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arxiv: 2606.25832 · v2 · pith:SC4RIWNLnew · submitted 2026-06-24 · 💻 cs.LG · cs.AI

MiniOpt: Reasoning to Model and Solve General Optimization Problems with Limited Resources

Ke Zhao , Zixiang Di , Hong Qian , Xiang Shu , Yaolin Wen , Qitao Shi , Bingdong Li , Xingyu Lu
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Xiangfeng Wang Jun Zhou Ke Tang Yang Yu
This is my paper

Pith reviewed 2026-06-26 05:16 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords optimization problemsreinforcement learninglanguage modelspolicy optimizationreward functiongeneralizationcompact modelssolving accuracy
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The pith

MiniOpt trains 3B language models to solve diverse optimization problems accurately via reinforcement learning without expert data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces MiniOpt, a reinforcement learning framework that teaches compact language models to handle general optimization tasks by decomposing reasoning into problem modeling and executable solver generation. It introduces OptReward, a hierarchical scoring function that evaluates both formulation quality and solution correctness to guide learning without large supervised datasets or expert demonstrations. An optimization-oriented policy optimization strategy is added to improve exploration and stabilize training for smaller models. Experiments show the resulting 3B model generalizes across optimization types, scenarios, and domains while achieving the highest average solving accuracy among models under 10B parameters.

Core claim

MiniOpt-3B exhibits strong optimization generalization across various optimization types, problem scenarios, and task domains. For models with fewer than 10B parameters, MiniOpt series achieves the highest average solving accuracy (SA). For models with more than 10B parameters, MiniOpt still shows competitive performance.

What carries the argument

The reasoning-to-model-and-solve paradigm together with OptReward, a hierarchical reward function that jointly scores formulation and solution, plus an optimization-oriented policy optimization strategy for efficient exploration.

If this is right

  • Compact models under 10B parameters reach the highest average solving accuracy on optimization tasks compared with other approaches.
  • Optimization problems can be addressed without large-scale supervised datasets, costly annotations, or intermediate step verification.
  • The hierarchical reward enables stable reinforcement learning and efficient exploration specifically for smaller models.
  • Generalization holds across optimization types, problem scenarios, and task domains.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same reward design could be adapted to train small models on other structured reasoning tasks such as planning or scheduling.
  • Deployment on edge devices becomes feasible once optimization capability fits inside a 3B model.
  • Hybrid systems might combine the generated solvers with traditional optimization libraries for further gains.

Load-bearing premise

The OptReward hierarchical scoring function can jointly evaluate formulation and solution quality to drive effective policy learning without any expert demonstrations.

What would settle it

A test showing that a 3B model trained with MiniOpt achieves no higher solving accuracy than baselines on a held-out class of optimization problems never encountered during training.

Figures

Figures reproduced from arXiv: 2606.25832 by Bingdong Li, Hong Qian, Jun Zhou, Ke Tang, Ke Zhao, Qitao Shi, Xiangfeng Wang, Xiang Shu, Xingyu Lu, Yang Yu, Yaolin Wen, Zixiang Di.

Figure 1
Figure 1. Figure 1: An overview of the proposed MiniOpt training paradigm. Sub-figure (a) demonstrates the reasoning-to-model-and-solve [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: An informative and easily verifiable reward function [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of training dynamics of reward values and [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of average SA against model parameter [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of training dynamics of reward function [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Histogram showing the distribution of optimization types across 8 benchmarks. We categorize the problems in the [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Histogram showing the distribution of optimization problem scenarios across 8 benchmarks. We categorize the [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Performance variations of the MiniOpt on benchmarks [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Proportion of every scenario of instances in OptMATH-Train (201K). [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Proportion of every problem type of instances in OptMATH-Train (201K). [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
read the original abstract

Achieving strong optimization generalization across diverse optimization problems while requiring limited training resources remains a challenging problem for optimization-oriented large language models (LLMs). Existing approaches typically rely on large-scale supervised datasets, costly reasoning annotations, and expensive intermediate step verification, resulting in substantial training overhead. To address these challenges, we propose MiniOpt, a reinforcement learning framework that learns to solve optimization problems through an "reasoning-to-model-and-solve" paradigm. MiniOpt decomposes optimization reasoning into structured optimization modeling and executable solver generation. Building upon this paradigm, we introduce OptReward, a reward function with hierarchical score structure that jointly evaluates formulation and solution, enabling effective policy learning without expert demonstrations. We further develop an optimization-oriented policy optimization strategy that improves exploration efficiency and stabilizes reinforcement learning for compact models. Extensive experiments show that MiniOpt-3B exhibits strong optimization generalization across various optimization types, problem scenarios, and task domains. For models with fewer than 10B parameters, MiniOpt series achieves the highest average solving accuracy (SA). For models with more than 10B parameters, MiniOpt still shows competitive performance. These results suggest that optimization-oriented reward design and reinforcement learning provide an effective pathway for developing compact optimization-specialized language models with strong optimization generalization capabilities. The code is available at https://github.com/Hsiang-1/MiniOpt.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper proposes MiniOpt, a reinforcement learning framework for optimization problems that decomposes reasoning into structured modeling and executable solver generation. It introduces OptReward, a hierarchical scoring function that jointly evaluates formulation and solution to enable policy learning without expert demonstrations, along with an optimization-oriented policy optimization strategy for improved exploration in compact models. The central claim is that MiniOpt-3B exhibits strong optimization generalization across problem types, scenarios, and domains, achieving the highest average solving accuracy (SA) among models with fewer than 10B parameters while remaining competitive for larger models.

Significance. If the experimental results hold, the work would demonstrate an effective pathway for resource-efficient, optimization-specialized LLMs via reward design and RL rather than large supervised datasets. The public release of code at https://github.com/Hsiang-1/MiniOpt is a positive contribution to reproducibility.

major comments (2)
  1. [Abstract] Abstract: the claim that MiniOpt-3B achieves the highest average SA among sub-10B models across diverse optimization types is presented without any description of datasets, baselines, statistical tests, number of runs, or controls for confounding factors, so the data-to-claim link cannot be evaluated.
  2. [OptReward] OptReward section: the hierarchical reward is load-bearing for the no-expert-demonstrations claim, yet the manuscript provides no analysis of whether its components were tuned post-hoc to the reported outcomes or whether any 'predictions' reduce to fitted quantities, raising a circularity risk for the generalization results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that MiniOpt-3B achieves the highest average SA among sub-10B models across diverse optimization types is presented without any description of datasets, baselines, statistical tests, number of runs, or controls for confounding factors, so the data-to-claim link cannot be evaluated.

    Authors: The abstract is intentionally concise. Full details on datasets (diverse optimization benchmarks spanning types, scenarios, and domains), baselines (comparable LLMs under 10B parameters), evaluation protocol, and controls appear in Sections 4 and 5. To strengthen the data-to-claim link within the abstract's length constraints, we will add a brief clause such as 'evaluated on standard optimization benchmarks against peer sub-10B models.' revision: yes

  2. Referee: [OptReward] OptReward section: the hierarchical reward is load-bearing for the no-expert-demonstrations claim, yet the manuscript provides no analysis of whether its components were tuned post-hoc to the reported outcomes or whether any 'predictions' reduce to fitted quantities, raising a circularity risk for the generalization results.

    Authors: OptReward components were fixed a priori using standard optimization metrics for formulation correctness and solution feasibility; no post-hoc tuning to experimental outcomes occurred. To directly address the circularity concern, we will expand the OptReward section with a short paragraph documenting the design rationale and confirming independence from reported results. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The abstract and description present an empirical RL framework (reasoning-to-model-and-solve paradigm, OptReward hierarchical scoring, optimization-oriented policy optimization) whose performance claims rest on experimental results across optimization problems. No equations, derivations, fitted parameters renamed as predictions, or self-citation chains are exhibited in the provided text that would reduce the central claims to inputs by construction. OptReward is described as an enabling design choice for policy learning without expert data, not a quantity whose components are shown to be post-hoc tuned or mathematically forced. This qualifies as a normal self-contained empirical paper with score 0.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no information on free parameters, background axioms, or newly postulated entities; the OptReward and policy optimization components are introduced but not decomposed into their constituent assumptions or fitted values.

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