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In this setting, correctness is not enough: two solvers may both return valid solutions on the deployment distribution while differing substantially in runtime. Given samples from an unknown task distribution, the learner returns code evaluated on fresh instances by both solution quality and execution time. Our central abstraction is a \\emph{solver hint}: reusable structure inferred from samples and compiled into specialized solver code. We prove that the empirically fastest sample-consistent solver from a fixed library generalizes in both correctness and runtime, and that statistically identifiable hints can be recovered and compiled from polynomially many samples.\n  Empirically, we instantiate the framework with LLM code agents on \\(21\\) structured combinatorial-optimization target distributions across seven problem classes. The synthesized sol","title":"Distribution-Aware Algorithm Design with LLM Agents","url":"https://arxiv.org/abs/2605.14141","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.14141v1 Announce Type: new \nAbstract: We study learning when the learned object is executable solver code rather than a predictor. In this setting, correctness is not enough: two solvers may both return valid solutions on the deployment distribution while differing substantially in runtime. Given samples from an unknown task distribution, the learner returns code evaluated on fresh instances by both solution quality and execution time. Our central abstraction is a \\emph{solver hint}: reusable structure inferred from samples and compiled into specialized solver code. We prove that the empirically fastest sample-consistent solver from a fixed library generalizes in both correctness and runtime, and that statistically identifiable hints can be recovered and compiled from polynomially many samples.\n  Empirically, we instantiate the framework with LLM code agents on \\(21\\) structured combinatorial-optimization target distributions across seven problem classes. 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