用分类视角设计可解释的快速探索策略，提升医疗等场景下的决策效率。
A Classification View on Meta Learning Bandits
- 将多臂老虎机问题转化为分类任务，通过决策树生成可解释的探索计划。
- 在随机与上下文设定下，测试误差随 $\log^2(MH)$ 增长，优于传统算法的 $\sqrt{H}$。
- 适合关注可解释性与快速决策的医疗、金融等实时应用领域。
上下文多臂老虎机是建模序列决策的常用方法。例如，在医疗应用中，我们可能进行多种检测以评估患者状况（探索），然后决定最佳治疗方案（利用）。当人类设计策略时，希望探索过程快速且结果对主治医生易懂。然而，常见的老虎机算法与此相去甚远：探索带来的损失随 $H$ 轮次增长为 $\sqrt{H}$，且决策策略依赖于难以理解的统计推断。本文提出一种新颖的分类视角，用于对固定集合 $\mathbb{M}$ 内的多个老虎机进行元学习，生成可解释且快速的探索计划。该计划由一个决策树实现，通过探测各老虎机的收益来分类并指导决策。在随机与上下文设置下，该计划的测试后悔值为 $O(λ^{-2} C_λ(\mathbb{M}) \log^2(MH))$，其中 $M$ 是 $\mathbb{M}$ 的大小，$λ$ 是老虎机间的分离参数，$C_λ(\mathbb{M})$ 是新提出的分类系数，将元学习老虎机与分类问题本质关联。通过近似匹配的下界证明，$C_λ(\mathbb{M})$ 本质上刻画了该问题的复杂度。
原文摘要 · Abstract (English)
Contextual multi-armed bandits are a popular choice to model sequential decision-making. E.g., in a healthcare application we may perform various tests to asses a patient condition (exploration) and then decide on the best treatment to give (exploitation). When humans design strategies, they aim for the exploration to be fast, since the patient's health is at stake, and easy to interpret for a physician overseeing the process. However, common bandit algorithms are nothing like that: The regret caused by exploration scales with $\sqrt{H}$ over $H$ rounds and decision strategies are based on opaque statistical considerations. In this paper, we use an original classification view to meta learn interpretable and fast exploration plans for a fixed collection of bandits $\mathbb{M}$. The plan is prescribed by an interpretable decision tree probing decisions' payoff to classify the test bandit. The test regret of the plan in the stochastic and contextual setting scales with $O (λ^{-2} C_λ (\mathbb{M}) \log^2 (MH))$, being $M$ the size of $\mathbb{M}$, $λ$ a separation parameter over the bandits, and $C_λ(\mathbb{M})$ a novel classification-coefficient that fundamentally links meta learning bandits with classification. Through a nearly matching lower bound, we show that $C_λ(\mathbb{M})$ inherently captures the complexity of the setting.
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