Best Arm Identification in Generalized Linear Bandits with 1-Bit Feedback

In many real-world applications such as IoT sensor networks, digital marketing, and clinical trials, decision-making often operates under strict 1-bit communication constraints and binary feedback (e.g., success/failure, click/no-click). Generalized Linear Models (GLMs) have been shown to be more efficient than linear models for binary data and are used effectively in contextual settings where decisions are driven by a multitude of high-dimensional variables. However, the existing literature on Best Arm Identification (BAI) in GLMs has focused almost exclusively on full-precision rewards, leaving a critical gap in communication-constrained settings. In this paper, we study Best Arm Identification in Generalized Linear Models with 1-bit observations, where the latent reward follows an exponential-family distribution but the learner observes only thresholded binary feedback. To the best of our knowledge, this is the first work to formulate and solve BAI in the 1-bit GLM setting. Our algorithm constructs confidence sets directly for the pairwise reward gaps between arms, formulated in terms of the feature matrices $V$ and an $m$-dimensional parameter vector $\theta$. Under standard regularity assumptions, we prove that the proposed algorithm is $(ϵ,\delta )$-PAC.