Agent tasks require sequences of interdependent decisions. Autoregressive models support more flexible decision interfaces than conventional classifiers but incur the latency of token-by-token generation. Recent shared-prefix methods reduce this cost by reusing encoded context and scoring multiple decisions in parallel, but do not model decision dependencies or verify execution. We propose SharedKV-BT, where each active node of a behavior tree (BT) exposes stage-local fields and candidates, and Shared-KV scores the candidates in parallel and passes the selected decision to a separate execution system. We tested SharedKV-BT on robot manipulation, mobile navigation, and computer-use tasks. Across three tasks, SharedKV-BT made typed decisions 2.36-4.15 times faster than prompt-matched autoregressive decoding. On the manipulation task, node-local Shared-KV improved joint decision accuracy from 75% to 94% and closed-loop success from 0% to 60%. Fixed-score policy replay showed that stage gating prevented out-of-order actions and external postconditions prevented premature completion.

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