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Frontier LLMs are effective batch optimizers: Assessing reasoning models in continuous and discrete settings

Frank Hu, Shriram Chennakesavalu, David Graff

arXiv:2609.03177v1cs.LG

TL;DR

The effectiveness of current reasoning LLMs as batch optimizers across continuous and discrete black-box optimization settings remains underexplored. The paper evaluates frontier models on numerical test functions and molecular optimization tasks. LLMs are competitive but brittle on numerical functions, while molecular optimization results are strong and sample-efficient.

  • Problem

    How effective current reasoning LLMs are as batch optimizers across continuous and discrete black-box optimization settings remains unclear.

    Source: §1 · p. 1

  • Method

    The study evaluates frontier Anthropic models as batch optimizers on continuous test functions and PMO molecular-oracle tasks.

    Source: §1 · p. 1

  • Results

    LLMs are competitive but brittle numerical optimizers, while on molecular optimization they are highly performant and sample-efficient, often beating specialist methods with a fraction of the oracle budget.

    Source: §1 · p. 2, §6 · p. 8

  • Takeaways & Limitations

    Frontier reasoning LLMs are powerful priors for batch discrete optimization even without additional tuning or problem scaffolding.

    Source: §6 · p. 8

    Comparisons with GenMol are qualified by its extensive SAFE small-molecule training, while MolLEO and ExLLM use more scaffolding.

    Source: §5.2 · p. 6

Abstract

from arXiv · show

Frontier large language models (LLMs) have become attractive priors for optimization due to their large-scale pretraining that enables them to navigate a variety of optimization settings. However, the effectiveness of modern reasoning LLMs in batch optimization settings remains underexplored. Here we investigate the performance of the current generation of frontier LLMs as batch optimizers in both continuous and discrete settings. We find that while LLMs are competitive zero-shot batch optimizers for numerical test functions, their performance is brittle compared to classical non-LLM optimization approaches. However, LLM priors are significantly better in semantically rich settings, indicating that their batch optimization behavior is highly effective when navigating and reasoning over the discrete spaces most similar in structure to their pretraining data.

1 Introduction

The paper evaluates current frontier reasoning LLMs as batch optimizers in continuous and discrete black-box optimization. It finds brittle but competitive numerical performance and stronger results in molecular optimization.

  • It remains unclear how current reasoning LLMs perform in batch optimization across continuous and discrete settings, despite prior work on specialist methods and earlier LLMs.The question matters for expensive black-box objectives, where restricted evaluation budgets meet combinatorially complex design spaces such as small-molecule discovery.Source: §1 · p. 1
  • The study evaluates Anthropic’s Sonnet 4.6, Opus 4.8, and Opus 5 on continuous test functions and discrete molecular optimization tasks.The continuous test functions are disguised to reduce memorization; molecular tasks use the PMO benchmark’s oracles and SMILES representations.Source: §1 · pp. 1–2
  • Frontier reasoning LLMs are competitive but brittle numerical optimizers, while molecular optimization performance is high and sample-efficient, often beating specialist methods with a fraction of the oracle budget.Source: §1 · p. 2

2 Related work

The related work reviews Bayesian optimization, pretrained models used for optimization, and LLM applications in molecular optimization. It highlights a gap in evaluating current LLMs as batched policies across standard optimization functions and molecular tasks.

  • Bayesian optimization uses a probabilistic surrogate and acquisition function to guide black-box evaluations, with Gaussian processes and expected improvement among common choices.Source: §2 · p. 2
  • Prior pretrained-model approaches either imitate synthetic optimization trajectories or use LLMs for components of Bayesian optimization; prompt-based policies had not covered batched standard test functions and molecular optimization.The authors note that frontier LLM capabilities have improved since the earlier studies.Source: §2 · p. 2
  • LLMs have been used to generate optimized molecules, learn molecular representations, predict properties, and augment closed-loop optimization.Molecular-property optimization supports applications including pharmaceuticals, photovoltaics, and batteries.Source: §2 · p. 2

3 Background

The background defines black-box optimization over continuous or discrete search spaces and describes iterative, potentially batched evaluation. It also specifies how autoregressive LLMs are used as optimization policies in single- and multi-turn settings.

3.1 Black-box optimization

  • Black-box optimization seeks to maximize an objective over a search space that may be continuous or discrete.Source: §3.1 · p. 2
  • When the optimum is known, instantaneous regret measures the gap from it, while simple regret is the minimum instantaneous regret across the trajectory.Lower simple regret is better.Source: §3.1 · p. 3

3.2 LLMs for black-box optimization

  • An autoregressive LLM acts as a policy that proposes individual points or batches; multi-turn use keeps one conversation so the model can reflect on prior reasoning.The study compares Sonnet 4.6, Opus 4.8, and Opus 5 in single- and multi-turn settings.Source: §3.2 · p. 3

4 Experimental design

The experimental design tests frontier LLMs on synthetic continuous functions and discrete molecular-oracle tasks. It controls evaluation budgets and varies batch size, task transformations, and interaction settings.

4.1 Synthetic optimization tasks

  • Synthetic evaluations use five classical test functions with known optima, normalized to [0, 1]^d and framed as maximization tasks.The LLMs are tested in single- and multi-turn settings with batch sizes q = 1, 2, 4.Source: §4.1 · p. 3
  • Disguised synthetic variants compose domain-axis permutation, independent flips, and power warps, then apply an affine transformation to the output.The domain transformation shifts the optimum’s location without changing the objective value at the optimum.Source: §4.1 · p. 3
  • Methods are compared against GP-EI and random search at matched batch sizes and sample budgets, using simple regret across five random seeds.The total budget is N = 120, with 2d initial points and trajectory length N/q.Source: §4.1 · p. 3

4.2 Molecular optimization tasks

  • Molecular evaluations use PMO’s discrete SMILES tasks and deterministic oracles; all three LLMs are tested on 23 oracles with a budget of 210 evaluations.The comparison uses Top-10 AUC, emphasizing sample efficiency, and Top-10 mean.Source: §4.2 · pp. 3–4

5 Results

Frontier reasoning LLMs can rival classical optimization on synthetic functions, but results vary with task transformations, dimensionality, and batch size. On molecular optimization, they perform strongly against specialist methods, though performance and sample efficiency vary by task and comparator.

5.1 Optimization on synthetic test functions

  • Opus 5 multi-turn outperformed GP-EI on most synthetic tasks, but its regret often worsened as batch size increased.GP-EI remained consistent across batch sizes; the increase was especially noticeable for Hartmann-3.Source: Figure 1 · p. 4, §5.1 · p. 4
  • Disguising domains and ranges hurt Opus 5, especially on higher-dimensional Hartmann-6, Ackley, and Rastrigin, where it no longer reached zero regret.For lower-dimensional Branin and Hartmann-3, performance on disguised tasks remained comparable to plain variants.Source: §5.1 · pp. 4–5
  • Plain-task trajectories showed rapid regret decreases that were absent on disguised tasks, consistent with the model recognizing function topology and using it to refine optimization.For simpler functions, the model could still recall some shape information despite disguise.Source: §5.1 · p. 5

5.2 Molecular optimization on PMO

  • Opus 5 was best on 17 of 23 PMO oracles by Top-10 AUC and 20 of 23 by Top-10 mean.The comparison covers all 23 oracles.Source: §5.2 · p. 6
  • Against specialist methods, Opus 5 was competitive at low budgets but fell behind GenMol, MolLEO, and ExLLM on selected tasks.GenMol won Top-10 AUC on 13 of 23 oracles; at budget 210, mean Top-10 mean was 0.590 for GenMol, 0.596 for Opus 5, and 0.738 for ExLLM.Source: §5.2 · p. 6
  • ExLLM matched Opus 5 performance with at most 1× the oracle calls on all four selected tasks, while other methods sometimes needed 20–40 times as many calls or never matched it.GenMol and MolLEO were also more sample-efficient than Opus 5 on the selected isomer task.Source: §5.2 · p. 7, Figure 5 · p. 8

6 Conclusion

The paper finds that frontier reasoning LLMs are brittle but competitive on continuous synthetic tasks, while performing strongly in discrete molecular optimization. Their molecular results are achieved without additional tuning or scaffolding, but specially trained or highly structured strategies can outperform them.

6 Conclusion

  • LLMs are competitive with GP-EI on synthetic test functions, but performance depends on batch size, dimensionality, and task transformation.The conclusion characterizes numerical optimization performance as brittle.Source: §6 · p. 8
  • On molecular optimization, LLMs are highly performant and sample-efficient, beating bespoke methods without additional tuning or problem scaffolding.They underperform only against specially trained or highly structured strategies.Source: §6 · p. 8
  • The authors identify additional numerical and discrete formulations and training protocols for open-weight reasoning LLMs as future directions.Source: §6 · p. 8

A Results on synthetic test functions

The synthetic benchmark uses classical test functions with plain and disguised variants. Runs use normalized unit-cube coordinates, and the disguised variant hides the optimizer while preserving dimensionality and optimal value.

A Results on synthetic test functions

  • Runs search the normalized unit cube [0, 1]^d, with Hartmann already defined there and Ackley and Rastrigin origins mapped to the cube center.Source: §A.1 · p. 14
  • Branin’s three equivalent global minimizers map to approximately (0.124, 0.818), (0.543, 0.152), and (0.962, 0.165) in the unit cube.Source: §A.1 · p. 14
  • The benchmark includes plain functions and disguised twins that hide the optimizer while preserving dimensionality and optimal value.Source: Table A1 · p. 14

A.2 Full results for synthetic optimization tasks

The appendix provides full synthetic-task comparisons across batch sizes, methods, and LLM protocols for plain and disguised tasks. It reports regrets in scientific notation, including exact-zero results up to machine precision.

A.2 Full results for synthetic optimization tasks

  • Tables A2 and A3 report final simple regret for every batch size q, arm, and LLM protocol on plain and disguised synthetic tasks.The tables cover q = 1, 2, 4 and matched budgets.Source: §A.2 · p. 14, Table A2 · p. 15, Table A3 · p. 16
  • Scientific notation preserves zero-regret results up to machine precision, which the LLMs can attain by emitting Ackley and Rastrigin analytical optima.Source: §A.2 · p. 14
  • The comparison uses 120/q batches, with lower regret better and bold marking the best arm for each task at that batch size.Source: §A.2 · p. 15, Table A3 · p. 16

A.3 Analysis of LLM memorization on synthetic tasks

Reasoning traces show that recalling a synthetic function can coincide with improved proposals. The regret reduction is stronger for plain tasks than for disguised variants, which require more genuine optimization.

A.3 Analysis of LLM memorization on synthetic tasks

  • For plain tasks, regret relative to the turn before function recall tends to drop by several orders of magnitude around recall.The analysis pools three models in multi-turn mode with q = 1; n marks detected recall events.Source: §A.3 · p. 17, Figure A1 · p. 17
  • After domain and range transformations, regret declines more slowly following recall; Branin still shows some benefit, but less than in the plain case.Source: §A.3 · p. 17
  • The authors interpret the disguised-task pattern as evidence that disguise forces genuine optimization even when pretraining recall remains helpful.Source: §A.3 · p. 17

B.1 Comparison to non-reproducible methods

At a 210-call budget, Opus 5 multi-turn reached 66% of LICO’s average Top-10 AUC using 21% of its oracle budget, and 64% of GP-MoLFormer-SIM’s using 2.1%. The comparison covers all 23 PMO oracles.

B.1 Comparison to non-reproducible methods

  • At 210 calls, Opus 5 multi-turn achieved 66% of LICO’s average Top-10 AUC with 21% of LICO’s oracle budget.LICO was evaluated at 1,000 calls.Source: §B.1 · p. 17
  • At 210 calls, Opus 5 multi-turn achieved 64% of GP-MoLFormer-SIM’s average Top-10 AUC with 2.1% of its oracle budget.GP-MoLFormer-SIM was evaluated at 10,000 calls.Source: §B.1 · p. 17
  • Both average comparisons were calculated across the 23 PMO oracles.The authors present the budget differences as evidence of the LLM’s strength as an optimization prior.Source: §B.1 · p. 17

B.2 Comparison between LLMs on PMO tasks

The appendix gives per-oracle tables for the three frontier LLMs in single- and multi-turn modes, alongside comparisons of Opus 5 multi-turn with LICO and GP-MoLFormer-SIM.

B.2 Comparison between LLMs on PMO tasks

  • Tables A6 and A7 provide per-oracle results for all three frontier LLMs in single- and multi-turn modes across the 23 PMO oracles.The tables report Top-10 AUC and Top-10 mean, respectively, at a 210-call budget; values are means ±1 SE over five seeds.Source: §B.2 · p. 17, Table A6 · p. 19, Table A7 · p. 19
  • Tables A4 and A5 compare Opus 5 multi-turn Top-10 AUC with LICO and GP-MoLFormer-SIM.Their captions specify error bars of ±1 standard deviation over five seeds.Source: Table A4 · p. 18, Table A5 · p. 18
  • Top-10 AUC is the area under the running Top-10 mean curve through 210 oracle calls, while Top-10 mean is the mean score of the 10 best molecules found within that budget.For both metrics, higher values are better, and the tables identify the best arm for each oracle.Source: Table A6 · p. 19, Table A7 · p. 19

B.3 Full results for molecular optimization tasks in PMO

The appendix lays out Opus 5 multi-turn results against the full PMO method panel and illustrates the prompts used for synthetic optimization and molecular generation. It reports Top-10 AUC and Top-10 mean at 210 calls, plus the oracle-call budget other methods need to reach the LLM’s Top-10 mean.

B.3 Full results for molecular optimization tasks in PMO

  • Tables A8–A16 compare Opus 5 multi-turn with 33 other methods across all 23 PMO oracles.The 34-method panel is split into three parts, with methods ranked by macro-average Top-10 AUC; Opus 5 multi-turn is repeated as a reference.Source: §B.3 · p. 20, Table A8 · p. 21, Table A9 · p. 22
  • Tables A8–A10 report Top-10 AUC@210, with each oracle-method cell giving mean ±1 SE over seeds.The tables also report macro-averages and the number of oracles each method wins.Source: §B.3 · p. 20, Table A8 · p. 21, Table A9 · p. 22
  • Tables A11–A13 report Top-10 mean@210, and Tables A14–A16 show the oracle-call budget fold needed for other methods to reach Opus 5’s Top-10 mean@210.For the fold measure, lower is more sample efficient; a dash means the method did not reach the LLM’s level within its run.Source: §B.3 · p. 20, Table A11 · p. 24, Table A12 · p. 25
  • The example prompts show stateful optimization: models receive prior measurements, the current best, and remaining budget before proposing new candidates.The synthetic prompt asks for points in a normalized continuous search space, while the molecular prompt asks for new molecules as SMILES.Source: §B.3 · pp. 30–31
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