Interactive Program Induction

Program induction refers to the process in which a learner aims to recover a program from a few given input-output examples. This paradigm broadens programming access by letting users demonstrate the rule-based behavior they want to apply to unseen data, instead of having to implement it themselves. However, recovering a program from finite input-output examples is fundamentally ambiguous, as a finite set of input-output examples is theoretically consistent with infinitely many programs whose output diverges on unseen inputs. We view this problem from a Bayesian perspective, where, given a prior $p^0$ over programs, identifying the target program means concentrating posterior probability mass on it by observing additional input-output examples. In the interactive program induction setting, the learner chooses maximally informative inputs and queries an oracle, such as the user, for their outputs. We derive a greedy query-selection algorithm and show that it identifies a target program $f^{\star }$ up to approximate equivalence after $\mathcal{O}(\log 1/p^0(f^{\star }))$ informative oracle queries. The algorithm uses a language model as the prior under a PAC-style relaxation of program equivalence, where the query-selection objective is estimated using importance sampling. On the CodeARC benchmark, the algorithm improves accuracy over the LM only agent by up to 22 percentage points while observing up to 10.5 fewer input-output examples.