Hyper Algorithm Design Agent: Evolving Learnable Optimizer from Zero

Zipei Yu; Yue-Jiao Gong; Zeyuan Ma; Yuncheng Jiang; Zhiguang Cao

cs.AISep 28, 2026

Hyper Algorithm Design Agent: Evolving Learnable Optimizer from Zero

Authors: Zipei Yu, Yue-Jiao Gong, Zeyuan Ma, Yuncheng Jiang, Zhiguang Cao

Organizations: South China University of Technology · South China Normal University · Singapore Management Univeristy

Abstract

Meta-Black-Box Optimization (MetaBBO) is one of the highlights in the recent AI for Optimization trend. This paradigm's bi-level workflow leverages the learnable algorithm design policy at meta level to ensure the performance and generalization improvement on the low-level optimization task. While MetaBBO helps advance the performance lower bound of the resulted optimization system, it is currently handcrafted and customized case by case to adapt different optimization problems, which inevitably introduces inherent subjectivity and hence restricts the performance upper bound and usability in practice. In this paper, we address this issue by regarding MetaBBO's design loop as coding task, where we could introduce openendedness into MetaBBO with recursive self-improvement capability of advanced coding agents. Specifically, we propose a dual-agent framework: i) a task agent continuously refines the codebase of a target MetaBBO approach through code evolution; ii) a hyper agent progressively modifies the task agent and itself to provide open-ended design behavior; iii) the evolved MetaBBO codebase is evaluated and all in-execution information is fed back to the agents for recursive self-referential improvement. As a result, given a naive MetaBBO template, our framework automates a design evolution and finds novel variants superior to up-to-date human-made MetaBBO baselines. Surprisingly, the experimental results also demonstrate that our framework supports fast adaption across different optimization domains. Solid interpretation analysis further reveals interesting design principles emerge in such open-ended process. This work serves as the first exploration on automating design of complex learning-assisted optimization algorithms.

Figures & tables

Figure 1: Left : The general workflow of our proposed HADA framework, which allows coordination between hyper agent and task agent for automatic MetaBBO design. Right : Essential differences between human-based design in BBO/MetaBBO and fully automated design in HADA.

	Method	$f_{3}$	$f_{4}$	$f_{6}$	$f_{7}$	$f_{9}$	$f_{13}$	$f_{14}$	$f_{16}$
BBO	DE	0.8773 $\pm$ 0.0355	0.9068 $\pm$ 0.0181	0.9999 $\pm$ 0.0000	0.9706 $\pm$ 0.0073	0.9997 $\pm$ 0.0001	0.9636 $\pm$ 0.0101	0.9981 $\pm$ 0.0006	0.4208 $\pm$ 0.0968
	SHADE	0.8639 $\pm$ 0.0403	0.8898 $\pm$ 0.0186	0.9999 $\pm$ 0.0000	0.9884 $\pm$ 0.0047	0.9998 $\pm$ 0.0001	0.9810 $\pm$ 0.0073	0.9990 $\pm$ 0.0003	0.4201 $\pm$ 0.1345
	JDE21	0.9705 $\pm$ 0.0110	0.9756 $\pm$ 0.0084	0.9999 $\pm$ 0.0000	0.9844 $\pm$ 0.0051	0.9997 $\pm$ 0.0001	0.9887 $\pm$ 0.0045	0.9992 $\pm$ 0.0006	0.4619 $\pm$ 0.1208
	MADDE	0.8892 $\pm$ 0.0261	0.9151 $\pm$ 0.0208	1.0000 $\pm$ 0.0000	0.9872 $\pm$ 0.0045	0.9997 $\pm$ 0.0001	0.9814 $\pm$ 0.0049	0.9967 $\pm$ 0.0014	0.6200 $\pm$ 0.1116
	CMAES	0.9652 $\pm$ 0.0254	0.9665 $\pm$ 0.0074	1.0000 $\pm$ 0.0000	0.9993 $\pm$ 0.0011	0.8289 $\pm$ 0.1400	0.9999 $\pm$ 0.0001	1.0000 $\pm$ 0.0000	0.5169 $\pm$ 0.1912
MetaBBO	RL-DAS	0.9362 $\pm$ 0.0104	0.9098 $\pm$ 0.0167	1.0000 $\pm$ 0.0000	0.9971 $\pm$ 0.0006	0.9999 $\pm$ 0.0000	0.9452 $\pm$ 0.0040	0.9970 $\pm$ 0.0013	0.6296 $\pm$ 0.0596

Table 1: Final performance on held-out BBOB functions (1/2). Each cell reports the mean

\pm

standard deviation over independent runs. Column bests are shaded and bold; runners-up are underlined.

	Method	$f_{17}$	$f_{18}$	$f_{19}$	$f_{20}$	$f_{21}$	$f_{22}$	$f_{23}$	$f_{24}$	Avg.
BBO	DE	0.9338 $\pm$ 0.0178	0.9095 $\pm$ 0.0143	0.7691 $\pm$ 0.0256	0.9999 $\pm$ 0.0000	0.9041 $\pm$ 0.0575	0.9386 $\pm$ 0.0742	0.4811 $\pm$ 0.1418	0.7134 $\pm$ 0.0275	0.8618 $\pm$ 0.0141
	SHADE	0.8935 $\pm$ 0.0309	0.8983 $\pm$ 0.0207	0.7686 $\pm$ 0.0330	0.9999 $\pm$ 0.0000	0.9322 $\pm$ 0.0579	0.9755 $\pm$ 0.0004	0.4063 $\pm$ 0.1562	0.7233 $\pm$ 0.0328	0.8594 $\pm$ 0.0132
	JDE21	0.8827 $\pm$ 0.0411	0.9157 $\pm$ 0.0405	0.7351 $\pm$ 0.0368	1.0000 $\pm$ 0.0000	0.9424 $\pm$ 0.0596	0.9726 $\pm$ 0.0063	0.4567 $\pm$ 0.0799	0.6997 $\pm$ 0.0315	0.8741 $\pm$ 0.0129
	MADDE	0.8541 $\pm$ 0.0407	0.8757 $\pm$ 0.0253	0.7887 $\pm$ 0.0294	0.9999 $\pm$ 0.0000	0.9963 $\pm$ 0.0060	0.9746 $\pm$ 0.0009	0.4601 $\pm$ 0.1062	0.6555 $\pm$ 0.0243	0.8748 $\pm$ 0.0138
	CMAES	0.9994 $\pm$ 0.0005	0.9990 $\pm$ 0.0006	0.0415 $\pm$ 0.0364	0.9999 $\pm$ 0.0000	0.9395 $\pm$ 0.0750	0.9602 $\pm$ 0.0454	0.5451 $\pm$ 0.1624	0.6221 $\pm$ 0.0314	0.8342 $\pm$ 0.0113
MetaBBO	RL-DAS	0.8955 $\pm$ 0.0074	0.8889 $\pm$ 0.0150	0.8188 $\pm$ 0.0148	1.0000 $\pm$ 0.0000	0.8635 $\pm$ 0.0438	0.9570 $\pm$ 0.026	0.4872 $\pm$ 0.2016	0.7172 $\pm$ 0.0229	0.8779 $\pm$ 0.0131

Table 2: Final performance on held-out set (2/2), last column denotes average across all.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Layer	Input Dim	Output Dim	Parameters
fc1	3	128	$3\times 128+128=512$
fc2	128	128	$128\times 128+128=16512$
fc3	128	128	$128\times 128+128=16512$
out	128	25	$128\times 25+25=3225$
Total	–	–	36761

Appendix

Table 3: Network architecture and parameter statistics of the DQN controller.

	Modifiable Policy		Initial Optimizer		LLM Backbone
	Yes	No	DE	PSO	Deepseek v4 pro	Kimi k3	Qwen3.7 Max	GPT 5.5	Grok 4
Score	0.9674	0.9039	0.9674	0.9421	0.9674	0.9542	0.9521	0.9617	0.9588
Std	$\pm$ 0.0078	$\pm$ 0.0033	$\pm$ 0.0078	$\pm$ 0.0134	$\pm$ 0.0078	$\pm$ 0.0058	$\pm$ 0.0069	$\pm$ 0.011	$\pm$ 0.0062

Appendix

Table 4: Ablation results on different parts in HADA.

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Large language models (LLMs) enable automated algorithm design (AAD) through reasoning and code synthesis. However, most existing LLM-based AAD methods separate algorithm design from target optimization, deploying a fixed design even as the optimization state evolves. Conventional adaptive optimizers can respond to such changes, but their adjustments remain confined to predefined parameters, operators, or strategies. To address these limitations, we introduce online LLM-based AAD, a novel optimization paradigm that treats the algorithm itself as a state-dependent decision variable. At each stage, LLM agents synthesize an algorithm with new behavior logic from the current optimization state. Executing the generated algorithm advances the search and provides feedback for subsequent designs, coupling algorithm design with target optimization without requiring a separate offline algorithm pretraining stage. To implement this paradigm, we propose OnDesign, a multi-agent framework that reconciles competing design perspectives to synthesize executable algorithms and uses execution feedback to refine how runtime evidence is interpreted for subsequent designs. We evaluate OnDesign across two mainstream black-box optimization paradigms on three scenarios: Bayesian optimization, evolutionary continuous optimization, and evolutionary mixed-variable optimization. Extensive experiments on six benchmark suites and one engineering problem across multiple problem dimensions demonstrate superior overall performance over conventional optimizers and offline LLM-based AAD methods.

Abstract

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