Sampling Complexity of TD and PPO in RKHS
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| Format: | Preprint |
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2025
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| _version_ | 1866918150721765376 |
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| author | Zou, Lu Ren, Wendi Zhang, Weizhong Ding, Liang Li, Shuang |
| author_facet | Zou, Lu Ren, Wendi Zhang, Weizhong Ding, Liang Li, Shuang |
| contents | 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 $k^{-1/2}$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_24991 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sampling Complexity of TD and PPO in RKHS Zou, Lu Ren, Wendi Zhang, Weizhong Ding, Liang Li, Shuang Machine Learning 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 $k^{-1/2}$ 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. |
| title | Sampling Complexity of TD and PPO in RKHS |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2509.24991 |