Regularized Contextual Bandits
This work addresses the contextual bandit problem for scenarios requiring policy adherence to baselines, offering incremental improvements in convergence analysis.
The paper tackles the stochastic contextual bandit problem by incorporating regularization to keep the agent's policy close to a baseline policy, using a nonparametric model that splits the context space into bins and solves regularized multi-armed bandit instances independently, resulting in derived slow and fast convergence rates and new margin conditions for problem-independent rates.
We consider the stochastic contextual bandit problem with additional regularization. The motivation comes from problems where the policy of the agent must be close to some baseline policy which is known to perform well on the task. To tackle this problem we use a nonparametric model and propose an algorithm splitting the context space into bins, and solving simultaneously - and independently - regularized multi-armed bandit instances on each bin. We derive slow and fast rates of convergence, depending on the unknown complexity of the problem. We also consider a new relevant margin condition to get problem-independent convergence rates, ending up in intermediate convergence rates interpolating between the aforementioned slow and fast rates.