Sign Betting for Misspecified Regression: Variance Adaptivity and Optimal Approximation
We study bounded regression under model misspecification, evaluating a function $f$ by its $L_1(P_X)$ distance to the conditional mean $η(x)=\mathbb{E}[Y\mid X=x]$, rather than the standard $L_2(P_X)$. This $L_1$ metric is natural for downstream decision problems such as bandits and reinforcement learning. We analyze the min--max estimator of Baraud & Maillard (2025), which we call \emph{sign-betting regression}. Our main results show that sign-betting regression achieves high-probability $L_1$ oracle inequalities under misspecification. Under realizability, our bound adapts to the average conditional variance and recovers the variance-adaptive rate of Li et al. (2026). We further charact...
| Authors | Yinan Li, Han Han, Kwang-Sung Jun |
|---|---|
| Primary category | cs.LG |
| Published | 14 October 2026 |
| Last updated at source | 14 October 2026 |
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