeneous units while respecting individualized constraints.
• It underpins methods in differential privacy, participatory budgeting, and personalized pricing by using tailored allocation rules to optimize utility, fairness, and proportionality.
• Empirical studies show that PBD mechanisms can significantly enhance performance by adapting budgets to local importance and sensitivity, outperforming uniform distribution techniques.

Personalized Budget Distribution (PBD) denotes a family of allocation designs in which a finite budget is distributed non-uniformly across heterogeneous units—such as records, users, features, tokens, time slots, projects, or customers—in order to respect individualized constraints while optimizing utility, fairness, proportionality, or access. In the literature covered here, the “budget” may be a differential privacy parameter, a virtual participatory budgeting entitlement, a subsidy or price discount schedule, or a schedulable resource in a privacy-aware system. The common structural feature is that allocation is individualized rather than uniform, and that the allocation rule is itself part of the mechanism design problem rather than a post hoc implementation choice (Liu et al., 2024, Fairstein et al., 2021, Kallus et al., 2020, Du et al., 9 May 2026).

1. Conceptual scope and recurring design pattern

Across the cited work, PBD appears in at least three technical settings. In differential privacy, it concerns how an overall privacy budget is split across records, queries, features, document chunks, or time windows. In participatory budgeting, it concerns how voters’ equal or personalized shares are translated into project funding decisions. In personalized pricing, it concerns individualized subsidies or prices that map a fixed or constrained budget into differentiated offers.

A concise way to organize the literature is to distinguish the resource being allocated, the personalization unit, and the main objective.

Domain	Personalization unit	Main objective
Differential privacy	Record, user, feature, token, query, time slot	Privacy-utility trade-off
Participatory budgeting	Voter, coalition, project group	Proportionality, welfare, exhaustiveness
Personalized pricing	Customer or group	Access, revenue, welfare, equity

Despite the diversity of domains, several recurring constraints are explicit. First, the resource is scarce: privacy budget is non-replenishable in PrivateKube, and public budgets are bounded in participatory budgeting (Luo et al., 2021, Kraiczy et al., 2023). Second, uniform allocation is repeatedly identified as inadequate when units differ in importance, sensitivity, or entitlements. Third, the benefit of personalization depends on the interaction between the budget rule and the aggregation or release mechanism, rather than on personalization alone.

A plausible implication is that PBD is best understood as a constrained allocation layer that mediates between heterogeneous local requirements and a global feasibility condition.

2. Differential privacy as a budget allocation problem

In differential privacy, PBD is often formalized by composition. For text obfuscation, a document $D$ is decomposed into chunks $C_1,\dots,C_k$, each chunk receives an individual budget $\varepsilon_i$, and the global document constraint is

$\sum_{i=1}^k \varepsilon_i = \varepsilon.$

The 2026 systematic study of text decomposition and budget distribution evaluates five chunking strategies and six budget distribution methods, showing that “such design choices are very important,” and that significant differences arise even under identical global $\varepsilon$ (Meisenbacher et al., 1 May 2026).

Record-level personalized differential privacy in cross-silo federated learning pushes the granularity further. The rPDP-FL framework uses a two-stage hybrid sampling scheme: uniform client-level Poisson sampling with probability $\lambda$, followed by non-uniform record-level Poisson sampling with per-record probabilities $q_{i,j}$ derived from personalized privacy budgets $\varepsilon_{i,j}$. Because the exact $q$–$\varepsilon$ relationship is analytically intractable, the paper introduces Simulation-CurveFitting, with an empirical exponential fit

$C_1,\dots,C_k$0

This permits direct mapping from target record-level privacy to sampling probabilities and is reported to provide significant performance gains over baselines that do not consider personalized privacy preservation (Liu et al., 2024).

For differentially private synthetic data, “Spending Privacy Budget Fairly and Wisely” treats budget allocation as a hierarchical mechanism-design problem. The total budget is split between a synthesizer and a family of DP classifiers:

$C_1,\dots,C_k$1

and classifier budgets are then weighted as

$C_1,\dots,C_k$2

The weighting is informed by feature importance or fairness-related performance objectives, with the explicit goal of maximizing predictive accuracy while bounding potential disparities in accuracy across groups (Rosenblatt et al., 2022).

The same literature also identifies limits. In heterogeneous DP mean estimation, the 2026 paper on the limits of personalizing differential privacy budgets compares a fully personalized affine estimator to a thresholding estimator that discards points with $C_1,\dots,C_k$3 and uses a single privacy level $C_1,\dots,C_k$4 on the remainder. For mixed public/private data, the thresholding estimator incurs at most a factor-2 loss relative to the optimal affine estimator; with two privacy levels, the worst-case factor is 4; and for arbitrary privacy profiles with $C_1,\dots,C_k$5 distinct levels, the gap is upper bounded by $C_1,\dots,C_k$6 (Cyffers et al., 13 May 2026). This directly contradicts the simplistic view that full per-individual personalization necessarily yields large utility gains.

3. Sequential, streaming, and schedulable PBD

A major branch of PBD research concerns repeated releases over time, where privacy budgets must be managed under composition. In private stream estimation with personalized $C_1,\dots,C_k$7-event privacy, the Personalized Window Size Mechanism supports per-user window sizes $C_1,\dots,C_k$8 and budgets $C_1,\dots,C_k$9, and PBD splits each user’s budget into calculation and publication components:

$\varepsilon_i$0

The mechanism uses a privatized dissimilarity test and an Optimal Budget Selection routine to decide whether to publish a new noisy aggregate or reuse the previous release, while maintaining the sliding-window invariant

$\varepsilon_i$1

Dynamic Personalized Budget Distribution extends this to time-varying backward and forward requirements and is proved to satisfy the corresponding personalized privacy guarantees (Du et al., 9 May 2026).

The earlier 2025 version of the same line of work describes the same core idea in fixed-requirement form: PBD provides “at least the same privacy budget for the next time step as the amount consumed in the previous release,” while Personalized Budget Absorption uses previous and future slots to increase current release budget. The reported utility gains are explicit: PBD achieves 68% less error than BD on average on real data sets, and PBA achieves 24.9% less error than BA on average on synthetic data sets (Du et al., 10 Sep 2025).

Personalized budgets also arise in social-network publication. For releasing connection fingerprints under Personalized Differential Privacy, DEBA allocates exponentially decaying per-query budgets

$\varepsilon_i$2

while DUBA-LF allocates uniform per-query budgets

$\varepsilon_i$3

Both mechanisms allow skipped budgets to be absorbed by later significant releases, and both are analyzed as satisfying $\varepsilon_i$4-PDP (Li et al., 2017).

At a system level, PrivateKube treats privacy as a first-class, non-replenishable resource. Dominant Private Block Fairness schedules privacy claims over private blocks, using gradual unlocking and all-or-nothing allocation. This is PBD at scheduler scale: pipelines request vector budgets across blocks, and allocation is personalized to job-specific demands rather than uniform shares. Compared to existing baselines, DPF allows training more models under the same global privacy guarantee, especially under Rényi DP (Luo et al., 2021).

4. Document, feature, and token granularity

Text privatization offers a particularly clear demonstration that “how” a budget is spent can matter as much as “how much” budget is available. The 2025 paper on intelligent distribution in differentially private text rewriting constructs a toolkit of token-level scoring methods: Information Content, Part-of-Speech informativeness, Named Entity Recognition, Word Importance, and Sentence Difference. Scores are normalized, aggregated, and then used to assign smaller per-token budgets to more sensitive tokens. Under identical overall privacy budgets, the paper reports higher privacy levels and more positive privacy-utility trade-offs than naive equal division (Meisenbacher et al., 28 Mar 2025).

The 2026 systematic exploration broadens this into a factorial study over decomposition and allocation. It evaluates association-based, POS-based, and WordNet-based decomposition together with Uniform, Attention Weights, Integrated Gradients, Information Content, KeyBERT, and YAKE allocation. The study reports that both decomposition choice and budget distribution choice produce significant differences in privacy-utility trade-offs, while their interaction is not significant. It also reports that personalized, non-uniform distribution often outperforms the uniform baseline, but that there is no universal best combination; the optimal pairing depends on whether the target objective is trade-off, utility, or privacy (Meisenbacher et al., 1 May 2026).

Synthetic data generation exhibits a related but not identical phenomenon. There, the “components” are typically features or subgroup-specific predictive objectives rather than tokens. The SuperQUAIL mechanism allocates more of the classifier budget to features or groups deemed important for predictive accuracy or fairness, and the reported consequence is improved accuracy and reduced subgroup variance relative to uniform allocation, especially on difficult or imbalanced tasks (Rosenblatt et al., 2022).

A plausible implication is that document-level or feature-level PBD is not merely a composition exercise. It is an attribution problem: the mechanism must estimate which units are informative, sensitive, or fairness-critical, and then convert those estimates into a feasible budget vector.

5. Participatory budgeting and personalized entitlements

In participatory budgeting, PBD refers to the way budget entitlements are represented and aggregated across voters. The 2021 paper on proportional participatory budgeting with project interaction shows why naive, project-separable elicitation can fail when projects are substitutes. It introduces an input format in which voters specify