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In this work, we propose ARCHITECT, a framework that treats robot policy acquisition as an interactive program synthesis task. ARCHITECT leverages the reasoning capabilities of LLM coding agents to synthesize modular robot programs that utilize a suite of perception and control tools. Unlike end-to-end models where distribution shift leads to unpredictable, cascading failures, our modular architecture allows users to isolate failures and localize feedback at the level of abstraction required. We introduce an iterative process where a human supervisor provides natural language corrections to steer the policy. 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