Online Continuous Hyperparameter Optimization for Generalized Linear Contextual Bandits

In stochastic contextual bandits, an agent sequentially makes actions from a time-dependent action set based on past experience to minimize the cumulative regret. Like many other machine learning algorithms, the performance of bandits heavily depends on the values of hyperparameters, and theoretically derived parameter values may lead to unsatisfactory results in practice. Moreover, it is infeasible to use offline tuning methods like cross-validation to choose hyperparameters under the bandit environment, as the decisions should be made in real-time. To address this challenge, we propose the first online continuous hyperparameter tuning framework for contextual bandits to learn the optimal parameter configuration in practice within a search space on the fly. Specifically, we use a double-layer bandit framework named CDT (Continuous Dynamic Tuning) and formulate the hyperparameter optimization as a non-stationary continuum-armed bandit, where each arm represents a combination of hyperparameters, and the corresponding reward is the algorithmic result. For the top layer, we propose the Zooming TS algorithm that utilizes Thompson Sampling (TS) for exploration and a restart technique to get around the \textit{switching} environment. The proposed CDT framework can be easily utilized to tune contextual bandit algorithms without any pre-specified candidate set for multiple hyperparameters. We further show that it could achieve a sublinear regret in theory and performs consistently better than all existing methods on both synthetic and real datasets.