Causally Abstracted Multi-armed Bandits

TL;DR

This paper introduces causally abstracted multi-armed bandits (CAMABs), extending transfer learning to decision problems with different variables and causal structures, and proposes algorithms with regret analysis for this setting.

Contribution

It formalizes CAMABs using causal abstraction theory and develops algorithms for learning in this new framework, addressing multi-scale and related decision problems.

Findings

Algorithms demonstrate effective learning in CAMAB scenarios.

Theoretical regret bounds are established for the proposed algorithms.

Real-world experiments show practical applicability in online advertising.

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.