B4: Towards Optimal Assessment of Plausible Code Solutions with
  Plausible Tests
Authors: name: Mouxiang Chen, name: Zhongxin Liu, name: He Tao, name: Yusu Hong, name: David Lo, name: Xin Xia, name: Jianling Sun

Selecting the best code solution from multiple generated ones is an essential
task in code generation, which can be achieved by using some reliable
validators (e.g., developer-written test cases) for assistance. Since reliable
test cases are not always available and can be expensive to build in practice,
researchers propose to automatically generate test cases to assess code
solutions. However, when both code solutions and test cases are plausible and
not reliable, selecting the best solution becomes challenging. Although some
heuristic strategies have been proposed to tackle this problem, they lack a
strong theoretical guarantee and it is still an open question whether an
optimal selection strategy exists. Our work contributes in two ways. First, we
show that within a Bayesian framework, the optimal selection strategy can be
defined based on the posterior probability of the observed passing states
between solutions and tests. The problem of identifying the best solution is
then framed as an integer programming problem. Second, we propose an efficient
approach for approximating this optimal (yet uncomputable) strategy, where the
approximation error is bounded by the correctness of prior knowledge. We then
incorporate effective prior knowledge to tailor code generation tasks. Both
theoretical and empirical studies confirm that existing heuristics are limited
in selecting the best solutions with plausible test cases. Our proposed
approximated optimal strategy B4 significantly surpasses existing heuristics in
selecting code solutions generated by large language models (LLMs) with
LLM-generated tests, achieving a relative performance improvement by up to 50%
over the strongest heuristic and 246% over the random selection in the most
challenging scenarios. Our code is publicly available at
https://github.com/ZJU-CTAG/B4.