Gaussian-Mixture-Model Q-Functions for Policy Iteration in Reinforcement Learning

• URL: http://arxiv.org/abs/2512.18763v1
• Date: Sun, 21 Dec 2025 15:00:32 GMT
• Title: Gaussian-Mixture-Model Q-Functions for Policy Iteration in Reinforcement Learning
• Authors: Minh Vu, Konstantinos Slavakis,
• Abstract summary: This paper introduces a novel function-approximation role for Gaussian mixture models (GMMs) as direct surrogates for Q-function losses.<n>These parametric models, termed GMM-QFs, possess substantial representational capacity.<n>They are shown to be universal approximators over a broad class of functions.
• Score: 7.056697401102689
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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