Managing Temporal Resolution in Continuous Value Estimation: A Fundamental Trade-off
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arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866911757245612032 |
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| author | Zhang, Zichen Kirschner, Johannes Zhang, Junxi Zanini, Francesco Ayoub, Alex Dehghan, Masood Schuurmans, Dale |
| author_facet | Zhang, Zichen Kirschner, Johannes Zhang, Junxi Zanini, Francesco Ayoub, Alex Dehghan, Masood Schuurmans, Dale |
| contents | A default assumption in reinforcement learning (RL) and optimal control is that observations arrive at discrete time points on a fixed clock cycle. Yet, many applications involve continuous-time systems where the time discretization, in principle, can be managed. The impact of time discretization on RL methods has not been fully characterized in existing theory, but a more detailed analysis of its effect could reveal opportunities for improving data-efficiency. We address this gap by analyzing Monte-Carlo policy evaluation for LQR systems and uncover a fundamental trade-off between approximation and statistical error in value estimation. Importantly, these two errors behave differently to time discretization, leading to an optimal choice of temporal resolution for a given data budget. These findings show that managing the temporal resolution can provably improve policy evaluation efficiency in LQR systems with finite data. Empirically, we demonstrate the trade-off in numerical simulations of LQR instances and standard RL benchmarks for non-linear continuous control. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_08949 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Managing Temporal Resolution in Continuous Value Estimation: A Fundamental Trade-off Zhang, Zichen Kirschner, Johannes Zhang, Junxi Zanini, Francesco Ayoub, Alex Dehghan, Masood Schuurmans, Dale Machine Learning Systems and Control A default assumption in reinforcement learning (RL) and optimal control is that observations arrive at discrete time points on a fixed clock cycle. Yet, many applications involve continuous-time systems where the time discretization, in principle, can be managed. The impact of time discretization on RL methods has not been fully characterized in existing theory, but a more detailed analysis of its effect could reveal opportunities for improving data-efficiency. We address this gap by analyzing Monte-Carlo policy evaluation for LQR systems and uncover a fundamental trade-off between approximation and statistical error in value estimation. Importantly, these two errors behave differently to time discretization, leading to an optimal choice of temporal resolution for a given data budget. These findings show that managing the temporal resolution can provably improve policy evaluation efficiency in LQR systems with finite data. Empirically, we demonstrate the trade-off in numerical simulations of LQR instances and standard RL benchmarks for non-linear continuous control. |
| title | Managing Temporal Resolution in Continuous Value Estimation: A Fundamental Trade-off |
| topic | Machine Learning Systems and Control |
| url | https://arxiv.org/abs/2212.08949 |