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Target Drift in Multi-Constraint Lagrangian RL: Theory and Practice

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Energy System OperationSafeRL
Abstract:

Lagrangian-based methods are one of the dominant approaches for safe reinforcement learning (RL) in constrained Markov decision processes, commonly used across domains with multiple constraints. While some implementations combine all constraints into a mixed penalty term and others use one estimator per constraint, the fundamental question of which design is theoretically sound has received little scrutiny. We provide the first theoretical analysis showing that the mixed-critic architecture induces a persistent bias due to target drift from evolving Lagrange multipliers. In contrast, dedicated-critic design—separate critics for reward and each constraint—avoids this issue. We also validate our findings in a simulated but realistic energy system with multiple physical constraints, where the dedicated-critic method achieves stable learning and consistent constraint satisfaction, while the mixed-critic method fails. Our results offer a principled argument for preferring dedicated-critic architectures in multi-constraint safe RL problems.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper contributes a theoretical analysis distinguishing mixed-critic from dedicated-critic architectures in multi-constraint Lagrangian RL, arguing that mixed critics induce persistent bias through target drift from evolving multipliers. It resides in the 'Multi-Constraint Architecture and Target Drift' leaf, which contains only four papers total, making this a relatively sparse research direction within the broader taxonomy of 50 papers. This leaf focuses specifically on architectural choices for handling multiple constraints simultaneously, excluding single-constraint methods and gradient manipulation techniques that belong elsewhere in the taxonomy.

The taxonomy reveals that neighboring leaves address related but distinct concerns: 'Gradient Manipulation and Multi-Objective Optimization' (2 papers) explores constraint aggregation and gradient shaping, while 'Multiplier Update and Control-Theoretic Enhancements' (4 papers) focuses on adaptive update mechanisms. The sibling papers in the same leaf examine target drift phenomena and architectural trade-offs, but the taxonomy structure suggests limited prior work explicitly comparing mixed versus dedicated critic designs. The broader 'Lagrangian Method Design and Optimization' branch contains 15 papers across four leaves, indicating moderate activity in foundational method development compared to application-focused branches.

Among 16 candidates examined across three contributions, no clearly refuting prior work was identified. The theoretical analysis of mixed-critic bias examined zero candidates, suggesting this specific framing may be novel or that semantic search did not surface relevant comparisons. The dedicated-critic design contribution examined six candidates with none refuting, while empirical validation examined ten candidates with none refuting. This limited search scope—16 total candidates rather than hundreds—means the analysis captures top semantic matches and immediate citations but cannot claim exhaustive coverage of all potentially overlapping work in multi-constraint architectures or target drift phenomena.

Based on the limited search scope, the work appears to occupy a relatively underexplored niche within multi-constraint Lagrangian RL, specifically addressing architectural design choices that have received less systematic theoretical treatment than multiplier update mechanisms or gradient manipulation techniques. The absence of refuting candidates among 16 examined suggests potential novelty, though the small search scale and sparse taxonomy leaf (4 papers) leave open the possibility of relevant work outside the top semantic matches or in adjacent research communities not fully captured by this taxonomy.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
16
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: Lagrangian reinforcement learning with multiple constraints. The field addresses how agents can optimize rewards while satisfying several simultaneous safety or resource limits, typically by adjusting Lagrange multipliers during training. The taxonomy reveals a rich structure spanning methodological innovations in Lagrangian optimization (including multi-constraint architectures and convergence guarantees), diverse safety formulations (from hard constraints to distributional risk measures), and a wide array of application domains such as power systems, autonomous driving, and network resource management. Several branches focus on learning paradigms that improve data efficiency or handle offline settings, while others explore multi-agent coordination, constraint learning from demonstrations, and budgeted or risk-adaptive frameworks. Representative works like PID Lagrangian Safety[1] and Safe RLHF[2] illustrate how controller-inspired updates and human-feedback integration can stabilize constraint satisfaction, whereas studies such as Conservative Distributional Safety[3] and Constraints as Rewards[4] show alternative formulations that blend distributional robustness with reward shaping. A particularly active line of research examines architectural and algorithmic refinements for handling multiple constraints simultaneously, balancing the need for stable multiplier updates against the risk of objective drift or oscillation. Target Drift Lagrangian[0] sits squarely in this branch, proposing mechanisms to prevent the primary reward objective from being overshadowed when many constraints compete for attention. Nearby works like Gradient Shaping Multi Constraint[18] and Objective Suppression Safety[32] tackle related trade-offs by reshaping policy gradients or dynamically adjusting constraint priorities, highlighting ongoing debates about how to maintain reward progress without violating safety bounds. Meanwhile, methods such as State Augmented Constrained[13] and Conditionally Adaptive Lagrangian[20] explore state-dependent or adaptive multiplier schedules, offering complementary perspectives on when and how aggressively to enforce each constraint. Collectively, these efforts underscore a central tension: achieving fast, stable convergence in multi-constraint settings while preserving the agent's ability to optimize its core objective.

Claimed Contributions

Theoretical analysis of mixed-critic bias in multi-constraint Lagrangian RL

The authors formally prove that training a single mixed critic on aggregated constraint signals introduces structural bias in actor updates. This bias arises because the critic's target drifts as Lagrange multipliers evolve during training, violating the stationarity assumption required by temporal-difference learning and leading to persistent error in policy gradient estimation.

0 retrieved papers
Dedicated-critic design eliminates dual-induced drift

The authors prove that maintaining separate critics for reward and each individual constraint eliminates the dual-driven drift problem entirely. This design yields stationary targets that depend only on the policy, not on evolving multipliers, enabling stable policy gradient estimation in multi-constraint settings.

6 retrieved papers
Empirical validation in constrained bandit and power system environments

The authors validate their theoretical results through experiments in both a constrained bandit problem and a complex energy control task with multiple interacting constraints. The dedicated-critic approach demonstrates stable training, lower constraint violations, and better Pareto frontiers compared to the mixed-critic baseline.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Theoretical analysis of mixed-critic bias in multi-constraint Lagrangian RL

The authors formally prove that training a single mixed critic on aggregated constraint signals introduces structural bias in actor updates. This bias arises because the critic's target drifts as Lagrange multipliers evolve during training, violating the stationarity assumption required by temporal-difference learning and leading to persistent error in policy gradient estimation.

Contribution

Dedicated-critic design eliminates dual-induced drift

The authors prove that maintaining separate critics for reward and each individual constraint eliminates the dual-driven drift problem entirely. This design yields stationary targets that depend only on the policy, not on evolving multipliers, enabling stable policy gradient estimation in multi-constraint settings.

Contribution

Empirical validation in constrained bandit and power system environments

The authors validate their theoretical results through experiments in both a constrained bandit problem and a complex energy control task with multiple interacting constraints. The dedicated-critic approach demonstrates stable training, lower constraint violations, and better Pareto frontiers compared to the mixed-critic baseline.

Table of Contents

Target Drift in Multi-Constraint Lagrangian RL: Theory and Practice | Novelty Validation