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Primal-Dual Policy Optimization for Adversarial Linear CMDPs

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Safe Reinforcement LearingAdversarial Linear Constrained MDPPolicy Optimization
Abstract:

Existing work on linear constrained Markov decision processes (CMDPs) has primarily focused on stochastic settings, where the losses and costs are either fixed or drawn from fixed distributions. However, such formulations are inherently vulnerable to adversarially changing environments. To overcome this limitation, we propose a primal-dual policy optimization algorithm for online finite-horizon {adversarial} linear CMDPs, where the losses are adversarially chosen under full-information feedback and the costs are stochastic under bandit feedback. Our algorithm is the \emph{first} to achieve sublinear regret and constraint violation bounds in this setting, both bounded by O~(K3/4)\widetilde{\mathcal{O}}(K^{3/4}), where KK denotes the number of episodes. The algorithm introduces and runs with a new class of policies, which we call weighted LogSumExp softmax policies, designed to adapt to adversarially chosen loss functions. Our main result stems from the following key contributions: (i) a new covering number argument for the weighted LogSumExp softmax policies, and (ii) two novel algorithmic components---periodic policy mixing and a regularized dual update---which allow us to effectively control both the covering number and the dual variable. We also report numerical results that validate our theoretical findings on the performance of the algorithm.

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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 proposes a primal-dual policy optimization algorithm for online finite-horizon adversarial linear CMDPs, achieving sublinear regret and constraint violation bounds of Õ(K^{3/4}). It resides in the 'Policy Optimization Methods' leaf under 'Full-Information Feedback', which contains only two papers total. This indicates a relatively sparse research direction within the broader taxonomy of 33 papers across the field, suggesting that policy optimization approaches for adversarial linear CMDPs with full-information feedback remain underexplored compared to bandit feedback or value-based methods.

The taxonomy tree shows neighboring leaves include 'Value-Based and Optimization Methods' (3 papers) under the same full-information branch, and 'Linear Function Approximation with Bandit Feedback' (6 papers total across two sub-leaves). The scope note for the paper's leaf explicitly excludes value-based or linear programming approaches, positioning this work as complementary to methods like mirror descent or value iteration. Nearby branches address adversarial constraints, hybrid stochastic-adversarial settings, and robustness under model uncertainty, indicating that the paper's focus on adversarial losses with stochastic constraints represents one of several active research threads in constrained adversarial RL.

Among the three identified contributions, the primal-dual algorithm examined 7 candidates with 0 refutations, the covering number argument examined 0 candidates, and the periodic mixing/dual update components examined 1 candidate with 0 refutations. Based on this limited search scope of 8 total candidates, none of the contributions appear clearly refuted by prior work. The algorithmic components (periodic policy mixing, regularized dual update) and the weighted LogSumExp softmax policy class show no overlapping prior work within the examined set, though the small candidate pool means the search does not comprehensively cover all related literature.

Given the sparse taxonomy leaf (2 papers) and the limited search scope (8 candidates examined), the work appears to occupy a relatively novel position within policy optimization for adversarial linear CMDPs. However, this assessment is constrained by the top-K semantic search methodology and does not reflect an exhaustive literature review. The absence of refutations among examined candidates suggests potential novelty, but broader coverage of the 33-paper taxonomy and adjacent research areas would be needed for a definitive evaluation.

Taxonomy

Core-task Taxonomy Papers
33
3
Claimed Contributions
8
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: online learning in adversarial linear constrained Markov decision processes. This field addresses sequential decision-making under adversarial losses while respecting constraints, typically formulated in linear function approximation settings. The taxonomy reveals several major branches: some works focus on adversarial losses paired with stochastic constraints, others tackle fully adversarial constraints, and a third group explores hybrid stochastic-adversarial settings. Additional branches address robustness and model uncertainty, dynamic regret under non-stationarity, strong regret and violation metrics, and specialized extensions such as continuous-time formulations or privacy considerations. Within the adversarial-loss-with-stochastic-constraints branch, methods diverge based on feedback models (full-information versus bandit) and algorithmic paradigms, including policy optimization approaches like Near-Optimal Policy Mixture[28] and primal-dual schemes. Recent activity has concentrated on refining regret and constraint-violation guarantees across these settings. For instance, works on dynamic regret such as Dynamic Regret Mixture[6] and Near-Optimal Dynamic Regret[20] study non-stationary environments, while strong regret analyses like Optimal Strong Regret[24] tighten per-episode performance bounds. Primal-Dual Adversarial CMDPs[0] sits within the policy optimization cluster under full-information feedback, emphasizing primal-dual methods to balance adversarial objectives and stochastic constraints. Compared to Near-Optimal Policy Mixture[28], which also operates in a similar feedback regime, Primal-Dual Adversarial CMDPs[0] leverages dual variable updates to handle constraint satisfaction more explicitly. Meanwhile, neighboring efforts like Logarithmic Regret Adversarial[1] and Robust Lagrangian Policy[2] explore alternative algorithmic structures or robustness considerations, highlighting ongoing debates about the optimal interplay between regret minimization, constraint enforcement, and computational efficiency in adversarial constrained RL.

Claimed Contributions

Primal-dual policy optimization algorithm for adversarial linear CMDPs

The authors propose the first algorithm for finite-horizon adversarial linear CMDPs that achieves sublinear regret and constraint violation bounds. The algorithm introduces weighted LogSumExp softmax policies designed to adapt to adversarially chosen loss functions.

7 retrieved papers
Covering number argument for weighted LogSumExp softmax policies

The authors establish a novel covering number analysis for a new class of policies induced by primal-dual policy optimization with policy mixing. The analysis shows that the covering number is bounded by eO(n²d²), where n is the maximum number of mixing steps and d is the feature dimension.

0 retrieved papers
Periodic policy mixing and regularized dual update components

The authors introduce two algorithmic innovations: periodic policy mixing that applies mixing once every specified period rather than every episode, and a regularized dual update with additional regularization terms. These components jointly enable effective control of both the covering number and the dual variable to achieve sublinear bounds.

1 retrieved paper

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Primal-dual policy optimization algorithm for adversarial linear CMDPs

The authors propose the first algorithm for finite-horizon adversarial linear CMDPs that achieves sublinear regret and constraint violation bounds. The algorithm introduces weighted LogSumExp softmax policies designed to adapt to adversarially chosen loss functions.

Contribution

Covering number argument for weighted LogSumExp softmax policies

The authors establish a novel covering number analysis for a new class of policies induced by primal-dual policy optimization with policy mixing. The analysis shows that the covering number is bounded by eO(n²d²), where n is the maximum number of mixing steps and d is the feature dimension.

Contribution

Periodic policy mixing and regularized dual update components

The authors introduce two algorithmic innovations: periodic policy mixing that applies mixing once every specified period rather than every episode, and a regularized dual update with additional regularization terms. These components jointly enable effective control of both the covering number and the dual variable to achieve sublinear bounds.

Table of Contents

Primal-Dual Policy Optimization for Adversarial Linear CMDPs | Novelty Validation