Multi-Environment Meta-Learning in Stochastic Linear Bandits
This work addresses the problem of efficient learning across multiple environments in bandit settings, representing an incremental advance by extending single-distribution meta-learning to mixture distributions.
The paper tackles meta-learning in multi-task linear stochastic bandits with parameters drawn from a mixture distribution, proposing a regularized OFUL algorithm that achieves low regret on new tasks without needing environment labels, with regret bounds showing benefits over separate learning or meta-learning without mixture recognition.
In this work we investigate meta-learning (or learning-to-learn) approaches in multi-task linear stochastic bandit problems that can originate from multiple environments. Inspired by the work of [1] on meta-learning in a sequence of linear bandit problems whose parameters are sampled from a single distribution (i.e., a single environment), here we consider the feasibility of meta-learning when task parameters are drawn from a mixture distribution instead. For this problem, we propose a regularized version of the OFUL algorithm that, when trained on tasks with labeled environments, achieves low regret on a new task without requiring knowledge of the environment from which the new task originates. Specifically, our regret bound for the new algorithm captures the effect of environment misclassification and highlights the benefits over learning each task separately or meta-learning without recognition of the distinct mixture components.