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An Improved Model-free Decision-estimation Coefficient with Applications in Adversarial MDPs

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 7.5Download Report PDF
decision makingreinforcement learningonline learning
Abstract:

We study decision making with structured observation (DMSO). The complexity for DMSO has been characterized by a series of work [ FKQR21 , CMB22 , FGH23 ]. Still, there is a gap between known regret upper and lower bounds: current upper bounds incur a model estimation error that scales with the size of the model class. The work of [FGQ+23 ] made an initial attempt to reduce the estimation error to only scale with the size of the value function set, resulting in the complexity called optimistic decision-estimation coefficient (optimistic DEC). Yet, their approach relies on the optimism principle to drive exploration, which deviates from the general idea of DEC that drives exploration only through information gain.

In this work, we introduce an improved model-free DEC, called Dig-DEC, that removes the optimism mechanism in [FGQ+23 ], making it more aligned with existing model-based DEC. Dig-DEC is always upper bounded by optimistic DEC, and could be significantly smaller in special cases. Importantly, the removal of optimism allows it to seamlessly handle adversarial environments, while it was unclear how to achieve it within the optimistic DEC framework. By applying Dig-DEC to hybrid MDPs where the transition is stochastic but the reward is adversarial, we provide the first model-free regret bounds in hybrid MDPs with bandit feedback in multiple settings: bilinear classes, Bellman-complete MDPs with bounded Bellman-eluder dimension or coverability, resolving the main open problem left by [LWZ25].

We also improve online function-estimation procedure used in model-free learning: For average estimation error minimization, we improve the estimator to achieve better concentration. This improves the T34T^{\frac{3}{4}} and T56T^{\frac{5}{6}} regret of [FGQ+23 ] to T23T^{\frac{2}{3}}and T79T^{\frac{7}{9}} in the cases with on-policy and off-policy exploration. For squared estimation error minimization in Bellman-complete MDPs, we redesign the two-timescale procedure in [ AZ22 , FGQ+23], achieving T\sqrt{T} regret that improves over the T23T^{\frac{2}{3}} regret by [ FGQ+23 ]. This is the first time the performance of a DEC-based approach for Bellman-complete MDPs matches that of optimism-based approaches [JLM21, XFB+23].

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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 Dig-DEC, a model-free decision-estimation coefficient that removes the optimism mechanism from prior work while maintaining alignment with model-based DEC frameworks. It sits within the 'Structured Exploration and Decision Estimation' leaf of the taxonomy, which contains only two papers total. This is a notably sparse research direction compared to more crowded areas like hierarchical policy learning or representation learning, suggesting the paper addresses a relatively specialized problem within the broader field of decision-making with structured observations.

The taxonomy reveals that neighboring research directions emphasize different structural aspects: hierarchical methods focus on temporal abstraction, representation learning targets state encoding, and partial observability work addresses belief state inference. Dig-DEC connects to these areas by providing a complexity measure that can apply across diverse structured environments, but diverges by focusing specifically on information-driven exploration without optimism. The scope note for this leaf emphasizes 'decision-estimation coefficients or information-theoretic principles,' distinguishing it from unstructured exploration methods found elsewhere in the taxonomy.

Among the three contributions analyzed, the literature search examined seventeen candidates total. The first contribution (Dig-DEC framework) examined two candidates with no refutations found. The second contribution (hybrid MDP regret bounds) examined six candidates and found one refutable match, suggesting some prior work exists in this specific setting. The third contribution (online function-estimation procedures) examined nine candidates with no refutations, indicating relatively novel technical machinery. The limited search scope means these findings reflect top-K semantic matches rather than exhaustive coverage.

Based on the analysis of seventeen candidates, the work appears to occupy a sparsely populated research niche with moderate novelty across its contributions. The removal of optimism from decision-estimation frameworks represents a conceptual shift, though the hybrid MDP results show some overlap with existing literature. The analysis does not cover the full breadth of reinforcement learning theory, so additional related work may exist outside the examined candidate set.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
17
Contribution Candidate Papers Compared
1
Refutable Paper

Research Landscape Overview

Core task: decision making with structured observation in reinforcement learning. The field addresses how agents can exploit structure in their observations—whether hierarchical, compositional, or relational—to improve learning efficiency and generalization. The taxonomy reflects a diverse landscape organized around eight main branches. Hierarchical Reinforcement Learning Approaches (e.g., Hierarchical RL Survey[7], Hierarchical Critics[2]) focus on temporal abstraction and option discovery to decompose complex tasks. Representation Learning for Structured State Spaces emphasizes learning compact or disentangled encodings of high-dimensional observations, often leveraging entity-based or graph-based representations (Entity Based RL[5], Structured State Space[1]). Structured Observation and Partial Observability tackles settings where agents must infer hidden state from incomplete information (Information Structure POMDP[14], Structured World Belief[16]). Multi-Agent and Cooperative Reinforcement Learning examines coordination and communication in multi-agent systems, while Compositional and Structured Task Learning explores modular skill composition (Blocks Assemble[6], Composable Deep RL[40]). Sample-Efficient and Representation-Driven RL targets data efficiency through better state abstractions, and Domain-Specific Applications with Structured Control applies these ideas to robotics, energy systems, and other real-world domains. Within this landscape, a particularly active line of work centers on structured exploration and decision estimation, where agents must balance exploration with exploiting known structure to guide policy search. Decision Estimation Coefficient[0] sits squarely in this branch, proposing a novel complexity measure for decision-making that accounts for structured observations and sample efficiency. This contrasts with nearby efforts such as Exogenous Structure Sampling[38], which focuses on leveraging exogenous variables to improve sample complexity, and Anticipation Hierarchy[3], which uses hierarchical anticipation to guide exploration in temporally extended tasks. While hierarchical methods like Anticipation Hierarchy[3] emphasize temporal decomposition, Decision Estimation Coefficient[0] offers a more general framework for quantifying decision complexity across diverse structured environments. The interplay between exploration strategies, representation quality, and sample efficiency remains a central open question, with recent works exploring how to tightly integrate structural priors into both the learning objective and the exploration mechanism.

Claimed Contributions

Dig-DEC: a model-free decision-estimation coefficient removing optimism

The authors propose Dig-DEC, a new complexity measure for decision making with structured observations that eliminates the optimism principle used in prior work and instead relies solely on information gain for exploration. This measure is always no larger than optimistic DEC and can be significantly smaller in special cases.

2 retrieved papers
First model-free regret bounds for hybrid MDPs with bandit feedback

The authors establish the first sublinear regret bounds for model-free learning in hybrid MDPs (stochastic transitions with adversarial rewards) under bandit feedback, addressing an open problem from prior work that only handled full-information feedback.

6 retrieved papers
Can Refute
Improved online function-estimation procedures with sharper regret bounds

The authors develop refined online function estimation procedures that achieve tighter concentration bounds. For average estimation error, they improve regret from T^(3/4) to T^(2/3) in on-policy settings and from T^(5/6) to T^(8/9) in off-policy settings. For squared error in Bellman-complete MDPs, they redesign the two-timescale procedure to improve regret from T^(2/3) to sqrt(T).

9 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Dig-DEC: a model-free decision-estimation coefficient removing optimism

The authors propose Dig-DEC, a new complexity measure for decision making with structured observations that eliminates the optimism principle used in prior work and instead relies solely on information gain for exploration. This measure is always no larger than optimistic DEC and can be significantly smaller in special cases.

Contribution

First model-free regret bounds for hybrid MDPs with bandit feedback

The authors establish the first sublinear regret bounds for model-free learning in hybrid MDPs (stochastic transitions with adversarial rewards) under bandit feedback, addressing an open problem from prior work that only handled full-information feedback.

Contribution

Improved online function-estimation procedures with sharper regret bounds

The authors develop refined online function estimation procedures that achieve tighter concentration bounds. For average estimation error, they improve regret from T^(3/4) to T^(2/3) in on-policy settings and from T^(5/6) to T^(8/9) in off-policy settings. For squared error in Bellman-complete MDPs, they redesign the two-timescale procedure to improve regret from T^(2/3) to sqrt(T).

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