Gaussian-Mixture-Model Q-Functions for Policy Iteration in Reinforcement Learning
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915688771223552 |
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| author | Vu, Minh Slavakis, Konstantinos |
| author_facet | Vu, Minh Slavakis, Konstantinos |
| contents | Unlike their conventional use as estimators of probability density functions in reinforcement learning (RL), this paper introduces a novel function-approximation role for Gaussian mixture models (GMMs) as direct surrogates for Q-function losses. These parametric models, termed GMM-QFs, possess substantial representational capacity, as they are shown to be universal approximators over a broad class of functions. They are further embedded within Bellman residuals, where their learnable parameters -- a fixed number of mixing weights, together with Gaussian mean vectors and covariance matrices -- are inferred from data via optimization on a Riemannian manifold. This geometric perspective on the parameter space naturally incorporates Riemannian optimization into the policy-evaluation step of standard policy-iteration frameworks. Rigorous theoretical results are established, and supporting numerical tests show that, even without access to experience data, GMM-QFs deliver competitive performance and, in some cases, outperform state-of-the-art approaches across a range of benchmark RL tasks, all while maintaining a significantly smaller computational footprint than deep-learning methods that rely on experience data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18763 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gaussian-Mixture-Model Q-Functions for Policy Iteration in Reinforcement Learning Vu, Minh Slavakis, Konstantinos Machine Learning Unlike their conventional use as estimators of probability density functions in reinforcement learning (RL), this paper introduces a novel function-approximation role for Gaussian mixture models (GMMs) as direct surrogates for Q-function losses. These parametric models, termed GMM-QFs, possess substantial representational capacity, as they are shown to be universal approximators over a broad class of functions. They are further embedded within Bellman residuals, where their learnable parameters -- a fixed number of mixing weights, together with Gaussian mean vectors and covariance matrices -- are inferred from data via optimization on a Riemannian manifold. This geometric perspective on the parameter space naturally incorporates Riemannian optimization into the policy-evaluation step of standard policy-iteration frameworks. Rigorous theoretical results are established, and supporting numerical tests show that, even without access to experience data, GMM-QFs deliver competitive performance and, in some cases, outperform state-of-the-art approaches across a range of benchmark RL tasks, all while maintaining a significantly smaller computational footprint than deep-learning methods that rely on experience data. |
| title | Gaussian-Mixture-Model Q-Functions for Policy Iteration in Reinforcement Learning |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2512.18763 |