  We study two randomized algorithms for generalized linear bandits. The first,
GLM-TSL, samples a generalized linear model (GLM) from the Laplace
approximation to the posterior distribution. The second, GLM-FPL, fits a GLM to
a randomly perturbed history of past rewards. We analyze both algorithms and
derive $\tilde{O}(d \sqrt{n \log K})$ upper bounds on their $n$-round regret,
where $d$ is the number of features and $K$ is the number of arms. The former
improves on prior work while the latter is the first for Gaussian noise
perturbations in non-linear models. We empirically evaluate both GLM-TSL and
GLM-FPL in logistic bandits, and apply GLM-FPL to neural network bandits. Our
work showcases the role of randomization, beyond posterior sampling, in
exploration.
