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XQC: Well-conditioned Optimization Accelerates Deep Reinforcement Learning

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.5Download Report PDF
Reinforcement Learning
Abstract:

Sample efficiency is a central property of effective deep reinforcement learning algorithms. Recent work has improved this through added complexity, such as larger models, exotic network architectures, and more complex algorithms, which are typically motivated purely by empirical performance. We take a more principled approach by focusing on the optimization landscape of the critic network. Using the eigenspectrum and condition number of the critic’s Hessian, we systematically investigate the impact of common architectural design decisions on training dynamics. Our analysis reveals that a novel combination of batch normalization (BN), weight normalization (WN), and a distributional cross-entropy (CE) loss produces condition numbers orders of magnitude smaller than baselines. This combination also naturally bounds gradient norms, a property critical for maintaining a stable effective learning rate under non-stationary targets and bootstrapping. Based on these insights, we introduce XQC: a well-motivated, sample-efficient deep actor-critic algorithm built upon soft actor-critic that embodies these optimization-aware principles. We achieve state-of-the-art sample efficiency across 55 proprioception and 15 vision-based continuous control tasks, all while using significantly fewer parameters than competing methods.

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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.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper introduces XQC, a sample-efficient actor-critic algorithm that combines batch normalization, weight normalization, and distributional cross-entropy loss to improve critic conditioning. It resides in the 'Critic Architecture and Conditioning' leaf, which contains only three papers total, indicating a relatively sparse research direction within the broader taxonomy. This leaf focuses specifically on architectural innovations for critic stability, distinguishing it from adjacent leaves that address update mechanisms or multi-step learning. The small population suggests this particular angle—optimizing conditioning through architectural choices—remains underexplored compared to other critic optimization strategies.

The taxonomy reveals that critic optimization branches into four distinct leaves: architecture/conditioning, update mechanisms, multi-step learning, and generalization/robustness. XQC's focus on Hessian conditioning and normalization techniques positions it closest to architectural concerns, while neighboring leaves like 'Critic Update Mechanisms' (containing TD learning variants) and 'Multi-Step Value Learning' pursue complementary angles. The broader 'Representation Learning' branch (four leaves, multiple papers per leaf) represents a parallel research thrust emphasizing feature quality over critic conditioning. XQC's approach diverges by treating conditioning as a first-order concern rather than relying primarily on representation improvements or update rule modifications.

Among 21 candidates examined across three contributions, the XQC algorithm itself shows overlap with prior work: 10 candidates examined, 2 refutable. The Hessian eigenvalue analysis contribution appears more novel (1 candidate, 0 refutable), while the cross-entropy versus squared error analysis examined 10 candidates with none refutable. This suggests the algorithmic combination may have precedent in the limited search scope, but the specific conditioning analysis and loss comparison appear less directly addressed. The modest search scale (21 total candidates, not hundreds) means these findings reflect top semantic matches rather than exhaustive coverage, leaving room for additional related work outside this scope.

Given the sparse taxonomy leaf and limited search scope, the work appears to occupy a relatively underexplored niche within critic optimization. The conditioning-focused perspective distinguishes it from update-mechanism or representation-centric approaches, though the algorithmic contribution shows some overlap among examined candidates. The analysis contributions (Hessian eigenvalues, loss comparison) seem less directly refuted within this search scope, suggesting potential novelty in the diagnostic framework even if the final algorithm builds on established components.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
21
Contribution Candidate Papers Compared
2
Refutable Paper

Research Landscape Overview

Core task: improving sample efficiency in deep reinforcement learning through well-conditioned critic optimization. The field addresses the challenge of learning effective policies from limited environment interactions by refining how value functions are estimated and how representations are learned. The taxonomy reveals a rich structure spanning ten major branches. Critic Optimization and Value Function Learning focuses on architectural choices and conditioning strategies that stabilize temporal-difference updates, while Representation Learning for Sample Efficiency explores how to extract compact, task-relevant features from high-dimensional observations. Policy Learning and Actor-Critic Integration examines the interplay between policy updates and value estimation, and Exploration and Data Collection Strategies investigates how agents can gather informative experiences. Experience Replay and Memory Management considers how stored transitions can be reused effectively, and Transfer Learning and Knowledge Reuse looks at leveraging prior knowledge across tasks. Scaling and Computational Efficiency addresses resource constraints, Domain-Specific Applications and Adaptations tailors methods to particular problem settings, Specialized Techniques and Constraints handles safety and multi-objective scenarios, and Surveys, Frameworks, and Theoretical Foundations provides overarching perspectives. Several active lines of work highlight contrasting emphases and open questions. One thread investigates critic architecture and conditioning—how the structure and update rules of value networks influence learning stability and sample complexity. For instance, Shallow Critic Updates[3] and CTD4 Kalman Fusion[12] explore different mechanisms for controlling critic complexity and noise. Another thread examines representation quality, asking whether good features alone suffice for efficiency or whether joint optimization of critics and encoders is essential, as debated in works like Good Representation Sufficient[14] and Value-Consistent Representation[23]. XQC[0] sits squarely within the critic architecture and conditioning cluster, emphasizing well-conditioned optimization to reduce variance in value estimates. Compared to Shallow Critic Updates[3], which limits network depth to improve conditioning, XQC[0] appears to pursue complementary regularization strategies that directly shape the critic's Hessian or gradient landscape, aiming for smoother, more stable learning dynamics without sacrificing representational capacity.

Claimed Contributions

XQC algorithm for sample-efficient deep reinforcement learning

The authors propose XQC, a deep actor-critic algorithm that extends soft actor-critic by combining batch normalization, weight normalization, and a distributional cross-entropy loss to create a well-conditioned optimization landscape. This design achieves state-of-the-art sample efficiency across 70 continuous control tasks while using significantly fewer parameters than competing methods.

10 retrieved papers
Can Refute
Hessian eigenvalue analysis of deep RL critic optimization

The authors conduct a systematic eigenvalue analysis of the critic's Hessian to investigate how architectural components affect the optimization landscape. They demonstrate that distributional critics with cross-entropy loss produce condition numbers orders of magnitude smaller than mean squared error losses, providing a principled explanation for performance differences.

1 retrieved paper
Theoretical analysis of cross-entropy versus squared error loss conditioning

The authors provide formal analysis showing that cross-entropy loss has bounded gradients and upper-bounded condition numbers, while mean squared error loss has unbounded gradients and cannot upper-bound the condition number. This theoretical framework explains why cross-entropy loss creates better-conditioned optimization landscapes for deep reinforcement learning.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

XQC algorithm for sample-efficient deep reinforcement learning

The authors propose XQC, a deep actor-critic algorithm that extends soft actor-critic by combining batch normalization, weight normalization, and a distributional cross-entropy loss to create a well-conditioned optimization landscape. This design achieves state-of-the-art sample efficiency across 70 continuous control tasks while using significantly fewer parameters than competing methods.

Contribution

Hessian eigenvalue analysis of deep RL critic optimization

The authors conduct a systematic eigenvalue analysis of the critic's Hessian to investigate how architectural components affect the optimization landscape. They demonstrate that distributional critics with cross-entropy loss produce condition numbers orders of magnitude smaller than mean squared error losses, providing a principled explanation for performance differences.

Contribution

Theoretical analysis of cross-entropy versus squared error loss conditioning

The authors provide formal analysis showing that cross-entropy loss has bounded gradients and upper-bounded condition numbers, while mean squared error loss has unbounded gradients and cannot upper-bound the condition number. This theoretical framework explains why cross-entropy loss creates better-conditioned optimization landscapes for deep reinforcement learning.

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