Cutting to the chase with warm-start contextual bandits

Abstract

Multi-armed bandits achieve excellent long-term performance in practice and sublinear cumulative regret in theory. However, a real-world limitation of bandit learning is poor performance in early rounds due to the need for exploration—a phenomenon known as the cold-start problem. While this limitation may be necessary in the general classical stochastic setting, in practice where “pre-training” data or knowledge is available, it is natural to attempt to “warm-start” bandit learners. This paper provides a theoretical treatment of warm-start contextual bandit learning, adopting Linear Thompson Sampling as a principled framework for flexibly transferring domain knowledge as might be captured by bandit learning in a prior related task, a supervised pre-trained Bayesian posterior, or domain expert knowledge. Under standard conditions, we prove a general regret bound. We then apply our warm-start algorithmic technique to other common bandit learners—the epsilon -greedy and upper-confidence bound contextual learners. An upper regret bound is then provided for LinUCB. Our suite of warm-start learners are evaluated in experiments with both artificial and real-world datasets, including a motivating task of tuning a commercial database. A comprehensive range of experimental results are presented, highlighting the effect of different hyperparameters and quantities of pre-training data.