  Despite achieving superior performance in human-level control problems,
unlike humans, deep reinforcement learning (DRL) lacks high-order intelligence
(e.g., logic deduction and reuse), thus it behaves ineffectively than humans
regarding learning and generalization in complex problems. Previous works
attempt to directly synthesize a white-box logic program as the DRL policy,
manifesting logic-driven behaviors. However, most synthesis methods are built
on imperative or declarative programming, and each has a distinct limitation,
respectively. The former ignores the cause-effect logic during synthesis,
resulting in low generalizability across tasks. The latter is strictly
proof-based, thus failing to synthesize programs with complex hierarchical
logic. In this paper, we combine the above two paradigms together and propose a
novel Generalizable Logic Synthesis (GALOIS) framework to synthesize
hierarchical and strict cause-effect logic programs. GALOIS leverages the
program sketch and defines a new sketch-based hybrid program language for
guiding the synthesis. Based on that, GALOIS proposes a sketch-based program
synthesis method to automatically generate white-box programs with
generalizable and interpretable cause-effect logic. Extensive evaluations on
various decision-making tasks with complex logic demonstrate the superiority of
GALOIS over mainstream baselines regarding the asymptotic performance,
generalizability, and great knowledge reusability across different
environments.
