Designing efficient general-purpose contextual bandit algorithms that work with large -- or even continuous -- action spaces would facilitate application to important scenarios such as information retrieval, recommendation systems, and continuous control. While obtaining standard regret guarantees can be hopeless, alternative regret notions have been proposed to tackle the large action setting. We propose a smooth regret notion for contextual bandits, which dominates previously proposed alternatives. We design a statistically and computationally efficient algorithm -- for the proposed smooth regret -- that works with general function approximation under standard supervised oracles. We also present an adaptive algorithm that automatically adapts to any smoothness level. Our algorithms can be used to recover the previous minimax/Pareto optimal guarantees under the standard regret, e.g., in bandit problems with multiple best arms and Lipschitz/H{\"o}lder bandits. We conduct large-scale empirical evaluations demonstrating the efficacy of our proposed algorithms.

提出了一种平滑遗憾函数的背景自适应算法，可用于大量或连续动作空间下的通用背景自适应问题，并能适应各种光滑度级别的问题，取得了先前优化遗憾函数的最优性保证。

具有平滑遗憾的情境臂控算法：连续行动空间高效学习