Bounded Personalization Frameworks

• Bounded personalization frameworks are defined as constrained optimization problems that restrict personalization through explicit limits on exposure, fairness, and data use.
• They integrate algorithmic approaches from bandits, reinforcement learning, supervised learning, and LLMs to enforce operational bounds on user-specific adaptations.
• Practical implementations demonstrate that enforcing these bounds optimizes reward, minimizes bias, and enhances privacy while preserving overall user satisfaction.

Across recent work, bounded personalization denotes formulations in which personalization is optimized under explicit limits rather than unconstrained per-user adaptation. The limits may be exposure intervals over sensitive content-groups, a hard cap on cross-user disparity, a budget of deployable policies, lower bounds on the reliability of subgroup audits, mutual-information caps on latent user information, tiered policy restrictions on model behavior, or local-processing constraints on cross-platform data use (Celis et al., 2017, Borgs et al., 2023, Ivanov et al., 2024, 2502.02786, Mishra, 8 Apr 2026, Kirk et al., 2023, Lin et al., 10 May 2026). Taken together, these works treat personalization as a constrained optimization problem whose objective may be reward, social welfare, explanation faithfulness, privacy-preserving relevance, or user-governed utility, while the constraint set specifies how far the system may deviate from uniform treatment, default alignment, or bounded data use.

1. Recurring formal structure

Several representative formulations make the bound explicit at the level of the feasible set.

Framework	Formal bound	Stated role
"Fair Personalization" (Celis et al., 2017) and "An Algorithmic Framework to Control Bias in Bandit-based Personalization" (Celis et al., 2018)	$\ell_i \le \sum_{a\in G_i} p_a^t(s) \le u_i$	controls how much personalization is allowed on group $i$
"Disincentivizing Polarization in Social Networks" (Borgs et al., 2023)	$$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$	$\gamma$ encodes a hard cap on the level of personalization
"Personalized Reinforcement Learning with a Budget of Policies" (Ivanov et al., 2024)	deploy only $k$ policies, with $k<n$	policy budget
"When Machine Learning Gets Personal: Understanding Fairness of Personalized Models" (2502.02786)	$d=2^k$ and $k_{\max}$	bounds the number of personal attributes that can be used to reliably validate benefits of personalization
"Personalisation within bounds" (Kirk et al., 2023)	Tier 1, Tier 2, Tier 3 constraint sets	policy-specified restrictions and requirements
"Personalization as a Game" (Mishra, 8 Apr 2026)	$I(\Theta;A)\le I^*$ or $\lambda_I\cdot I(\Theta;A)$	privacy-personalization tradeoff
"LLM Agents Enable User-Governed Personalization Beyond Platform Boundaries" (Lin et al., 10 May 2026)	$i$0 may not condition on any dataset $i$1	bounded scope

In these formulations, the personalized system is not defined only by a user-conditioned predictor or policy. It is defined jointly by an objective and a restriction on admissible personalization. This suggests that bounded personalization is less a single fairness metric than a family of constrained learning and decision problems.

A second recurring feature is that the bound is operational rather than merely descriptive. In the bandit literature it appears as a polytope or a $i$2-constraint; in represented MDPs it appears as an upper bound on the number of policies; in personalized supervised learning it appears as a limit on the number of personal attributes that can be audited reliably; in LLM work it appears as policy tiers, discrete reasoning modes, privacy caps, or local-only data processing. The significance of the framework lies in making these restrictions first-class objects of optimization rather than post hoc evaluation criteria.

2. Fairness-constrained bandits and the original bounded-personalization formulation

The foundational bandit formulation models personalization as a contextual bandit. At each round $i$3, a user arrives with type $i$4, there are $i$5 items $i$6, and after choosing arm $i$7 one receives a stochastic reward $i$8. The unconstrained objective is to learn a policy $i$9 maximizing $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$0. Bounded personalization replaces this with a randomized policy $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$1 satisfying a linear constraint set

$$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$2

where the items are partitioned or grouped into content-groups $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$3. The practitioner-supplied bounds $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$4 control how much personalization is allowed on group $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$5; smaller intervals $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$6 force more uniform treatment, while larger intervals allow more extreme personalization. Under the requirement

$$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$7

the worst-case disparity in the total mass placed on any group $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$8 between any two user types is at most $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$9, which leads to the group-fairness metric $\gamma$0 defined from $\gamma$1 in eqs. (1)–(2) (Celis et al., 2017).

Algorithmically, the original proposal uses optimism over the feasible polytope: initialize mean estimates, compute upper-confidence rewards, solve a linear program over $\gamma$2, sample an arm from the resulting distribution, and update the estimates. In the single-context case, the expected fair regret is

$\gamma$3

where $\gamma$4 is the vertex gap of $\gamma$5; if $\gamma$6, the regret grows only poly-logarithmically in $\gamma$7, and in the multi-context case the bound scales linearly in $\gamma$8 (Celis et al., 2017).

The later full version sharpens the algorithmic picture with two concrete methods. L$\gamma$9-OFUL adapts OFUL to an L$k$0-confidence set so that the inner maximization over $k$1 remains a small LP; Constrained-$k$2-Greedy mixes exploitation on the current empirical best $k$3 with forced exploration from a fixed interior point $k$4. The corresponding guarantees are

$k$5

with probability at least $k$6 for L$k$7-OFUL, and

$k$8

for Constrained-$k$9-Greedy when $k<n$0. Empirically, on the YOW news dataset, enforcing a risk-difference guarantee by setting $k<n$1 yields revenue loss $k<n$2 for the $k<n$3-rule ($k<n$4), while Fair-EPS runs in $k<n$5 versus Fair-OFUL’s $k<n$6 for $k<n$7 on the same machine (Celis et al., 2018).

These bandit formulations established the canonical bounded-personalization pattern: optimize reward, but only over a restricted family of recommendation distributions. Their importance is that the restriction is enforced at every round, not only in expectation over a population.

3. Cross-user homogenization caps and anti-polarization constraints

A distinct line of work studies bounded personalization in multi-user social networks. Here the platform interacts with $k<n$8 users over $k<n$9 timesteps, choosing content for each user from $d=2^k$0 categories. To avoid filter bubbles while still allowing personalization, the platform imposes the $d=2^k$1-constraint

$d=2^k$2

for every round $d=2^k$3, every user $d=2^k$4, and every arm $d=2^k$5. Full personalization corresponds to $d=2^k$6 and complete homogenization corresponds to $d=2^k$7; hence, $d=2^k$8 encodes a hard cap on the level of personalization (Borgs et al., 2023).

The paper first analyzes a naive formalization of the intuition that if some users are shown some category of content, then all users should see at least a small amount of that content. It shows that this naive formalization has unintended consequences: it leads to “tyranny of the majority” with the burden of diversification borne disproportionately by those with minority interests. The adopted $d=2^k$9-constraint distributes this burden more equitably. Under the hard-constraint formulation, the platform competes with the best fixed distributions $k_{\max}$0 satisfying the same constraint. For $k_{\max}$1, the multi-agent UCB algorithm solves at each round a linear program with objective $k_{\max}$2 and achieves

$k_{\max}$3

while for $k_{\max}$4 robust-UCB achieves

$k_{\max}$5

The lower bounds are nearly matching: for $k_{\max}$6 and $k_{\max}$7, any algorithm must suffer $k_{\max}$8, and for all $k_{\max}$9, all $I(\Theta;A)\le I^*$0, $I(\Theta;A)\le I^*$1 (Borgs et al., 2023).

The framework also analyzes penalty-augmented variants in which the platform can exceed the cap but pays a penalty proportional to constraint violation. Penalty-UCB achieves $I(\Theta;A)\le I^*$2 regret to the best fixed penalized policy, and under taxation on empirical frequencies it achieves

$I(\Theta;A)\le I^*$3

On MovieLens with $I(\Theta;A)\le I^*$4 users and $I(\Theta;A)\le I^*$5 genres, the empirical picture is nuanced: for polarized subgroups such as romance versus thriller, homogeneity sets in only near $I(\Theta;A)\le I^*$6, whereas for similar subgroups such as thriller versus horror, convergence occurs much earlier near $I(\Theta;A)\le I^*$7. Utility loss is minor even for moderate $I(\Theta;A)\le I^*$8, with only a few percent drop in average reward (Borgs et al., 2023).

This work is important because it separates two ideas that are often conflated. Diversification is not identical to fairness, and a poorly designed diversification rule can itself be inequitable. The bounded parameter $I(\Theta;A)\le I^*$9 therefore functions as both a technical constraint and a normative control knob.

4. Policy budgets and continuously adaptive personalization

Bounded personalization also appears as a hard limit on the number of deployable policies. In represented MDPs,

$\lambda_I\cdot I(\Theta;A)$0

there are $\lambda_I\cdot I(\Theta;A)$1 agents, each with its own reward function $\lambda_I\cdot I(\Theta;A)$2, but only $\lambda_I\cdot I(\Theta;A)$3 policies may be deployed, with $\lambda_I\cdot I(\Theta;A)$4. Each agent $\lambda_I\cdot I(\Theta;A)$5 is assigned to a representative via $\lambda_I\cdot I(\Theta;A)$6, and the objective is to jointly choose $\lambda_I\cdot I(\Theta;A)$7 and $\lambda_I\cdot I(\Theta;A)$8 to maximize utilitarian social welfare:

$\lambda_I\cdot I(\Theta;A)$9

The extreme cases are explicit: $i$00 recovers a single “universal” policy for everyone, while $i$01 recovers unconstrained full personalization. The EM-like algorithm alternates PPO-based policy improvement on aggregated rewards

$i$02

with hard reassignment

$i$03

whereas the end-to-end variant parameterizes $i$04 by a softmax over logits $i$05 and updates assignments jointly with the actor parameters. Under standard assumptions on the RL sub-solver, the alternating E- and M-steps never decrease utilitarian social welfare and converge in finitely many steps to a local maximum; no formal global-optimality or approximation-ratio bounds are provided, and the problem is NP-hard in general. In Resource Gathering, EM/end2end reach $i$06 already at $i$07 and $i$08 at $i$09, while in MuJoCo both proposed methods uniformly outperform random and clustering baselines for all $i$10 (Ivanov et al., 2024).

A different extension treats bounded personalization as online adaptation under controlled feedback. In the continuous-feedback framework, at each round $i$11 a user arrives in context $i$12, the system samples an action

$i$13

observes scalar feedback $i$14, computes the policy-gradient estimate

$i$15

updates a momentum term $i$16, uses an adaptive learning rate

$i$17

and updates

$i$18

Explicit feedback is solicited only when model uncertainty exceeds $i$19, enough steps have passed since the last request, and user engagement is above $i$20. Under standard assumptions, the regret is

$i$21

and after a change point $i$22 at which user preferences become stationary, the iterates converge at rate

$i$23

Empirically, dynamic personalization improves user satisfaction by $i$24–$i$25 compared to static methods, while selective feedback prioritization can cut the full-update fraction by $i$26–$i$27 and latency per update remains under $i$28 in the recommendation domain and under $i$29 for the virtual assistant (He, 14 Jan 2026).

These two lines suggest that bounded personalization can be imposed either on the deployed policy set itself or on the rate and circumstances of adaptation.

5. Auditing subgroup benefit, fairness, and explanation quality

In personalized supervised learning, bounded personalization is not only about the model class but also about what can be validated reliably. The framework compares a generic model $i$30 with a personalized model $i$31, where $i$32 is a vector of $i$33 binary personal attributes. It defines prediction cost and explanation cost via deletion-based faithfulness measures, with sufficiency

$i$34

or $i$35, and comprehensiveness

$i$36

or the corresponding probability form. The population and group benefits of personalization are

$i$37

with analogous BoP-X quantities for explanation costs. The minimal-group benefit

$i$38

captures worst-case subgroup gain and is negative if any group is harmed (2502.02786).

The key theoretical result is a minimax lower bound on the error probability for testing $i$39 versus $i$40 from a finite audit sample. When $i$41, the number of subgroups grows exponentially in the number of personal attributes, while subgroup sample counts shrink. Under categorical, Gaussian, and Laplace models for the per-individual BoP random variable, closed forms follow. Imposing $i$42 and approximating $i$43 yields

$i$44

and

$i$45

Numerically, even if $i$46 and $i$47, one finds $i$48 for classification but $i$49 (Gaussian) or $i$50 (Laplace) for regression. The paper therefore concludes that regression models can potentially utilize more personal attributes than classification models if BoP variability is low (2502.02786).

The framework also separates predictive benefit from explanatory benefit. Theorem 3.1 states that there exist distributions where two Bayes-optimal classifiers have identical $i$51–$i$52 error, so BoP-P$i$53, yet the personalized model yields strictly better sufficiency and comprehensiveness. Theorem 3.2 states that under a linear additive model, BoP-X$i$54 implies BoP-P$i$55. On MIMIC-III, the empirical picture is mixed: in regression, personalization improves minimal BoP-P$i$56 and BoP-X$i$57 but BoP-X$i$58 for some subgroups; in classification, overall BoP-P$i$59 yet minimal BoP-P$i$60, and BoP-X$i$61 for two subgroups (2502.02786).

This is a direct rebuttal to the common assumption that average accuracy gain suffices to justify personalization. In this framework, bounded personalization includes a statistical limit on what claims about subgroup benefit can be supported at all.

6. LLM alignment, adaptive reasoning, and privacy-constrained personalization

In the LLM literature, bounded personalization is often framed as alignment within policy or architectural limits. One proposal defines personalized alignment by fine-tuning a base model $i$62 to user-specific parameters $i$63 using user feedback data $i$64:

$i$65

while the bounds of personalization are the policy-specified restrictions and requirements imposed at three tiers: Tier 1 immutable restrictions set at the national or supra-national level, Tier 2 optional restrictions and requirements set by the application provider, and Tier 3 tailored requirements specified by the end-user. Formally, personalization is a constrained optimization problem over nested sets $i$66, and the output space must exclude proscribed behaviors $i$67 while satisfying required properties $i$68. The same work provides a risk taxonomy with individual-level benefits such as Efficiency, Utility, Autonomy, and Empathy/Companionship; individual-level risks such as Effort, Addiction/Over-reliance, Homogenization & Bias Reinforcement, Essentialism & Profiling, Anthropomorphism, and Privacy; and societal-level benefits and risks including Inclusion & Accessibility, Diversity & Representation, Democratization & Participation, Access Disparities, Polarization, Malicious Use, Labor Displacement, and Environmental Harms (Kirk et al., 2023).

A more model-internal solution is PersonaDual, which supports two reasoning modes for a query $i$69 and persona $i$70: general-purpose mode $i$71 and personalized mode $i$72. Mode selection is governed by

$i$73

and generation proceeds with a learned control prefix:

$i$74

After supervised fine-tuning on mixed-mode data, DualGRPO updates the selector and prefix embeddings using rewards based on objective accuracy in general mode and preference match in personalized mode. The resulting system is reported as near interference-free: under unaligned personas, objective average accuracy is $i$75, only $i$76 points below the no-persona upper bound $i$77; under aligned personas, objective average is $i$78, a $i$79 improvement over $i$80; and on personalization tasks PersonaDual achieves $i$81 accuracy, the best among the listed baselines. Ablations show that removing the Dual-mode advantage decomposition drops objective/aligned performance by $i$82 points and personalization by $i$83 points (Liu et al., 13 Jan 2026).

Privacy-constrained personalization appears explicitly in EGPF, which models the mapping from hidden physician type $i$84 to engagement action $i$85 as a noisy communication channel. With distortion

$i$86

the classical rate-distortion function is

$i$87

or equivalently

$i$88

The Rate-Distortion Equilibrium criterion selects an equilibrium $i$89 such that further improving relevance would violate a hard privacy budget. Operationally, the framework enforces $i$90 or adds a soft penalty $i$91, tracks $i$92 in the loop, and clips or regularizes the LLM prompt so that the effective channel capacity per interaction never exceeds the chosen RDE point. The same framework gives a Bayesian-game formulation of physician engagement, proves belief convergence at

$i$93

and establishes regret

$i$94

In experiments on SynthRx and HCPilot, EGPF-Full improves AUC from $i$95 and $i$96, and content relevance from $i$97 to $i$98 (Mishra, 8 Apr 2026).

These LLM-oriented frameworks differ substantially in mechanism, but they converge on the same principle: user-specific adaptation is permitted only within explicit bounds on behavior, interference, or information flow.

7. User-governed and anti-over-personalization architectures

A further shift relocates the locus of control from the platform to the user. In user-governed personalization, the agent implements

$i$99

where $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$00 is the user’s collection of cross-platform data exports. The system is bounded by three families of constraints: all raw $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$01 remains on the user’s own device and the agent operates on de-identified data $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$02; legal rules such as GDPR Article 20, DMA Article 5(2), and CPRA cross-context opt-out imply that $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$03 is user export only, with no automated server-side data pooling; and the personalization function may not condition on any external dataset, so $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$04 may not use $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$05. The proposed architecture is ingestion and de-identification, a RAG index over $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$06, LLM reasoning with user goals plus retrieved memory, and tool invocation or action execution. In proof-of-concept studies with $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$07 participants, Amazon future-purchase prediction improves from Hit@5 $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$08 to $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$09, NDCG@5 $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$10 to $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$11, and Recall@5 $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$12 to $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$13, all with $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$14; in YouTube recommendation, overall “would you watch this?” rises from $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$15 to $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$16, with exploration improving from $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$17 to $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$18 (Lin et al., 10 May 2026).

Anti-over-personalization can also be imposed by symbolic adaptation of user-side knowledge structures. In the PKG framework, each user is represented by a Personalized Knowledge Graph

$$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$19

with user-specific edge weights $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$20. Over-personalization is detected through feature-pair co-occurrence patterns. For a requested feature $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$21 and a secondary attribute $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$22, the bias score is

$$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$23

with $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$24. If $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$25, the pair is treated as a Personalized Information Environment. The framework then applies one of three symbolic operators to a fraction $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$26 of PIE-aligned triples: soft reweighting, hard inversion, or targeted triple removal. Adaptation strength is tuned online to minimize residual bias

$$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$27

subject to a relevance constraint

$$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$28

On a recipe recommendation benchmark, soft adaptation with personalized tuning achieves the highest Out-PIE rate, $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$29, compared with $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$30 for soft global tuning and $$p_{i,a}(t) \ge \gamma \cdot \frac{1}{n}\sum_{j=1}^n p_{j,a}(t)$$31 for naive prompt-based steering, while also reducing invalid responses relative to naive prompting (Spadea et al., 8 Sep 2025).

These user-side frameworks sharpen an important distinction. Cross-platform scope or diversity-oriented adaptation does not remove the need for bounds; it relocates them. In the user-governed setting, the hard boundary is local, consented, de-identified data only. In the PKG setting, the hard boundary is relevance-preserving suppression of co-occurrence patterns that reinforce filter bubbles. Together they suggest that bounded personalization is compatible with stronger user control, but not with unconstrained inference over arbitrary personal data.