OpenNovelty.org

Sampling Complexity of TD and PPO in RKHS

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Kernel methodKernel gradient descentPPOTemporal difference
Abstract:

We revisit Proximal Policy Optimization (PPO) from a function-space perspective. Our analysis decouples policy evaluation and improvement in a reproducing kernel Hilbert space (RKHS): (i) A kernelized temporal-difference (TD) critic performs efficient RKHS-gradient updates using only one-step state–action transition samples. (ii) a KL-regularized, natural-gradient policy step exponentiates the evaluated action-value, recovering a PPO/TRPO-style proximal update in continuous state-action spaces. We provide non-asymptotic, instance-adaptive guarantees whose rates depend on RKHS entropy, unifying tabular, linear, Sobolev, Gaussian, and Neural Tangent Kernel (NTK) regimes, and we derive a sampling rule for the proximal update that ensures the optimal k−1/2k^{-1/2} convergence rate for stochastic optimization. Empirically, the theory-aligned schedule improves stability and sample efficiency on common control tasks (e.g., CartPole, Acrobot), while our TD-based critic attains favorable throughput versus a GAE baseline. Altogether, our results place PPO on a firmer theoretical footing beyond finite-dimensional assumptions and clarify when RKHS-proximal updates with kernel-TD critics yield global policy improvement with practical efficiency.

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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 unified RKHS framework for PPO that decouples policy evaluation (via kernelized TD) and improvement (via natural-gradient proximal updates), accompanied by non-asymptotic sampling complexity guarantees. It resides in the 'RKHS-Based PPO with Sampling Complexity Analysis' leaf, which contains only this single paper. This positioning reflects a sparse research direction: while the broader 'Proximal Policy Optimization in RKHS and Function Spaces' branch includes five leaves, most sibling leaves address architectural stability or metric modifications rather than sampling complexity theory.

The taxonomy reveals that neighboring work clusters around two distinct themes. The 'Temporal Difference Learning in RKHS' branch (comprising four subtopics and roughly fifteen papers) focuses on kernel-based value approximation—methods like Gaussian Process TD and sparse LSTD variants—but does not integrate policy optimization. Meanwhile, sibling leaves in the PPO branch (e.g., 'Kernel Policy Networks for Stability', 'Correntropy-Induced Metric PPO Variants') emphasize empirical robustness or alternative divergence measures without theoretical sampling analysis. The original paper bridges these areas by combining kernel TD evaluation with proximal policy steps under a single convergence framework.

Among twenty-three candidates examined, the kernelized TD critic (Contribution 1) encountered three potentially overlapping works out of eight reviewed, while the KL-regularized natural-gradient update (Contribution 2) found one refutable candidate among six. The instance-adaptive convergence guarantees (Contribution 3) showed no clear refutation across nine candidates. These statistics suggest that the TD component has more substantial prior work in kernel methods, whereas the unified sampling complexity analysis across tabular, linear, Sobolev, and NTK regimes appears less directly anticipated by the limited search scope.

Given the restricted search scale (top-23 semantic matches), the analysis captures immediate neighbors but cannot claim exhaustive coverage. The sparse taxonomy leaf and the absence of refutation for the unified convergence guarantees hint at novelty in the theoretical synthesis, though the kernelized TD and natural-gradient components build on established kernel RL techniques. A broader literature review would clarify whether the integration of these elements under a single sampling complexity framework represents a significant theoretical advance or an incremental unification of known results.

Taxonomy

Core-task Taxonomy Papers
24
3
Claimed Contributions
23
Contribution Candidate Papers Compared
4
Refutable Paper

Research Landscape Overview

Core task: sampling complexity of temporal difference and proximal policy optimization in reproducing kernel Hilbert spaces. The field structure reflects a natural division into three main branches. The first branch, Temporal Difference Learning in RKHS, encompasses a substantial body of work on kernel-based value function approximation, ranging from foundational methods like Gaussian Process TD Learning[1] and early sparse approaches such as Sparse Kernel LSTD[17] to more recent algorithmic refinements including Online Attentive Kernel TD[3] and Optimal Kernel TD[6]. The second branch, Proximal Policy Optimization in RKHS and Function Spaces, explores policy optimization in infinite-dimensional settings, with works like Residual Kernel Policy Network[2] and variants employing alternative loss metrics such as PPO Liu Correntropy[20]. The third branch, Distributional and Regularized Policy Iteration, addresses regularization strategies and distributional perspectives, exemplified by Regularized Policy Iteration[14] and Distributional TD Freedman Inequality[4]. Together, these branches capture the interplay between function approximation theory, sample efficiency, and algorithmic design in kernel-based reinforcement learning. A particularly active line of work centers on establishing finite-sample guarantees for kernel TD methods, with studies like Nonparametric TD Analysis[5] and Optimal Kernel TD[6] investigating convergence rates and sample complexity under various kernel choices. In contrast, the PPO-focused branch remains less densely populated, with only a handful of papers exploring how proximal updates behave in RKHS settings. Sampling Complexity TD PPO[0] sits at the intersection of these themes, directly addressing sample efficiency for both TD and PPO in reproducing kernel Hilbert spaces. Compared to neighboring works such as Residual Kernel Policy Network[2], which emphasizes architectural design, or Nonparametric TD Analysis[5], which focuses on TD convergence alone, the original paper[0] provides a unified treatment of sampling complexity across both value-based and policy-gradient paradigms. This dual focus highlights ongoing questions about how kernel smoothness, exploration strategies, and policy parameterization jointly influence learning efficiency in continuous or large state spaces.

Claimed Contributions

Kernelized temporal-difference critic with RKHS-gradient updates

The authors introduce a kernel gradient-based TD evaluator in a reproducing kernel Hilbert space that acts as an implicit preconditioner and achieves geometric convergence without requiring costly matrix inversions. The evaluator leverages N-step TD learning and provides non-asymptotic TD-error bounds attaining the minimax rate up to logarithmic factors.

8 retrieved papers
Can Refute
KL-regularized natural-gradient policy update for continuous spaces

The authors design a KL-regularized proximal update implementable in continuous action spaces that exponentiates the value estimate. They explicitly quantify the per-iteration sample size needed to achieve intended improvement, addressing a gap where policy expectations are often treated as exact or left unspecified.

6 retrieved papers
Can Refute
Instance-adaptive convergence guarantees unifying multiple RKHS regimes

The authors establish non-asymptotic convergence guarantees that depend on RKHS entropy and unify multiple function-approximation regimes including tabular, linear, Sobolev spaces, Gaussian kernels, and Neural Tangent Kernels. They derive a sampling rule for the proximal update ensuring optimal k to the power negative one-half convergence rate for stochastic optimization.

9 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Within the taxonomy built over the current TopK core-task papers, the original paper is assigned to a leaf with no direct siblings and no cousin branches under the same grandparent topic. In this retrieved landscape, it appears structurally isolated, which is one partial signal of novelty, but still constrained by search coverage and taxonomy granularity.

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Kernelized temporal-difference critic with RKHS-gradient updates

The authors introduce a kernel gradient-based TD evaluator in a reproducing kernel Hilbert space that acts as an implicit preconditioner and achieves geometric convergence without requiring costly matrix inversions. The evaluator leverages N-step TD learning and provides non-asymptotic TD-error bounds attaining the minimax rate up to logarithmic factors.

Contribution

KL-regularized natural-gradient policy update for continuous spaces

The authors design a KL-regularized proximal update implementable in continuous action spaces that exponentiates the value estimate. They explicitly quantify the per-iteration sample size needed to achieve intended improvement, addressing a gap where policy expectations are often treated as exact or left unspecified.

Contribution

Instance-adaptive convergence guarantees unifying multiple RKHS regimes

The authors establish non-asymptotic convergence guarantees that depend on RKHS entropy and unify multiple function-approximation regimes including tabular, linear, Sobolev spaces, Gaussian kernels, and Neural Tangent Kernels. They derive a sampling rule for the proximal update ensuring optimal k to the power negative one-half convergence rate for stochastic optimization.

Table of Contents