Balanced Unlearning Strategies

• Balanced unlearning is an algorithmic framework that removes undesired data contributions while retaining key model utilities and privacy.
• It employs multi-objective optimization techniques—including gradient projection, bi-level optimization, and game-theoretic approaches—to balance forgetting and retention.
• Evaluation metrics such as forgetting rate, knowledge preservation, and compliance with privacy regulations validate its effectiveness in sensitive domains.

Balanced unlearning strategies are algorithmic frameworks designed to remove specific undesired knowledge or data contributions from a machine learning model while optimally preserving desired competencies, generalization, and privacy characteristics. These strategies address the inherent tension between effective removal (forgetting) and retention of utility (preserving information) in the context of regulation, privacy compliance, and ethical constraints in sensitive domains such as healthcare, natural language processing, and federated learning.

1. Core Principles and Problem Statement

Balanced unlearning formulates the unlearning process as a multi-objective optimization problem involving at least two competing objectives: minimizing the model's performance on the “forget set” (data, task, or knowledge to be erased) and maximizing or at least safeguarding performance on the “retain set” (data, knowledge, or tasks that must remain intact). The canonical formulation for parameter vector $\theta \in \mathbb{R}^d$ is: $$\theta' = \arg\min_\theta \big[ L_\text{retain}(\theta) - \lambda L_\text{forget}(\theta) + \gamma R(\theta) \big]$$ where $L_\text{retain}$ and $L_\text{forget}$ are empirical losses on the retain and forget sets, $\lambda$ is a trade-off coefficient, and $R(\theta)$ is a regularizer, often encoding privacy, fairness, or smoothness constraints. Variant formulations, such as bi-level optimization in BLUR (Reisizadeh et al., 9 Jun 2025), seek solutions for $$\min_{\theta_u \in \Theta} L_\text{retain}(\theta_u)$$ subject to $\Theta = \arg\min_\theta L_\text{forget}(\theta)$, establishing a strict prioritization for forgetting.

2. Representative Frameworks and Mechanisms

Several architectural motifs and algorithmic mechanisms have been established to achieve balanced unlearning:

• Hierarchical Dual-Strategy Unlearning (Zhang et al., 23 Nov 2025): Integrates geometric-constrained gradient projections (projecting forget gradients away from retain gradients, modulated by task-specific coefficients) and concept-aware token-level interventions (token-wise gradient intensity scaling based on concept hierarchy) within a unified multi-level medical knowledge hierarchy. This arrangement ensures effective erasure of surgical knowledge while tightly controlling retention of core clinical concepts.
• Dual-Space Smoothness (Yan et al., 27 Sep 2025): PRISM applies smoothness constraints both in hidden representation space (using adversarial probe-based regularization to resist jailbreak/recovery attacks) and parameter space (sharpness-aware minimization coupled with first-order projection/decoupling to mitigate relearning), thereby enlarging attack margins without catastrophic forgetting.
• Bi-Level Optimization (Reisizadeh et al., 9 Jun 2025): BLUR enforces lower-level optimality for forgetting and then finds, within that solution set, a parameter configuration with optimal utility for retention, using explicit orthogonalization between gradients to avoid destructive interference.
• Nash Bargaining and Game-Theoretic Formulation (Wu et al., 23 Nov 2024): MUNBa treats forgetting and retention as two cooperative players and uses a closed-form Nash bargaining solution to calculate a joint update direction maximizing the logarithmic product of both utilities, automatically balancing parameter movement so as to reach a Pareto-optimal solution.
• Adaptive Weighting and Meta-Learning: Approaches such as Ready2Unlearn (2505.10845) use meta-learning to endow models with preparedness for future unlearning and explicitly balance forgetting speed, retention, and resilience to knowledge recovery. Gradient harmonization strategies (Huang et al., 15 Jul 2024) project potentially conflicting meta-gradients to reduce destructive interference.
• Unlearning in Data-Scarce and Imbalanced Regimes: Frameworks like GENIU (Zhang et al., 12 Jun 2024) and UPCORE (Patil et al., 20 Feb 2025) address the challenge of unlearning without full data access or under class imbalance, using proxy sample generation and coreset selection (via outlier pruning in hidden space) to maintain a balanced trade-off in practical constraints.

3. Mathematical Techniques for Trade-off Management

Balanced unlearning strategies employ several mathematical techniques to maintain the trade-off:

• Gradient Projection/Orthogonalization: Project the gradient of the unlearning objective onto the orthogonal complement of the retain objective to suppress interference (e.g., OrthoGrad (Shamsian et al., 4 Mar 2025), geometric-constrained projections in (Zhang et al., 23 Nov 2025, Yan et al., 27 Sep 2025)).
• Adaptive Coefficients and Scheduling: Varying trade-off coefficients (e.g., $\lambda$ in (Zhang et al., 23 Nov 2025); dynamic adjustment in MCU (2505.10859)) based on real-time performance metrics (e.g., validation/retain accuracy) suppresses both under- and over-forgetting incidents.
• Game-Theoretic Closed-Form Solutions: Nash bargaining frameworks (Wu et al., 23 Nov 2024) offer a principled method to adaptively solve for optimal trade-off weights at every update without hand-tuning.
• Meta-Learning and Bi-Level Optimization: Inner-loop unlearning update simulations and outer-loop utility optimization (Ready2Unlearn, (2505.10845); BLUR, (Reisizadeh et al., 9 Jun 2025); LTU, (Huang et al., 15 Jul 2024)) support anticipation of future unlearning requests and structured trade-off across conflicting objectives.
• Masking and Saliency Modulation: Masking parameters important to retention, and focusing updates to those most relevant for unlearning, further reduce collateral degradation (2505.10859, Huang et al., 21 May 2025).

4. Evaluation Metrics and Empirical Trade-offs

Quantitative evaluation of balanced unlearning strategies consistently employs dual-metric or aggregate trade-off scores, including:

• Forgetting Rate (FR): Relative drop in accuracy or knowledge on the forget set.
• Knowledge Preservation Rate (KPR): Retained accuracy on the retain set post-unlearning.
• Task Aggregate / Harmonic Mean Metrics: Combined indices (e.g., HMTA in (Zhang et al., 23 Nov 2025), geometric mean in (Yan et al., 27 Sep 2025)) express the quality of trade-off between conflicting goals.
• Membership Inference Attack Resistance: Adversarial privacy guarantee (e.g., 1 - 2|AUC-0.5|).
• Area-Under-the-Curve (AUC) Utility-Forget Curves: As in UPCORE (Patil et al., 20 Feb 2025), AUC over utility-forgetting Pareto curves provides a global measure of the trade-off quality.
• Class-wise/Contextual Retention: Accuracy per class or concept level before and after unlearning (Zhang et al., 12 Jun 2024).

Empirical studies report that balanced strategies yield substantial improvements in utility preservation at negligible cost to forgetting quality. In (Zhang et al., 23 Nov 2025), the hierarchical framework achieved FR=82.7%, KPR=88.5%, and HMTA=0.847, surpassing gradient ascent and prior art such as AILS-NTUA. Ablations confirm a consistent ~3–4% improvement in HMTA from each structural addition (hierarchy, dual strategy, privacy).

5. Privacy, Auditability, and Compliance

Balanced unlearning frameworks in high-stakes domains implement explicit privacy and compliance safeguards:

• Differential Privacy (DP): Gaussian noise injection calibrated to (ε, δ)-DP, often with tunable σ, guarantees privacy during parameter updates (Zhang et al., 23 Nov 2025, Yan et al., 27 Sep 2025).
• Auditability: Hierarchical concept decomposition or explicit parameter/token logging allows for reversible mapping of specific knowledge to model components, supporting regulatory audits and traceable revocation (Zhang et al., 23 Nov 2025).
• Regulatory Compliance: Mechanisms satisfy legal requirements such as GDPR “right to be forgotten” and HIPAA, particularly by restricting unlearning interventions to domain-specific target levels (e.g., L4 in medicine), thereby limiting clinical risks.
• Federated Fairness: Federated frameworks introduce fairness metrics quantifying both efficiency (per-client cost) and performance (per-client utility drop), promoting equitable unlearning and preventing cascade effects or adversarial manipulation (Wen et al., 13 Aug 2025).

6. Limitations, Open Questions, and Future Directions

Despite advancements, balanced unlearning strategies face important remaining challenges:

• Non-Convexity and Convergence: Most mechanisms guarantee only local stationarity or Pareto equilibrium; global guarantees remain difficult in deep non-convex landscapes (Reisizadeh et al., 9 Jun 2025, Wu et al., 23 Nov 2024).
• Hyperparameter Sensitivity: Choice of trade-off coefficients, buffer sizes, or smoothing parameters can significantly impact outcome; adaptive or meta-optimized schedules are emerging to address this (2505.10859, Huang et al., 21 May 2025).
• Data-Free and Imbalanced Settings: Scenarios without full data access or with severe class imbalance require generative proxies (e.g., VAE) and explicitly balanced update schemes (Zhang et al., 12 Jun 2024).
• Scalability and Computational Cost: Some meta-learning or dual-space frameworks (e.g., PRISM, Ready2Unlearn) double per-iteration computational requirements. Approximations and scalable variants remain under active investigation.
• Robustness to Attacks: Recovery, jailbreak, and prompt-injection attacks necessitate resilience-focused design, with strong smoothness constraints or auxiliary probes augmenting baseline strategies (Yan et al., 27 Sep 2025).

Ongoing research continues to refine both the mathematical underpinnings and practical deployments of balanced unlearning, emphasizing scalable, compositional solutions that can flexibly adapt to new legal, ethical, and operational demands in dynamic, high-stakes environments.