arXiv 20 May 2025 · Econometrics
arXiv:2505.14913 · PDF · DOI · OpenAlex · Extracted main text
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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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | White, Halbert (1982) Maximum likelihood estimation of misspecified models | 0.843 | 3 | 3 | 100% |
| 2 | Kim, Michael Jong (2017) Thompson sampling for stochastic control: The finite parameter case | 0.511 | 3 | 2 | 33% |
| 3 | Fan, Lin, Glynn, Peter W (2021) Diffusion Approximations for Thompson Sampling | 0.511 | 2 | 1 | 100% |
| 4 | Esponda, Ignacio, Pouzo, Demian, Yamamoto, Yuichi (2021) Asymptotic behavior of Bayesian learners with misspecified models | 0.405 | 1 | 1 | 100% |
| 5 | Foster, Dylan J, Gentile, Claudio, Mohri, Mehryar, Zimmert, Julian,… (2020) Adapting to Misspecification in Contextual Bandits | 0.405 | 1 | 1 | 100% |
| 6 | Bogunovic, Ilija, Krause, Andreas, Ranzato, M., Beygelzimer, A., Dau… (2021) Misspecified Gaussian Process Bandit Optimization | 0.405 | 1 | 1 | 100% |
| 7 | Adusumilli, Karun (2021) Risk and optimal policies in bandit experiments | 0.405 | 1 | 1 | 100% |
| 8 | Andrews, Isaiah, Barahona, Nano, Gentzkow, Matthew, Rambachan, Ashes… (2023) Structural estimation under misspecification: theory and implications for practice | 0.405 | 1 | 1 | 100% |
| 9 | Armstrong, Timothy, Kline, Patrick M, Sun, Liyang (2024) Adapting to Misspecification | 0.405 | 1 | 1 | 100% |
| 10 | Ba, Cuimin (2023) Robust Misspecified Models and Paradigm Shifts | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 23 scored citations.