Causally Abstracted Multi-armed Bandits

Fabio Massimo Zennaro, Nicholas George Bishop, Joel Dyer, Yorgos Felekis, Ani Calinescu, Michael J. Wooldridge, Theodoros Damoulas

Keywords: causality, structural causal models, causal abstraction, causal bandits

Abstract: Multi-armed bandits (MAB) and causal MABs (CMAB) are established frameworks for decision-making problems. The majority of prior work typically studies and solves individual MAB and CMAB in isolation for a given problem and associated data. However, decision-makers are often faced with multiple related problems and multi-scale observations where joint formulations are needed in order to efficiently exploit the problem structures and data dependencies. Transfer learning for CMABs addresses the situation where models are defined on identical variables, although causal connections may differ. In this work, we extend transfer learning to setups involving CMABs defined on potentially different variables, with varying degrees of granularity, and related via an abstraction map. Formally, we introduce the problem of causally abstracted MABs (CAMABs) by relying on the theory of causal abstraction in order to express a rigorous abstraction map. We propose algorithms to learn in a CAMAB, and study their regret. We illustrate the limitations and the strengths of our algorithms on a real-world scenario related to online advertising.

List Of Authors: Zennaro, Fabio Massimo and Bishop, Nicholas and Dyer, Joel and Felekis, Yorgos and Calinescu, Anisoara and Wooldridge, Michael and Damoulas, Theodoros

Code Url: https://github.com/FMZennaro/causally-abstracted-multiarmed-bandits

Submission Number: 500