For max@k (best-of-K) finite-horizon MDPs, Markovian policies are suboptimal, a compact (previous-best, current-cumulative) state augmentation restores optimality, exact planning is NP-hard but an FPTAS exists, and the minimax generative-model sample complexity is Θ(KH³SA/ε²).
Max k-armed bandit: On the extremehunter algorithm and beyond
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Theoretical Foundations of $\max$@$k$ Reinforcement Learning
For max@k (best-of-K) finite-horizon MDPs, Markovian policies are suboptimal, a compact (previous-best, current-cumulative) state augmentation restores optimality, exact planning is NP-hard but an FPTAS exists, and the minimax generative-model sample complexity is Θ(KH³SA/ε²).