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Entropy Regularization under Bayesian Drift Uncertainty

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  • Andy Au

Abstract

We study entropy-regularized mean-variance portfolio optimization under Bayesian drift uncertainty. Gaussian policies remain optimal under partial information, the value function is quadratic in wealth, and belief-dependent coefficients admit closed-form solutions. The mean control is identical to deterministic Bayesian Markowitz feedback; entropy regularization affects only the policy variance. Additionally, this variance does not affect information gain, and instead provides belief-dependent robustness. Notably, optimal policy variance increases with posterior conviction $|m_t|$, forcing greater action randomization when mean position is most aggressive.

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  • Andy Au, 2026. "Entropy Regularization under Bayesian Drift Uncertainty," Papers 2602.16862, arXiv.org, revised Apr 2026.
    • Handle: RePEc:arx:papers:2602.16862
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    References listed on IDEAS

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