Likelihood Hacking in Probabilistic Program Synthesis
When language models are trained by reinforcement learning (RL) to write probabilistic programs, they can artificially inflate their marginal-likelihood reward by producing programs whose data distribution fails to normalise instead of fitting the data better. We call this failure likelihood hacking (LH). We formalise LH in a core probabilistic programming language (PPL) and give sufficient syntactic conditions for its prevention, proving that a safe language fragment $\mathcal{L}_{\text{safe}}$ satisfying these conditions cannot produce likelihood-hacking programs. Empirically, we show that GRPO-trained models generating PyMC code discover LH exploits within the first few training steps,...
| Authors | Jacek Karwowski, Younesse Kaddar, Zihuiwen Ye et al. |
|---|---|
| Primary category | cs.LG |
| Published | 25 March 2026 |
| Last updated at source | 18 August 2026 |
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