Reserve-Aware Contrast Certificates for Conservative Bandits with Uncertain Baselines

The paper introduces Reserve-C4B, a method for conservative bandits that ensures improvement over an incumbent policy while respecting a performance budget, even when the incumbent’s reward is uncertain. By focusing on the baseline-relative contrast and using a shared confidence set, the approach derives an exact expression for the avoidable penalty and a tighter admissibility test at each history. The method incorporates a reserve ledger to separate statistical evidence from performance deficit and a prefix-refresh extension to recertify decisions without discarding prior credit, achieving high-probability conditional-mean performance guarantees for linear rewards.

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