A Causal Decomposition Approach for Fair Contextual Multi-Armed Bandits

Counterfactual reasoning is one of the fundamental facets of human cognition, involved in various tasks such as explanation, credit assignment, blame, and responsibility. It describes the queries what would have happened had some intervention been performed given that something else, corresponding to Layer 3 of the Pearl Causal Hierarchy. In this project, we examine a specific type of counterfactual quantities, called counterfactual direct (Ctf-DE), indirect (Ctf-IE), and spurious (Ctf-SE) effects for quantifying fairness in a sequential decision-making framework. Building on these measures, we formulate an online causally-fair learning problem with multiple long-term constraints and study it in both non-parametric contextual bandits and parametric logistic bandits settings. We achieve sublinear regret and violations bounds for both bandits settings with roundwise counterfactual fairness constraints (that are a priori unknown) without Slater's condition. For logistic bandits, our method achieves $\mathcal{O}(1)$ per-round time complexity using an online mirror descent estimator, yielding an efficient algorithm.

• We study fairness in a sequential decision-making framework, where fairness is defined through equal outcome/reward using counterfactuals along different pathways in a causal graph. - Our algorithm allows the learner to make potentially unfair decisions, but bounds its cumulative constraint violations. - These results contribute to the broader research on causal decision-making systems.