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In many applications, e.g. in healthcare and e-commerce, the goal of acontextual bandit may be to learn an optimal treatment assignment policy at theend of the experiment. That is, to minimize simple regret. However, thisobjective remains understudied. We propose a new family of computationallyefficient bandit algorithms for the stochastic contextual bandit setting, wherea tuning parameter determines the weight placed on cumulative regretminimization (where we establish near-optimal minimax guarantees) versus simpleregret minimization (where we establish state-of-the-art guarantees). Ouralgorithms work with any function class, are robust to model misspecification,and can be used in continuous arm settings. This flexibility comes fromconstructing and relying on "conformal arm sets" (CASs). CASs provide a set ofarms for every context, encompassing the context-specific optimal arm with acertain probability across the context distribution. Our positive results onsimple and cumulative regret guarantees are contrasted with a negative result,which shows that no algorithm can achieve instance-dependent simple regretguarantees while simultaneously achieving minimax optimal cumulative regretguarantees.

Proportional Response: Contextual Bandits for Simple and Cumulative Regret Minimization