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Dynamic Decision-Making under Model Misspecification

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  • Xinyu Dai

Abstract

In this study, I investigate the dynamic decision problem with a finite parameter space when the functional form of conditional expected rewards is misspecified. Traditional algorithms, such as Thompson Sampling, guarantee neither an $O(e^{-T})$ rate of posterior parameter concentration nor an $O(T^{-1})$ rate of average regret. However, under mild conditions, we can still achieve an exponential convergence rate of the parameter to a pseudo truth set, an extension of the pseudo truth parameter concept introduced by White (1982). I further characterize the necessary conditions for the convergence of the expected posterior within this pseudo-truth set. Simulations demonstrate that while the maximum a posteriori (MAP) estimate of the parameters fails to converge under misspecification, the algorithm's average regret remains relatively robust compared to the correctly specified case. These findings suggest opportunities to design simple yet robust algorithms that achieve desirable outcomes even in the presence of model misspecifications.

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  • Xinyu Dai, 2025. "Dynamic Decision-Making under Model Misspecification," Papers 2505.14913, arXiv.org.
    • Handle: RePEc:arx:papers:2505.14913
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    References listed on IDEAS

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    1. Stéphane Bonhomme & Martin Weidner, 2022. "Minimizing sensitivity to model misspecification," Quantitative Economics, Econometric Society, vol. 13(3), pages 907-954, July.
    2. Jin Li & Ye Luo & Xiaowei Zhang, 2021. "Dynamic Selection in Algorithmic Decision-making," Papers 2108.12547, arXiv.org, revised Sep 2023.
    3. Takeshi Murooka & Yuichi Yamamoto, 2023. "Higher-Order Misspecification and Equilibrium Stability," OSIPP Discussion Paper 23E002Rev., Osaka School of International Public Policy, Osaka University, revised Sep 2023.
    4. Cuimin Ba, 2021. "Robust Misspecified Models and Paradigm Shifts," Papers 2106.12727, arXiv.org, revised Aug 2023.
    5. Esponda, Ignacio & Pouzo, Demian & Yamamoto, Yuichi, 2021. "Asymptotic behavior of Bayesian learners with misspecified models," Journal of Economic Theory, Elsevier, vol. 195(C).
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