Vector Policy Optimization Training For Diversity Improves Testtime Search

# Vector Policy Optimization: Training for Diversity Improves Test-Time Search

**arXiv ID:** 2605.22817
**Authors:** Ryan Bahlous-Boldi, Isha Puri, Idan Shenfeld, Akarsh Kumar, Mehul Damani, Sebastian Risi, Omar Khattab, Zhang-Wei Hong, Pulkit Agrawal
**Published:** 2026-05-21T17:59:26Z
**Abstract:**
Language models must now generalize out of the box to novel environments and work inside inference-scaling search procedures, such as AlphaEvolve, that select rollouts with a variety of task-specific reward functions. Unfortunately, the standard paradigm of LLM post-training optimizes a pre-specified scalar reward, often leading current LLMs to produce low-entropy response distributions and thus to struggle at displaying the diversity that inference-time search will require. We propose Vector Policy Optimization (VPO), an RL algorithm that explicitly trains policies to anticipate diverse downstream reward functions and to produce diverse solutions. VPO exploits that rewards are often vector-valued in practice, like per-test-case correctness in code generation or, say, multiple different user personas or reward models. VPO is essentially a drop-in replacement for the GRPO advantage estimator, but it trains the LLM to output a set of solutions where individual solutions specialize to different trade-offs in the vector reward space. Across four tasks, VPO matches or beats the strongest scalar RL baselines on test-time search (e.g. pass@k and best@k), with the gap widening as the search budget grows. For evolutionary search, VPO models unlock problems that GRPO models cannot solve at all. As test-time search becomes more standardized, optimizing for diversity may need to become the default post-training objective.

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## References

- [arXiv:2605.22817](http://arxiv.org/abs/2605.22817v1)