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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.17744 |
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| _version_ | 1866914489272631296 |
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| author | Yue, Wu |
| author_facet | Yue, Wu |
| contents | Continuous-control reinforcement learning (RL) often exhibits large closed-loop variance, high-frequency control jitter, and sensitivity to disturbance injection. Existing explanations usually emphasize disturbance sources such as action noise, exploration perturbations, or policy nonsmoothness. This letter studies a complementary amplifier-side perspective: in nominally stable yet strongly non-normal closed loops, small input perturbations can undergo transient amplification and lead to disproportionately large state covariance. Motivated by this source--amplifier decomposition, we introduce an input-side variance suppression layer that operates between the learned policy and the plant input to reduce applied-input variance and step-to-step jitter. To separate mechanism from correlation, we use two control-theoretic interventions: one varies only eigenvector geometry under fixed eigenvalues and spectral radius, and the other varies only applied-input statistics under fixed strongly non-normal geometry. We then provide mechanism-consistent external validation on planar quadrotor tasks. Throughout, Koopman/ALE surrogates are used only as analysis and certification tools, not as direct performance paths. Taken together, the results support a narrower claim: in the studied settings, non-normal transient amplification is an important and under-emphasized contributor to execution-time closed-loop variance, and source-side suppression can reduce downstream covariance without changing the structural peak gain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17744 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Input-Side Variance Suppression under Non-Normal Transient Amplification in Continuous-Control Reinforcement Learning Yue, Wu Systems and Control Continuous-control reinforcement learning (RL) often exhibits large closed-loop variance, high-frequency control jitter, and sensitivity to disturbance injection. Existing explanations usually emphasize disturbance sources such as action noise, exploration perturbations, or policy nonsmoothness. This letter studies a complementary amplifier-side perspective: in nominally stable yet strongly non-normal closed loops, small input perturbations can undergo transient amplification and lead to disproportionately large state covariance. Motivated by this source--amplifier decomposition, we introduce an input-side variance suppression layer that operates between the learned policy and the plant input to reduce applied-input variance and step-to-step jitter. To separate mechanism from correlation, we use two control-theoretic interventions: one varies only eigenvector geometry under fixed eigenvalues and spectral radius, and the other varies only applied-input statistics under fixed strongly non-normal geometry. We then provide mechanism-consistent external validation on planar quadrotor tasks. Throughout, Koopman/ALE surrogates are used only as analysis and certification tools, not as direct performance paths. Taken together, the results support a narrower claim: in the studied settings, non-normal transient amplification is an important and under-emphasized contributor to execution-time closed-loop variance, and source-side suppression can reduce downstream covariance without changing the structural peak gain. |
| title | Input-Side Variance Suppression under Non-Normal Transient Amplification in Continuous-Control Reinforcement Learning |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2604.17744 |