Graph Learning is Suboptimal in Causal Bandits
Mohammad Shahverdikondori, Jalal Etesami, Negar Kiyavash
TL;DR
This work analyzes regret minimization in causal bandits under causal sufficiency with an unknown graph. It shows that identifying the reward’s parent set can be suboptimal and proves lower bounds for both known and unknown numbers of parents, motivating direct regret-focused algorithms. The authors introduce phase-based adaptive strategies that bypass explicit graph or parent recovery, achieving near-optimal regret in both known and unknown $k$ regimes and establishing Pareto-optimality across $k$. Empirical results on random graphs demonstrate substantial performance gains over baselines, underscoring the practical value of bypassing causal discovery for regret minimization.
Abstract
We study regret minimization in causal bandits under causal sufficiency where the underlying causal structure is not known to the agent. Previous work has focused on identifying the reward's parents and then applying classic bandit methods to them, or jointly learning the parents while minimizing regret. We investigate whether such strategies are optimal. Somewhat counterintuitively, our results show that learning the parent set is suboptimal. We do so by proving that there exist instances where regret minimization and parent identification are fundamentally conflicting objectives. We further analyze both the known and unknown parent set size regimes, establish novel regret lower bounds that capture the combinatorial structure of the action space. Building on these insights, we propose nearly optimal algorithms that bypass graph and parent recovery, demonstrating that parent identification is indeed unnecessary for regret minimization. Experiments confirm that there exists a large performance gap between our method and existing baselines in various environments.