在损失含全局约束扰动的非凸带宽问题中，实现更优的预测误差控制。
Adversarial Bandit Optimization with Globally Bounded Perturbations to Linear Losses
- 引入全局扰动预算，约束非凸损失中的额外噪声。
- 在期望与高概率下均获得紧致的后悔界，优于经典线性带宽方法。
- 适用于对噪声鲁棒性要求高的在线学习场景，如推荐系统。
我们研究一类对抗性带宽优化问题，其中损失函数可为非凸且非光滑。每轮中，学习者观察到的损失由基础线性部分和选择动作后施加的扰动组成。扰动相对于线性损失进行度量，并受全局预算约束，该预算限制其随时间累积的总幅度。在此模型下，我们建立了期望与高概率下的后悔保证。作为分析的特例，我们恢复了经典带宽线性优化的改进高概率后悔界，对应于无扰动的情形。此外，我们通过证明期望后悔的下界，进一步补充了上界结果。
原文摘要 · Abstract (English)
We study a class of adversarial bandit optimization problems in which the loss functions may be non-convex and non-smooth. In each round, the learner observes a loss that consists of an underlying linear component together with an additional perturbation applied after the learner selects an action. The perturbations are measured relative to the linear losses and are constrained by a global budget that bounds their cumulative magnitude over time. Under this model, we establish both expected and high-probability regret guarantees. As a special case of our analysis, we recover an improved high-probability regret bound for classical bandit linear optimization, which corresponds to the setting without perturbations. We further complement our upper bounds by proving a lower bound on the expected regret.
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