Generalized Linear Bandits

Generalized linear bandits model rewards as a nonlinear link applied to features and an unknown parameter, supporting settings such as logistic click or choice feedback and Poisson demand. Algorithms use confidence-based optimism (UCB), Thompson sampling, or online mirror descent to balance reward estimation with exploration, with applications including contextual pricing and slate selection. Regret analyses often approach square-root growth in the horizon, while practical work also targets efficient updates, limited adaptivity, heavy-tailed noise, and changing environments. Open tensions include how to preserve strong guarantees under model drift or corruption and whether variance-sensitive Thompson sampling can avoid a warm-up period without worsening regret.