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arXiv · 2606.05464

Step-by-Step Optimization-like Reasoning in LLMs over Expanding Search Spaces

Nicolás Astorga·Nabeel Seedat·Mihaela van der Schaar
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Abstract

Verifiable reward training has improved mathematical and coding reasoning, but these domains capture only part of step-by-step decision making. Many real-world tasks require finding a high-value feasible plan among many valid alternatives. We introduce OPT*, a scalable family of optimization-style tasks for training and evaluating LLM step-by-step optimization-like reasoning along a complexity axis: each task provides a feasibility checker and evaluator, while a complexity parameter expands the search space without requiring new human labels. This motivates studying these tasks in two regimes: (i) solver-guided online policy optimization, which uses a solver as a value oracle for partial states and applies rank-based reward shaping to reinforce better next steps, and (ii) search-based offline RL when such solvers are unavailable. Theoretically, we relate success in large search spaces to the information a reasoner extracts per unit of search budget. Empirically, we ablate the ingredients that make search efficient on OPT* and show that training on OPT* improves step-by-step optimization-like reasoning.

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Nicolás Astorga, Nabeel Seedat, Mihaela van der Schaar. 2026-06-03. Step-by-Step Optimization-like Reasoning in LLMs over Expanding Search Spaces. https://arxiv.org/abs/2606.05464

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