Improved High-Probability Bounds for the Temporal Difference Learning Algorithm via Exponential Stability
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929386909859840 |
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| author | Samsonov, Sergey Tiapkin, Daniil Naumov, Alexey Moulines, Eric |
| author_facet | Samsonov, Sergey Tiapkin, Daniil Naumov, Alexey Moulines, Eric |
| contents | In this paper we consider the problem of obtaining sharp bounds for the performance of temporal difference (TD) methods with linear function approximation for policy evaluation in discounted Markov decision processes. We show that a simple algorithm with a universal and instance-independent step size together with Polyak-Ruppert tail averaging is sufficient to obtain near-optimal variance and bias terms. We also provide the respective sample complexity bounds. Our proof technique is based on refined error bounds for linear stochastic approximation together with the novel stability result for the product of random matrices that arise from the TD-type recurrence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_14286 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Improved High-Probability Bounds for the Temporal Difference Learning Algorithm via Exponential Stability Samsonov, Sergey Tiapkin, Daniil Naumov, Alexey Moulines, Eric Machine Learning Optimization and Control 62L20, 60J20 In this paper we consider the problem of obtaining sharp bounds for the performance of temporal difference (TD) methods with linear function approximation for policy evaluation in discounted Markov decision processes. We show that a simple algorithm with a universal and instance-independent step size together with Polyak-Ruppert tail averaging is sufficient to obtain near-optimal variance and bias terms. We also provide the respective sample complexity bounds. Our proof technique is based on refined error bounds for linear stochastic approximation together with the novel stability result for the product of random matrices that arise from the TD-type recurrence. |
| title | Improved High-Probability Bounds for the Temporal Difference Learning Algorithm via Exponential Stability |
| topic | Machine Learning Optimization and Control 62L20, 60J20 |
| url | https://arxiv.org/abs/2310.14286 |