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Computational protein design typically employs a sequential workflow of structure generation followed by sequence (re)design. While structure generators can be explicitly conditioned on functional objectives, inverse folding models are constrained by their function-agnostic nature and sequence-structure degeneracy. More critically, the associated training objectives do not account for the *Best-of-N* (BoN) inference protocol, resulting in a fundamental training-inference misalignment. Here, we propose FIDIA, a reinforcement learning framework that enables **F**unction-**I**nformed sequence **D**esign via **I**nference-**A**ligned policy optimization. Specifically, FIDIA integrates functional constraints into composite rewards and explicitly optimize the induced policy under BoN toward high-fitness sequence regions. We achieve this via a grounded gradient estimator that directly maximizes the expected maximum reward. FIDIA consistently outperforms both standard and RL-optimized baselines in success rate and precision on a general motif scaffolding benchmark. Further experiments on realworld cases including vaccine and affinity-enhancing enzyme design validate FIDIA’s efficacy in complex therapeutic and biocatalytic contexts.