Lifelong Bandit Optimization: No Prior and No Regret

In practical applications, machine learning algorithms are often repeatedly applied to problems with similar structure over and over again. We focus on solving a sequence of bandit optimization tasks and develop LiBO, an algorithm which adapts to the environment by learning from past experience and becoming more sample-efficient in the process. We assume a kernelized structure where the kernel is unknown but shared across all tasks. LiBO sequentially meta-learns a kernel that approximates the true kernel and simultaneously solves the incoming tasks with the latest kernel estimate. Our algorithm can be paired with any kernelized bandit algorithm and guarantees oracle optimal performance, meaning that as more tasks are solved, the regret of LiBO on each task converges to the regret of the bandit algorithm with oracle knowledge of the true kernel. Naturally, if paired with a sublinear bandit algorithm, LiBO yields a sublinear lifelong regret. We also show that direct access to the data from each task is not necessary for attaining sublinear regret. The lifelong problem can thus be solved in a federated manner, while keeping the data of each task private.