Coding Agents with Environment Interaction: A Theoretical Perspective
This work provides a theoretical foundation for understanding and improving coding agents' interaction with execution environments, which is significant for researchers and developers working on automated software development.
This paper theoretically investigates the environment-interaction strategies of coding agents, focusing on code selection and generation conditioned on feedback. It proves that fuzzy functional similarity estimators strictly dominate functional equivalence in signal-to-noise ratio for code selection and derives a novel regret bound for backprompting, showing its effectiveness is limited by task description ambiguity.
Coding agents are increasingly utilized in test-driven software development, yet the theoretical mechanisms behind their environment-interaction strategies remain underexplored. We provide a probabilistic framework for two dominant paradigms: code selection after generation using the execution environment, and code generation conditioned on environment feedback. First, we formalize several well-established selection heuristics as environment-aware estimators of code correctness. We theoretically prove that estimators based on fuzzy functional similarity add an inductive bias and strictly dominate estimators based on functional equivalence in terms of signal-to-noise ratio. Second, we frame backprompting as an in-context approximation of Thompson sampling. We derive a novel regret bound for reward functions with unobservable components, theoretically explaining why the effectiveness of backprompting is limited by the ambiguity of the informal task description (an irreducible regret). Using three state-of-the-art open weight models, we corroborate these findings across BigCodeBenchHard, LeetCodeDataset, and QiskitHumanEvalSim. Our formalization also suggests how to improve task descriptions effectively, leading to a new benchmark, QiskitHumanEvalSimX.