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Bid optimization in online advertising relies on black-box machine-learning models that learn bidding decisions from historical data. However, these approaches fail to replicate human experts' adaptive, experience-driven, and globally coherent decisions. Specifically, they generalize poorly in data-sparse cases because of missing structured knowledge, make short-sighted sequential decisions that ignore long-term interdependencies, and struggle to adapt in out-of-distribution scenarios where human experts succeed. To address this, we propose KBD (Knowledge-informed Bidding with Dual-process control), a novel method for bid optimization. KBD embeds human expertise as inductive biases through the informed machine-learning paradigm, uses Decision Transformer (DT) to globally optimize multi-step bidding sequences, and implements dual-process control by combining a fast rule-based PID (System 1) with DT (System 2). Extensive experiments highlight KBD's advantage over existing methods and underscore the benefit of grounding bid optimization in human expertise and dual-process control.