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Agentic Resource Allocation for Batch Multi-Objective Bayesian Optimization in Autonomous Materials Discovery

Robert Robinson, Shakti Prasad Padhy, Sushant Sinha, Sk Md Ahnaf Akif Alvi, Juan Florez Coronel, Brent Vela, Trevor Hastings, Douglas Allaire, Raymundo Arróyave

arXiv:2610.04134v1cond-mat.mtrl-scics.AIcs.LG

TL;DR

Fixed BO policies have limited capacity to adapt when resource constraints change during multi-objective materials campaigns. This paper adds an LLM-guided allocation layer to batch MOBO and evaluates it on two alloy-design problems. Mixed allocations substantially increase cumulative mutual information over qEHVI, with the reported hypervolume and AUC-HV costs varying by system.

  • Problem

    BO workflows often rely on fixed or manually tuned strategies despite changing campaign goals, budgets, and timelines that make exploration–exploitation balance non-stationary.

    Source: §1 · p. 2

  • Method

    An LLM-guided layer selects among structured batch allocation policies using optimization-state summaries, while conventional MOBO components model outcomes and select candidates.

    Source: §1 · p. 3

  • Results

    Adaptive-β accumulated approximately 37% more cumulative MI than qEHVI in the RHEA baseline and approximately 49% more in the Fe-Co-Ni magnet problem, with the reported hypervolume and AUC-HV comparisons differing by system.

    Source: §5 · p. 24

  • Takeaways & Limitations

    Mixed allocations trade AUC-HV and convergence speed for greater uncertainty reduction around the Pareto front, while downstream value for materials analysis remains unmeasured.

    Source: §4 · p. 22

    Both LLM strategies used optimization statistics without prior knowledge of the materials systems, so early allocations lacked composition–objective knowledge.

    Source: §5 · p. 25

Abstract

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The discovery and development of advanced materials is a challenging process constrained by the high time and monetary costs of synthesis, processing, and characterization. The underlying design spaces can be enormous, often with multiple competing objectives. Bayesian optimization (BO) provides a principled approach for efficiently navigating such spaces, but most workflows rely on fixed exploration-exploitation policies that lack the capacity to adapt to shifting constraints in dynamic campaigns typical of self-driving laboratories. In this work, we develop a multi-objective BO framework for alloy design under resource constraints, benchmarking strategies for adaptive policy tuning at each iteration. Our evaluation covers a septenary refractory high-entropy alloy (RHEA) system focused on maximizing melting temperature and minimizing density, and an Fe-Co-Ni-based soft magnetic alloy system targeting saturation magnetization, coercivity, and hardness. We compare an exploitation-focused strategy, a fixed mixed exploratory/exploitative policy, and two distinct LLM-based adaptive strategies with different approaches to batch allocation and campaign signal interpretation, evaluated across baseline and mid-campaign resource event conditions including budget reductions, timeline cuts, and combined disruptions. Our results show that mixed allocation strategies accumulate substantially more mutual information than the exploitation-focused baseline at a proportionally smaller cost to hypervolume and optimization speed, with adaptive strategies outperforming a fixed-mixed allocation policy by adjusting their allocation in response to both evolving campaign statistics and resource constraints. These findings suggest that adaptive resource allocation offers a favorable tradeoff for materials discovery campaigns in reducing predictive uncertainty on Pareto-optimal compositions.

1. Introduction

Autonomous materials discovery uses closed-loop modeling and experimentation to navigate costly, multi-objective design spaces, but campaign constraints can change while fixed BO policies assume stable conditions. The paper proposes an LLM-guided policy-selection layer for batched MOBO and evaluates it in alloy-design campaigns under resource disruptions.

1. Introduction

  • Self-driving laboratories use iterative surrogate updates and acquisition functions to recommend informative experiments balancing exploration and exploitation.MOBO is established in materials and chemical sciences for expensive, noisy, data-scarce experiments with multiple objectives.Source: §1 · p. 2
  • Fixed BO strategies assume stable conditions, while real campaigns face changing goals, budgets, and timelines that make exploration–exploitation balance non-stationary.The gap is especially pronounced in batched, multi-objective settings with parallel allocations and finite resources.Source: §1 · p. 2
  • Prior LLM work spans literature and planning assistance, language-based BO inputs, and acquisition-function selection, but evidence for LLMs as adaptive policy controllers in dynamic multi-objective campaigns remains limited.The paper frames the gap as policy selection rather than candidate generation alone.Source: §1 · pp. 2–3
  • The framework uses an LLM agent to select structured exploration–exploitation allocation policies from optimization-state summaries, while conventional MOBO components handle modeling and candidate selection.Signals include campaign history, estimated hypervolume improvement, information gain, and remaining budget and time.Source: §1 · p. 3, Figure 1 · p. 4
  • The evaluation tests two discrete alloy-design optimization problems under simulated mid-campaign disruptions, including budget reductions and shortened timelines.The comparison includes an exploitation-focused qEHVI baseline and a deterministic fixed mixed-allocation strategy.Source: §1 · p. 3

2. Methods

The framework combines ground-truth alloy proxies, batch multi-objective Bayesian optimization, and a resource-allocation layer that selects exploration–exploitation policies under changing constraints. It evaluates two alloy design problems across fixed and adaptive allocation strategies.

2.1. Test Problems: Alloy Composition Optimization

  • The Fe-Co-Ni-based soft-magnetic problem maximizes saturation magnetization and hardness while minimizing coercivity; the septenary RHEA problem maximizes melting temperature and minimizes density.The soft-magnetic task has three objectives, while the RHEA task has two.Source: §2.1 · pp. 4–5

2.2. Ground Truth Models

  • Ground-truth random forests serve as deterministic experiment proxies; test R² values are 0.97 for Ms, 0.91 for log Hc, 0.77 for log HV, 0.89 for Tm, and 0.93 for ρ.The lower log HV accuracy reflects scatter in hardness measurements, while the models capture broad trends for strategy comparisons.Source: §2.2 · p. 5, Figure 2 · p. 6

2.3. Batch Multi-Objective Bayesian Optimization (MOBO) Engine

  • At each iteration, the engine fits a GP, builds batches from qEHVI exploitation and qUCB exploration, selects one batch, evaluates it, and updates resource state.A distance bonus steers qUCB candidates away from qEHVI selections.Source: §2.3 · pp. 6–7

2.4. Resource Allocation Layer

  • The allocation layer constructs q+1 mixtures of qEHVI and qUCB, then supplies each option’s expected hypervolume improvement and mutual information to the allocator.EHVI represents expected Pareto-front improvement; MI measures expected uncertainty reduction about the Pareto-optimal region.Source: §2.4 · pp. 7–8

2.5. Resource Allocation Strategies

  • qEHVI always exploits, Fixed Mixed follows a remaining-resource schedule, Rule-Swap explores in response to crowding or stagnation, and Adaptive-β weighs broader campaign signals.Adaptive-β uses HV velocity, MI change, Pareto-front composition ranges, and a rolling history; agents are notified of resource events.Source: §2.5 · pp. 9–10

2.6. Experimental Design

  • Campaigns share seed-specific initial compositions across strategies and run for 25 seeds; event conditions reduce resources mid-campaign, and evaluation tracks normalized hypervolume, AUC-HV, and cumulative MI.The initial sample size is 15 compositions for Fe-Co-Ni and 5 for RHEA; event campaigns can terminate when a constraint is exhausted.Source: §2.6 · pp. 10–11, Table 2 · p. 11

3. Results

Across two alloy landscapes, optimization outcomes and agent decisions varied with system difficulty and resource events. Mixed-allocation strategies gained substantially more information than qEHVI at a smaller proportional cost to optimization speed, while adaptive strategies adjusted β or exploration allocation under constraints.

3.1. Design Space and Objective Space Structure

  • RHEA has a compact, smooth Pareto front, whereas Fe-Co-Ni has a larger, fragmented front with distinct clusters.The contrasting landscapes were selected to test allocation strategies across different optimization regimes.Source: §3.1 · pp. 11, 13, Figure 3 · p. 12

3.2. Baseline Optimization Performance

  • Adaptive-β gained roughly 37% more cumulative information than qEHVI over 55 RHEA iterations and 49% more over 50 Fe-Co-Ni iterations.At baseline, qEHVI had the highest RHEA AUC-HV (52.02 ± 0.08), while Fe-Co-Ni strategies had no statistically distinguishable final hypervolume differences.Source: §3.2 · pp. 13, 15, Figure 4 · p. 14
  • Across all eight configurations, mixed-allocation strategies gained substantially more cumulative MI than qEHVI without outperforming it in final hypervolume or AUC-HV.Figure 5 places every mixed-allocation strategy above the equal-trade line comparing information gained with convergence speed given up.Source: Figure 5 · p. 15

3.3. Optimization Performance Under Time and Budget Constraints

  • Under RHEA budget and time cuts, qEHVI led in final hypervolume while Adaptive-β led in MI; dual-event compression changed the hypervolume ordering, whereas Fe-Co-Ni outcomes remained largely indistinguishable.Across RHEA budget and time events, all mixed-allocation strategies significantly exceeded qEHVI in MI; Figure 6 shows event timing alongside hypervolume trajectories.Source: §3.3 · pp. 15, 17, Figure 6 · p. 16

3.4. Convergence to Milestone Hypervolume Thresholds

  • All strategies reached RHEA’s 50% milestone in 2.0–2.4 batches; qEHVI reached 90% fastest in baseline, budget, and time cases, while dual-event compression narrowed Fixed Mixed’s gap.In the dual event, Fixed Mixed reached 90% in 7.8 ± 0.2 batches, while Adaptive-β coverage fell to 88%.Source: §3.4 · pp. 17, 19, Table 3 · p. 18
  • Fe-Co-Ni’s 80% milestone was reached by 92–96% of seeds at baseline, but only 28–64% under resource events, with no consistent strategy ordering.The fragmented design space and campaign truncation made event-condition milestone comparisons unreliable.Source: Table 3 · p. 18, §3.4 · p. 19

3.5. β Coefficient Trajectories Under Baseline and Event Conditions

  • Rule-Swap β stayed near 2.5, while Adaptive-β rose through mid-campaign; only RHEA’s dual event drove β above its baseline trajectory.In RHEA budget and time events, Adaptive-β’s post-event β tracked baseline values at matching iterations, suggesting the events advanced the campaign clock.Source: §3.5 · pp. 19–20

3.6. Constraint Influence on Decision Making

  • Rule-Swap reduced exploration slots after every event, whereas Adaptive-β mostly held allocations steady except under RHEA time cuts.Adaptive-β treated a time constraint as a more direct reason to reduce exploration than a budget constraint; it showed no significant allocation change in Fe-Co-Ni events.Source: §3.6 · pp. 20, 22, Figure 8 · p. 21

4. Discussion

Across both alloy systems, mixed strategies gained more mutual information without outperforming qEHVI in final hypervolume or AUC-HV. Resource events mainly changed strategy comparisons in shortened campaigns, where history-dependent allocation could struggle when too little campaign history had accumulated.

4. Discussion

  • Across both alloy systems, mixed strategies accumulated more cumulative MI, but none beat qEHVI in final hypervolume or AUC-HV; all 24 tradeoffs favored information gain.The median ratio of proportional information gained to proportional AUC-HV given up was roughly 28, with no configuration below 3; Adaptive-β accumulated the most MI and qEHVI the least.Source: §4 · p. 22
  • Whether greater mutual information produces practically useful downstream records for objective refinement or follow-on campaigns was not measured.Source: §4 · p. 22
  • Single resource events left 90%-hypervolume milestone counts within one batch of baseline, with only a few significant Fe-Co-Ni strategy differences.Under a budget event, Adaptive-β exceeded Fixed Mixed in final hypervolume, qEHVI led Fixed Mixed in AUC-HV, and under a time event Rule-Swap led Fixed Mixed in AUC-HV.Source: §4 · p. 23
  • In RHEA event campaigns, Fixed Mixed’s AUC-HV gap widened while Adaptive-β retained its cumulative-MI lead over qEHVI under every event condition.Rule-Swap compressed its end-of-campaign exploration allocation; Adaptive-β stayed near baseline under budget constraints and reduced allocation more under time constraints.Source: §4 · p. 23
  • After two events cut RHEA to ten iterations, Adaptive-β finished below qEHVI and Fixed Mixed in final hypervolume, reversing its baseline statistical tie with Fixed Mixed.Adaptive-β finished at 0.9341 ± 0.00602, versus 0.9486 ± 0.00318 for qEHVI and 0.9488 ± 0.00216 for Fixed Mixed; three seeds failed to reach the 90% threshold.Source: §4 · p. 23
  • Both LLM strategies advanced their allocation trajectories after resource events rather than changing their overall patterns; Adaptive-β’s beta trajectory ramped early and then cycled downward.Rule-Swap maintained beta near 2.5 and reduced exploration candidates near campaign end; Adaptive-β averaged approximately 1.5 exploration candidates per batch.Source: §4 · pp. 23–24
  • Budget cuts and timeline cuts produced similar beta trajectories, while Adaptive-β selected fewer candidates under time constraints than budget cuts.Adaptive-β selected 1.00 ± 0.09 versus 1.36 ± 0.06 candidates per batch; Rule-Swap’s allocation was 0.59 ± 0.06 under budget constraints and 0.58 ± 0.05 under time constraints.Source: §4 · p. 24
  • The agents used optimization statistics only, limiting their behavioral range; material-family prior information could improve early allocation before enough campaign history accumulates.Source: §4 · p. 24

5. Conclusion

Across two alloy design problems and eight resource conditions, mixed allocation strategies gained more cumulative mutual information than they lost in hypervolume and AUC-HV relative to qEHVI. Adaptive policies responded to campaign statistics and resource events, while the framework’s LLM agents lacked prior materials-system knowledge.

5. Conclusion

  • 37% more cumulative MI than qEHVI (19.54 ± 0.41 versus 14.23 ± 0.45 nats) left Adaptive-β within 0.2% in final hypervolume and 0.8% in AUC-HV in the RHEA baseline.In the Fe-Co-Ni magnet problem, Adaptive-β accumulated approximately 49% more MI than qEHVI at no measurable cost in optimization performance; Rule-Swap and Fixed Mixed fell between these values in the same ordering across both systems.Source: §5 · p. 24
  • Exploration-biased campaigns acquired a more informative characterization of the Pareto-front neighborhood even when optimization convergence appeared uniform.The practical value described is the experimental record’s downstream utility for objective refinement and follow-up work.Source: §5 · p. 24
  • Adaptive policies outperformed Fixed Mixed in responding to evolving campaign statistics and mid-campaign resource events, advancing their allocation trajectory without changing the underlying strategy.Fixed Mixed’s predetermined exploration schedule could not be revised for shortened campaigns.Source: §5 · p. 24
  • Both LLM-based strategies used optimization statistics and remaining resources but had no prior knowledge of the materials system or composition–objective relationships.Consequently, early-campaign allocation decisions were made without that materials knowledge.Source: §5 · p. 25
  • Agents equipped with materials-system prior information could direct early sampling toward composition regions more likely to yield Pareto-relevant candidates.This proposed direction would extend their influence beyond choosing among acquisition-function suggestions.Source: §5 · p. 25
  • Whether the mutual-information advantages translate into measurable Pareto-front prediction accuracy remains an open question.The paper concludes that LLM agents can serve as structured, beneficial high-level controllers in multi-objective campaigns with evolving constraints.Source: §5 · p. 25

Conflicts of interest

The authors declare no conflicts of interest.

Conflicts of interest

Appendix A.1. The ARMOTE-MO Workflow

ARMOTE-MO automates multi-output regression by searching hyperparameters, selecting a non-dominated configuration, refitting the model, and returning held-out test performance.

Appendix A.1. The ARMOTE-MO Workflow

  • ARMOTE-MO is an automated multi-output regression workflow with multi-objective hyperparameter optimization.Source: Appendix A.1 · p. 30
  • The workflow splits data 80/20, standardizes inputs and outputs using training-set scalers, and evaluates 100 Tree-Parzen Estimator trials with five-fold cross-validation.Each trial records mean standardized-target MSE and mean R2 averaged across outputs.Source: Appendix A.1 · p. 30
  • It selects the non-dominated configurations in MSE–R2 space, chooses the one with the highest cross-validated mean R2, and refits on all standardized training data.Source: Appendix A.1 · p. 30
  • The workflow returns the model, fitted scalers, and held-out test R2 per output and averaged across outputs in original target units.Source: Appendix A.1 · p. 30

Appendix A.2. Hyperparameter Search Spaces

Table A.4 reports inclusive hyperparameter search ranges for both alloy systems; other random forest settings remain at scikit-learn defaults.

Appendix A.2. Hyperparameter Search Spaces

  • Table A.4 gives inclusive ARMOTE-MO hyperparameter search ranges for both alloy systems; other random forest settings use scikit-learn defaults.The selected configurations are reported in Table 1.Source: Table A.4 · p. 30

Appendix A.3. Truth-Function Generated Datasets

Appendix B describes two-call prompt pipelines for LLM resource allocation, with separate procedures for Adaptive-β and Rule-Swap agents and instructions for handling resource events.

Appendix B. Prompts Used by the LLM Allocation Agents

  • The two LLM allocation strategies use separate two-call prompt pipelines, with dynamic campaign quantities inserted into the prompts.The prompts use GPT-4o through LangChain; campaign temperatures differ between RHEA and Fe-Co-Ni campaigns.Source: Appendix B · p. 30

Appendix B.1. Adaptive-β Agent Prompts

  • Adaptive-β selects β from campaign-state and optimization signals, then chooses among batch options trading qEHVI improvement for qUCB information gain.The prompts include hypervolume velocity, mutual information, Pareto coverage, and recent history; they caution that elevated β is unreliable early when the GP posterior is poorly constrained.Source: Appendix B.1 · pp. 31–32

Appendix B.2. Rule-Swap Agent Prompts

  • Rule-Swap assesses hypervolume-per-point trends on qEHVI-primary iterations, distinguishing crowding, stagnation, and healthy expansion before selecting an allocation.It treats low gains during deliberate exploration as expected, accounts for a one-iteration lag, and favors exploitation when few iterations remain.Source: Appendix B.2 · p. 33

Appendix B.3. Event Handling in Agent Prompts

  • Resource events enter the prompts through campaign-state and remaining-iteration fields, and Rule-Swap is told to use the event-adjusted iteration estimate.Source: Appendix B.3 · p. 34

Appendix C.1. Per-Experiment Cumulative Mutual Information

Table C.5 reports cumulative mutual information, final normalized hypervolume, and area under the hypervolume curve across systems, experiments, and strategies.

Appendix C.1. Per-Experiment Cumulative Mutual Information

  • Table C.5 covers every system, experiment, and strategy.Source: Table C.5 · p. 34
  • The reported measures are cumulative mutual information, final normalized hypervolume, and area under the hypervolume curve.Source: Table C.5 · p. 34
  • Values are summarized as mean ± SEM over 25 seeds.Source: Table C.5 · p. 34

Appendix C.2. Pairwise Significance Tests

Table C.6 gives pairwise strategy tests for three outcomes, using matched seeds and uncorrected two-sided paired Wilcoxon signed-rank tests.

Appendix C.2. Pairwise Significance Tests

  • The comparisons use two-sided paired Wilcoxon signed-rank tests on per-seed differences.Source: Appendix C.2 · p. 35
  • Each comparison pairs strategies across 25 shared random seeds, matching their initial designs and random states.Source: Appendix C.2 · p. 35
  • The 144 tests across six strategy pairs, three metrics, and eight experiments are uncorrected, so near-0.05 p-values are descriptive rather than confirmatory.Table C.6 reports final normalized hypervolume, AUC-HV, and cumulative mutual information.Source: Appendix C.2 · p. 35, Table C.6 · p. 36

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