Dealing With Misspecification In Fixed-Confidence Linear Top-m Identification
This addresses the challenge of model misspecification in linear bandits for applications like medicine and recommendation systems, offering an incremental improvement by adapting to deviation from linearity.
The paper tackles the problem of identifying the top-m arms with largest means in misspecified linear bandit models under a fixed error rate, and presents an algorithm that adapts to misspecification with sample complexity matching a derived lower bound as the error rate approaches zero.
We study the problem of the identification of m arms with largest means under a fixed error rate $δ$ (fixed-confidence Top-m identification), for misspecified linear bandit models. This problem is motivated by practical applications, especially in medicine and recommendation systems, where linear models are popular due to their simplicity and the existence of efficient algorithms, but in which data inevitably deviates from linearity. In this work, we first derive a tractable lower bound on the sample complexity of any $δ$-correct algorithm for the general Top-m identification problem. We show that knowing the scale of the deviation from linearity is necessary to exploit the structure of the problem. We then describe the first algorithm for this setting, which is both practical and adapts to the amount of misspecification. We derive an upper bound to its sample complexity which confirms this adaptivity and that matches the lower bound when $δ$ $\rightarrow$ 0. Finally, we evaluate our algorithm on both synthetic and real-world data, showing competitive performance with respect to existing baselines.