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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.02577 |
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| _version_ | 1866912939124981760 |
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| author | Li, Yunxiang Schmidt, Mark Babanezhad, Reza Vaswani, Sharan |
| author_facet | Li, Yunxiang Schmidt, Mark Babanezhad, Reza Vaswani, Sharan |
| contents | Temporal difference (TD) learning is a fundamental algorithm for estimating value functions in reinforcement learning. Recent finite-time analyses of TD with linear function approximation quantify its theoretical convergence rate. However, they often require setting the algorithm parameters using problem-dependent quantities that are difficult to estimate in practice -- such as the minimum eigenvalue of the feature covariance (\(ω\)) or the mixing time of the underlying Markov chain (\(τ_{\text{mix}}\)). In addition, some analyses rely on nonstandard and impractical modifications, exacerbating the gap between theory and practice. To address these limitations, we use an exponential step-size schedule with the standard TD(0) algorithm. We analyze the resulting method under two sampling regimes: independent and identically distributed (i.i.d.) sampling from the stationary distribution, and the more practical Markovian sampling along a single trajectory. In the i.i.d.\ setting, the proposed algorithm does not require knowledge of problem-dependent quantities such as \(ω\), and attains the optimal bias-variance trade-off for the last iterate. In the Markovian setting, we propose a regularized TD(0) algorithm with an exponential step-size schedule. The resulting algorithm achieves a comparable convergence rate to prior works, without requiring projections, iterate averaging, or knowledge of \(τ_{\text{mix}}\) or \(ω\). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02577 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Towards Parameter-Free Temporal Difference Learning Li, Yunxiang Schmidt, Mark Babanezhad, Reza Vaswani, Sharan Machine Learning Temporal difference (TD) learning is a fundamental algorithm for estimating value functions in reinforcement learning. Recent finite-time analyses of TD with linear function approximation quantify its theoretical convergence rate. However, they often require setting the algorithm parameters using problem-dependent quantities that are difficult to estimate in practice -- such as the minimum eigenvalue of the feature covariance (\(ω\)) or the mixing time of the underlying Markov chain (\(τ_{\text{mix}}\)). In addition, some analyses rely on nonstandard and impractical modifications, exacerbating the gap between theory and practice. To address these limitations, we use an exponential step-size schedule with the standard TD(0) algorithm. We analyze the resulting method under two sampling regimes: independent and identically distributed (i.i.d.) sampling from the stationary distribution, and the more practical Markovian sampling along a single trajectory. In the i.i.d.\ setting, the proposed algorithm does not require knowledge of problem-dependent quantities such as \(ω\), and attains the optimal bias-variance trade-off for the last iterate. In the Markovian setting, we propose a regularized TD(0) algorithm with an exponential step-size schedule. The resulting algorithm achieves a comparable convergence rate to prior works, without requiring projections, iterate averaging, or knowledge of \(τ_{\text{mix}}\) or \(ω\). |
| title | Towards Parameter-Free Temporal Difference Learning |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2603.02577 |