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The Sample Complexity of Online Reinforcement Learning: A Multi-model Perspective

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.5Download Report PDF
control theoryreinforcement learning theorydynamical systemslearning theory
Abstract:

We study the sample complexity of online reinforcement learning in the general setting of nonlinear dynamical systems with continuous state and action spaces. Our analysis accommodates a large class of dynamical systems ranging from a finite set of nonlinear candidate models to models with bounded and Lipschitz continuous dynamics, to systems that are parametrized by a compact and real-valued set of parameters. In the most general setting, our algorithm achieves a policy regret of O(Nϵ2+ln(m(ϵ))/ϵ2)\mathcal{O}(N \epsilon^2 + \mathrm{ln}(m(\epsilon))/\epsilon^2), where NN is the time horizon, ϵ\epsilon is a user-specified discretization width, and m(ϵ)m(\epsilon) measures the complexity of the function class under consideration via its packing number. In the special case where the dynamics are parametrized by a compact and real-valued set of parameters (such as neural networks, transformers, etc.), we prove a policy regret of O(Np)\mathcal{O}(\sqrt{N p}), where pp denotes the number of parameters, recovering earlier sample-complexity results that were derived for linear time-invariant dynamical systems. While this article focuses on characterizing sample complexity, the proposed algorithms are likely to be useful in practice, due to their simplicity, their ability to incorporate prior knowledge, and their benign transient behaviors.

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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 develops online reinforcement learning algorithms with nonasymptotic policy-regret guarantees for nonlinear continuous-state-action systems, accommodating finite candidate model sets, Lipschitz-bounded dynamics, and compact parameter spaces. It resides in the 'General Nonlinear Dynamics and Multi-Model Settings' leaf, which contains four papers total—a moderately populated niche within the broader 'Theoretical Foundations and Sample Complexity Bounds' branch. This leaf explicitly focuses on broad nonlinear classes and multi-model scenarios, distinguishing it from specialized structural assumptions like Koopman operators or kernel embeddings found in sibling leaves.

The taxonomy reveals neighboring leaves addressing structured representations (Koopman/kernel methods, three papers), robustness under distributional shift (three papers), stability-constrained learning (three papers), and reward-free exploration (three papers). The paper's multi-model framing and general function-class treatment position it at the intersection of model-selection uncertainty and nonlinear complexity, diverging from operator-based linearization strategies and from purely adversarial robustness analyses. Its scope note explicitly excludes specialized structural assumptions, aligning with the leaf's mandate to handle parametric and function-approximation settings without restrictive linearity or embedding constraints.

Among 26 candidates examined across three contributions, none yielded clear refutations. The first contribution (suite of algorithms with regret guarantees) examined 10 candidates with zero refutable overlaps; the second (frequentist guarantees under persistence of excitation) examined 6 with zero refutations; the third (separation principle for model identification and control) examined 10 with zero refutations. This limited search scope—top-K semantic matches plus citation expansion—suggests that within the examined neighborhood, the specific combination of multi-model handling, general nonlinear function classes, and nonasymptotic regret bounds appears less directly addressed by prior work.

Based on the 26-candidate search, the work's novelty appears to stem from its unified treatment of diverse nonlinear model classes and its explicit multi-model perspective, rather than from introducing entirely new algorithmic primitives. The taxonomy context indicates a moderately active research direction with established sibling papers, yet the contribution-level statistics show no immediate prior work overlap within the examined set. Acknowledging the search's limited scope, a more exhaustive review might uncover closer antecedents, particularly in adjacent leaves addressing parametric or function-approximation settings.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
26
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: sample complexity of online reinforcement learning with nonlinear dynamics. The field addresses how many interactions an agent needs to learn effective policies when the underlying system evolves according to complex, nonlinear rules. The taxonomy organizes research into three main branches: Theoretical Foundations and Sample Complexity Bounds, which develops rigorous guarantees for learning efficiency under various structural assumptions; Algorithm Design and Optimization Methods, which proposes concrete techniques—ranging from model-based planning to policy gradient stabilization—that exploit or adapt to nonlinear structure; and Application Domains and Empirical Studies, which demonstrate these ideas in robotics, power systems, and other real-world settings. Representative works span from early neural dynamics models like Neural Dynamics Model-Based[4] to recent advances in robust off-dynamics transfer (Robust Off-Dynamics RL[1]) and reward-free exploration (Reward-free Nonlinear Efficiency[23]), illustrating both the maturation of theoretical tools and the growing diversity of practical deployment scenarios. Several active lines of work highlight key trade-offs and open questions. One thread examines how structural properties—such as low-dimensional latent representations (Rich-observation Latent Dynamics[2]) or specific function classes—can be leveraged to improve sample efficiency, while another explores robustness when the learned model or policy must transfer across different dynamics (Robust Off-Dynamics RL[1], Hybrid Transfer RL[17]). Safety-aware methods (Safe Learning Barrier Functions[13], Krasovskii-Constrained RL[6]) balance exploration with constraint satisfaction, a concern especially pressing in physical systems. Within this landscape, Multi-model Online RL[0] sits naturally among works addressing general nonlinear settings and multi-model scenarios, sharing thematic ground with Nonlinear Dynamics Complexity[5] and Learning Dynamical Systems Complexity[34]. Its emphasis on handling multiple candidate models distinguishes it from single-model analyses, offering a complementary perspective on how uncertainty over system structure affects sample complexity and algorithmic design.

Claimed Contributions

Suite of online RL algorithms with nonasymptotic policy-regret guarantees for nonlinear continuous systems

The authors introduce multiple algorithms that achieve provable policy-regret bounds in the online non-episodic setting with continuous state-action spaces and nonlinear dynamics. These algorithms build on Hedge-type updates and posterior sampling while incorporating exploration to ensure rapid convergence of the posterior distribution over models.

10 retrieved papers
Frequentist policy-regret guarantees via additional exploration under persistence of excitation

Unlike prior posterior sampling reinforcement learning works that provide Bayesian guarantees, the authors' algorithms add deliberate exploration (Gaussian noise) and establish frequentist policy-regret bounds. The analysis relies on persistence of excitation assumptions from system identification rather than mixing assumptions, making it applicable near stability boundaries.

6 retrieved papers
Separation principle decoupling model identification and certainty-equivalent control for nonlinear dynamics

The authors establish a separation principle where the algorithm decouples best model identification (via posterior sampling over candidate models) from certainty-equivalent control (applying policies corresponding to sampled models). This simplifies policy evaluation and enables explicit characterization of policy regret via packing numbers rather than more complex measures like eluder dimension.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Suite of online RL algorithms with nonasymptotic policy-regret guarantees for nonlinear continuous systems

The authors introduce multiple algorithms that achieve provable policy-regret bounds in the online non-episodic setting with continuous state-action spaces and nonlinear dynamics. These algorithms build on Hedge-type updates and posterior sampling while incorporating exploration to ensure rapid convergence of the posterior distribution over models.

Contribution

Frequentist policy-regret guarantees via additional exploration under persistence of excitation

Unlike prior posterior sampling reinforcement learning works that provide Bayesian guarantees, the authors' algorithms add deliberate exploration (Gaussian noise) and establish frequentist policy-regret bounds. The analysis relies on persistence of excitation assumptions from system identification rather than mixing assumptions, making it applicable near stability boundaries.

Contribution

Separation principle decoupling model identification and certainty-equivalent control for nonlinear dynamics

The authors establish a separation principle where the algorithm decouples best model identification (via posterior sampling over candidate models) from certainty-equivalent control (applying policies corresponding to sampled models). This simplifies policy evaluation and enables explicit characterization of policy regret via packing numbers rather than more complex measures like eluder dimension.

Table of Contents