Minimax Optimal Regret for Causal Logistic Bandits with Counterfactual Fairness

The paper proves matching minimax regret bounds for causal logistic bandits under counterfactual fairness.

The paper studies causal logistic bandits in which factual and counterfactual feature maps share an unknown logistic reward parameter, while the learner sees only factual rewards. It shows that some coverage condition is necessary, because otherwise factually indistinguishable environments can force linear expected joint loss. Under a weaker full-rank condition, the authors identify an information scale V-star and prove a matching lower bound of order (V-star times the minimum of log K and d) to the one-third times T to the two-thirds. Explore-then-exploit and adaptive algorithms achieve the same leading dependence, up to logarithmic factors, while controlling cumulative fairness violations.