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Minzu University of China

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Beyond Peak Backlog: Conditional Energy and Temporal Geometry in Capacity-Constrained Delayed Bandit Optimization

Aug 17, 2026

This study addresses the dependence of regret bounds on peak backlog in capacity-constrained multi-armed bandits with delayed feedback. We propose a scheduler-side conditional energy interface that decouples rate adaptation from disturbance filtering to optimize delay complexity. By revealing how temporal geometry influences regret, we demonstrate that minimax regret can differ polynomially under identical delay statistics, thereby overcoming the limitations of aggregated metrics. Leveraging semi-transparent oracles and strong convexity analysis, we derive a parameter-free regret bound with a delay term of o(√(e_c d_tot)) and establish a lower bound for capacity-scarce regimes. These contributions significantly refine the theoretical granularity of regret analysis in delayed feedback settings beyond conventional aggregate measures.

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