Isoperimetry is All We Need: Langevin Posterior Sampling for RL with Sublinear Regret
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866915139337322496 |
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| author | Jorge, Emilio Dimitrakakis, Christos Basu, Debabrota |
| author_facet | Jorge, Emilio Dimitrakakis, Christos Basu, Debabrota |
| contents | Common assumptions, like linear or RKHS models, and Gaussian or log-concave posteriors over the models, do not explain practical success of RL across a wider range of distributions and models. Thus, we study how to design RL algorithms with sublinear regret for isoperimetric distributions, specifically the ones satisfying the Log-Sobolev Inequality (LSI). LSI distributions include the standard setups of RL theory, and others, such as many non-log-concave and perturbed distributions. First, we show that the Posterior Sampling-based RL (PSRL) algorithm yields sublinear regret if the data distributions satisfy LSI and some mild additional assumptions. Also, when we cannot compute or sample from an exact posterior, we propose a Langevin sampling-based algorithm design: LaPSRL. We show that LaPSRL achieves order-optimal regret and subquadratic complexity per episode. Finally, we deploy LaPSRL with a Langevin sampler -- SARAH-LD, and test it for different bandit and MDP environments. Experimental results validate the generality of LaPSRL across environments and its competitive performance with respect to the baselines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20824 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Isoperimetry is All We Need: Langevin Posterior Sampling for RL with Sublinear Regret Jorge, Emilio Dimitrakakis, Christos Basu, Debabrota Machine Learning Common assumptions, like linear or RKHS models, and Gaussian or log-concave posteriors over the models, do not explain practical success of RL across a wider range of distributions and models. Thus, we study how to design RL algorithms with sublinear regret for isoperimetric distributions, specifically the ones satisfying the Log-Sobolev Inequality (LSI). LSI distributions include the standard setups of RL theory, and others, such as many non-log-concave and perturbed distributions. First, we show that the Posterior Sampling-based RL (PSRL) algorithm yields sublinear regret if the data distributions satisfy LSI and some mild additional assumptions. Also, when we cannot compute or sample from an exact posterior, we propose a Langevin sampling-based algorithm design: LaPSRL. We show that LaPSRL achieves order-optimal regret and subquadratic complexity per episode. Finally, we deploy LaPSRL with a Langevin sampler -- SARAH-LD, and test it for different bandit and MDP environments. Experimental results validate the generality of LaPSRL across environments and its competitive performance with respect to the baselines. |
| title | Isoperimetry is All We Need: Langevin Posterior Sampling for RL with Sublinear Regret |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2412.20824 |