We study the generalized linear contextual bandit problem within the constraints of limited adaptivity. In this paper, we present two algorithms, $\\texttt{B-GLinCB}$ and $\\texttt{RS-GLinCB}$, that address, respectively, two prevalent limited adaptivity settings. Given a budget $M$ on the number of policy updates, in the first setting, the algorithm needs to decide upfront $M$ rounds at which it will update its policy, while in the second setting it can adaptively perform $M$ policy updates during its course. For the first setting, we design an algorithm $\\texttt{B-GLinCB}$, that incurs $\\tilde{O}(\\sqrt{T})$ regret when $M = \\Omega\\left( \\log{\\log T} \\right)$ and the arm feature vectors are generated stochastically. For the second setting, we design an algorithm $\\texttt{RS-GLinCB}$ that updates its policy $\\tilde{O}(\\log^2 T)$ times and achieves a regret of $\\tilde{O}(\\sqrt{T})$ even when the arm feature vectors are adversarially generated. Notably, in these bounds, we manage to eliminate the dependence on a key instance dependent parameter $\\kappa$, that captures non-linearity of the underlying reward model. Our novel approach for removing this dependence for generalized linear contextual bandits might be of independent interest.<\/p>\n","protected":false},"excerpt":{"rendered":"
We study the generalized linear contextual bandit problem within the constraints of limited adaptivity. In this paper, we present two algorithms, $\\texttt{B-GLinCB}$ and $\\texttt{RS-GLinCB}$, that address, respectively, two prevalent limited adaptivity settings. Given a budget $M$ on the number of policy updates, in the first setting, the algorithm needs to decide upfront $M$ rounds at 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