因果 logistic bandits 在反事实公平约束下的 Minimax 最优遗憾

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Abstract:We study causal logistic bandits with counterfactual fairness constraints. The causal structure is given through known factual and counterfactual feature maps that share an unknown logistic reward parameter, but the learner observes only factual rewards. Consequently, the directions determining counterfactual feasibility need not be identifiable from the available feedback. The closest prior analyses either omit a coverage condition or impose a comparatively strong one, and do not establish matching lower bounds. We first show that some coverage condition is necessary: without a coverage-type restriction, factually indistinguishable environments with different optimal fair actions force $\Omega(T)$ expected joint loss. Under a weaker full-rank condition on the factual covariance pooled across actions, we identify a target-specific information scale $V_\star$ that measures the difficulty of estimating rewards and counterfactual effects from factual feedback. We construct worst-case families satisfying this condition on which every policy incurs expected joint loss $\Omega\left(\left[V_\star\min\{\log K,d\}\right]^{1/3}T^{2/3}\right)$. We also give an explore--then--exploit procedure tuned using $V_\star$ and an adaptive algorithm that does not require its value. Both algorithms achieve $\max\{R_T,V_T\}=\widetilde{O}\left(\left[V_\star\min\{\log K,d\}\right]^{1/3}T^{2/3}+\kappa d/\sigma_0^2\right)$, where $R_T$ is regret relative to the best fair action and $V_T$ denotes the cumulative stage-wise positive violations. Thus the upper and lower bounds match in their leading dependence on $T$, $V_\star$, and $\min\{\log K,d\}$, up to logarithmic factors.

Submission history

From: Seoungbin Bae [view email]
[v1] Thu, 1 Oct 2026 09:44:44 UTC (1,365 KB)