Strategist: Evolving Reasoning with Agents

Taiming Lu; Qi Xu; Zhigang Hua; Zhuang Liu

cs.AINov 2, 2026

Strategist: Evolving Reasoning with Agents

Authors: Taiming Lu, Qi Xu, Zhigang Hua, Zhuang Liu

Organizations: Princeton University · Meta

Abstract

A model is only half of an AI agent system. The other half is the inference strategy: the reasoning procedure that turns model calls into a response. Today that second half is written by hand, and the experience of building one strategy never carries to the next. We introduce Strategist, a meta-agent that evolves inference strategies across tasks. Each strategy is written as a blueprint,executable code that other strategies can reuse, and together the blueprints form a library. Given a task and a small development set, Strategist retrieves related blueprints, writes candidate strategies, tests them on real samples, and revises them from the results. Every candidate then enters the library, so later tasks build on earlier discoveries. On 30 benchmarks, Strategist beats the strongest baseline on 24 and matches its average accuracy (74.7% vs.74.0%) at 39% lower inference cost. Its strategies also transfer to unseen tasks and other models without further search. The part of an AI system that is not improved on its own now does.

Figures & tables

Figure 2: Strategy design is per task; Strategist makes it cumulative. By hand and in prior automated search, nothing carries between tasks. Strategist keeps every strategy in a library that the next task starts from.

Figure 3: The Strategy Blueprint is a freeform graph that grows through the library. (a) Two foundations ( chat and agent ) sit at the top. Strategies compose from them and from each other, forming a directed graph whose levels emerge naturally from composition depth. (b) Four protocols govern the graph: every node shares one abstract interface, each node can only call nodes created before it, no cycles are allowed, and no duplicates should exist.

Figure 4: Strategy blueprint captures reasoning structure. This simplified blueprint example defines the steps, control flow, and the model tier for each step. Prompts are not specified; filling in produces a runnable strategy.

Figure 5: The Strategist four-stage iterative pipeline. Each iteration: (1) Retrieve relevant blueprints and diverse inspiration from the Library; (2) Propose $K$ candidates as a mix of new , composed , and reuse blueprints paired with task-specific prompts; (3) Evaluate each candidate, seeing full traces on the training set and aggregated scores on validation; (4) Accumulate the underlying blueprints into the library with measurement cards and experience notes.

Math	AQuA-RAT ( Ling et al., 2017 )	Gaokao-Math ( Zhong et al., 2024 )	GSM8K ( Cobbe et al., 2021 )
	AIME 2024 (MAA, 2024 )	MATH500 ( Hendrycks et al., 2021b )	ASDiv ( Miao et al., 2020 )
	SVAMP ( Patel et al., 2021 )	MinervaM ( Lewkowycz et al., 2022 )
Commonsense	StrategyQA ( Geva et al., 2021 )	CommonsenseQA ( Talmor et al., 2019 )	PIQA ( Bisk et al., 2020 )
	HellaSwag ( Zellers et al., 2019 )	OpenBookQA ( Mihaylov et al., 2018 )	SIQA ( Sap et al., 2019 )
	COPA ( Roemmele et al., 2011 )	WinoGrande ( Sakaguchi et al., 2020 )	SciQ ( Welbl et al., 2017 )
	BoolQ ( Clark et al., 2019 )

Table 1: 40 benchmarks across seven task categories. We randomly select 30 for the main iterative search and hold out the remaining 10 for one-shot retrieval. Each benchmark is split into training, validation, hidden, and test sets.

Figure 6: Ours among all 108 baseline cells (accuracy vs weighted cost per sample, test set). Each small marker is one baseline cell (a baseline strategy at one model tier and mode); the star is Strategist ’s strategy. BL, the comparison point, is the cell chosen on the training split (Figure 7 ). The highest marker in a panel is the best of 108 cells chosen by looking at the test results , which no method can do in advance; it is shown for context, not as the comparison point. Appendix Figure 10 shows the same view on the training split, where the bias runs the other way. Against BL, Ours is more than 2% cheaper on 26 of 30 benchmarks and within 2 accuracy points or better on 28.

Figure 7: Per-benchmark head-to-head: Strategist vs the baseline (BL) on the 30 main benchmarks. For each benchmark, test accuracy (%, left axis) and weighted cost per sample (log scale, right axis) of Ours and of BL. BL is the baseline cell (one of the

18\times 6

baseline–configuration pairs) that is most accurate on the benchmark’s training split, scored on the test set; Strategist ’s strategy is also chosen without seeing the test set, so this is the like-for-like comparison behind the win counts. Numbers above each pair are relative changes (green: improvement; grey: regression under 2%; orange: larger regression).

Table 8

Figure 8: An example reasoning strategy discovered by Strategist for the Amazon-Rec task. The strategy decomposes the task into a profile, signal extraction, conditional judge, merge, and audit stage. The structure and branch conditions were generated by the strategist, not by us.

Figure 9: Accuracy across data splits over the 10-iteration search loop. Each point is the mean accuracy of an iteration’s five candidates on a split. Bold curves are the mean across the 30 main benchmarks; faint background curves are individual benchmarks. The training–hidden gap stays between

1.2

and

2.5

points, not widening over iterations.

	Strategist variants			Other frameworks
Benchmark	full	no library	zero-shot	AFlow	ADAS	EvoFlow	StrategyLLM	AgentSquare
BBH	85.0	31.0	27.5	38.0	34.5	34.5	35.5	27.5
Gaokao-Math	94.5	65.5	81.5	84.0	82.0	86.5	89.5	82.5
LSAT-LR	82.0	81.0	71.5	81.0	74.5	75.5	77.0	73.5
LSAT-RC	81.5	75.0	38.0	74.5	75.5	75.0	74.5	74.0
SAT-Math	98.2	99.0	failed	99.0	96.9	96.9	97.9	97.9

Table 5: Ablations and cross-framework comparison on 10 benchmarks. Test accuracy (%); best per row bolded. External frameworks share the same meta-LLM and executor; “failed” is runtime crash.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Tier	Model	Parameters	Cost weight
fast	Qwen3-0.6B	$0.60$ B	$1.00\times$
balanced	Qwen3-1.7B	$1.70$ B	$2.83\times$
complex	Qwen3-4B	$4.00$ B	$6.67\times$

Appendix

Table 6: Tier cost weights used throughout the paper. Per-token weights are proportional to parameter counts, matching the leading

2N

FLOPs/token term for dense transformers ( Kaplan et al., 2020 ) .

Tier/mode	GPT-5 backend	Gemini-2.5 backend
fast/nothink	gpt-5-nano (effort=minimal)	gemini-2.5-flash-lite
fast/thinking	gpt-5-nano (effort=medium)	gemini-2.5-flash-lite (thinking)
balanced/nothink	gpt-5-mini (effort=minimal)	gemini-2.5-flash
balanced/thinking	gpt-5-mini (effort=medium)	gemini-2.5-flash (thinking)
complex/nothink	gpt-5 (effort=minimal)	gemini-2.5-flash
complex/thinking	gpt-5 (effort=medium)	gemini-2.5-flash (thinking)

Appendix

Table 7: Tier-mode mapping for cross-model transfer. GPT-5 uses three model sizes (nano/mini/full) crossed with two reasoning-effort levels (minimal/medium). Gemini-2.5 uses flash-lite for the fast tier and flash for the balanced and complex tiers; the API sets its own thinking budget, so the nothink and thinking modes issue the same call. Each strategy executes its own routing; only the tier-to-model mapping changes.

Field	Sample value
search_queries	“cite-then-extract on long context multi-hop”
	“self-consistency vote at fast tier with 3 samples”
	“multi-agent debate but only on questionable cases”
	“decomposition into sub-questions then aggregate”
experience (workflow, obs, rec)	self_consistency : “card shows +12pp on math/fast/nothink; blind matched at 11pp” / “use as cheap lift on short-math fast-tier; skip on commonsense.”
	multi_agent_debate : “2-agent fails by mutual-error agreement on 30% of NQ-Open misses” / “add a third tie-breaking agent or vote.”

Appendix

Table 8: Sampled search_queries and experience notes. The strategist writes both at every iteration; queries are the input to library retrieval, and experience notes are the writeback that next-iteration strategists (or strategists on a different task) read in the card.

Iter	Kind	Best candidate on hidden	Hidden Acc	Hidden Cost ( $k$ )
1	reference	baseline_cot (BL)	85.0	21.2
2	reuse	difficulty_routed_certificate_mcq	89.0	18.5
3	reuse	difficulty_routed_certificate_mcq	91.0	21.7
4	reuse	difficulty_routed_certificate_mcq	92.0	20.9
5	composed	intended_operation_commitment_cot_math	90.0	16.2
6	new	rotated_label_invariance_math	88.0	18.6

Appendix

Table 9: Iteration-by-iteration progression on AQuA-RAT. For each iteration, the candidate with the highest hidden-set accuracy and its weighted cost per sample; iteration 1 is the reference BL (CoT on complex/thinking ). The final strategy (bold, from iteration 5) beats BL on both validation and hidden (

+5

points at

0.77\times

cost on hidden); the iteration-4 candidate, the most accurate on hidden, is not picked because on validation it matches BL’s accuracy at

14\%

higher cost.

Benchmark	Ours Acc	BL Acc	$\Delta$ Acc	Ours Cost ( $k$ )	BL Cost ( $k$ )	$\Delta$ Cost	Result
SQuAD v2	79.1	73.2	$\uparrow$ 8.0%	5.6	25.0	$\downarrow$ 77.4%	Win
TruthfulQA	69.0	64.5	$\uparrow$ 7.0%	5.8	7.5	$\downarrow$ 21.9%	Win
2WikiMQA	76.5	72.5	$\uparrow$ 5.5%	33.8	98.6	$\downarrow$ 65.7%	Win
Amazon-Rec	28.0	24.0	$\uparrow$ 16.7%	45.6	70.3	$\downarrow$ 35.1%	Win
SAT-Math	98.2	94.5	$\uparrow$ 3.8%	4.9	12.1	$\downarrow$ 59.4%	Win
LSAT-AR	81.0	77.6	$\uparrow$ 4.4%	54.9	82.0	$\downarrow$ 33.0%	Win

Appendix

Table 10: Per-benchmark main results across 30 benchmarks. BL is the baseline cell (of the

18\times 6

matrix) with the highest accuracy on the benchmark’s training split, scored on the test set.

\Delta

values are relative changes; colors follow the 2-point accuracy and 2% cost tie bands. Result: Win = better on accuracy or cost and worse on neither; Mixed = better on one and worse on the other; Lose = worse on at least one and better on neither. Cost is weighted tokens per sample (parameter-count weights), in thousands.

Figure 10: The same view on the training split. As Figure 6 , but every baseline cell and Strategist ’s final strategy are scored on the benchmark’s training split (the rows the strategist sees) instead of the test set. This comparison is biased toward BL: BL is, by definition, the most accurate of the 108 cells on exactly these rows, so it sits at the top of each panel, while Strategist ’s strategy was chosen on the separate validation and hidden splits. Only the test set (Figure 7 , Figure 6 ) scores both on questions neither was chosen on, which is why the paper reports it.

Benchmark	Ours Acc	Ours Cost ( $k$ )	BL Acc	BL Cost ( $k$ )	$\Delta$ Acc	$\Delta$ Cost
ReCLor	83.5	47.4	85.0	72.0	$\downarrow$ 1.8%	$\downarrow$ 34.2%
SAT-EN	86.5	16.7	86.5	37.6	0.0%	$\downarrow$ 55.6%
TriviaQA	50.5	25.8	46.0	64.6	$\uparrow$ 9.8%	$\downarrow$ 60.0%
MATH500	94.5	47.2	92.5	61.0	$\uparrow$ 2.2%	$\downarrow$ 22.6%
BoolQ	85.5	32.7	73.5	1.0	$\uparrow$ 16.3%	$\uparrow$ 3103%
SIQA	77.5	6.7	73.5	1.5	$\uparrow$ 5.4%	$\uparrow$ 337%

Appendix

Table 11: Full per-benchmark one-shot library retrieval results. Accuracy is on the test set; cost is weighted tokens per sample (parameter-count weights).

\Delta

Acc and

\Delta

Cost are relative changes vs the baseline (formula and color/arrow conventions match Table 10 ).

Benchmark	BL Acc	Ours Acc	$\Delta$ Acc	BL $	Ours $	$\Delta$ Cost	BL Acc	Ours Acc	$\Delta$ Acc	BL $	Ours $	$\Delta$ Cost
	GPT-5						Gemini-2.5
AQuA-RAT	31.0	89.5	$\uparrow$ 189%	12.39	1.67	$\downarrow$ 86.5%	71.0	90.5	$\uparrow$ 27.5%	2.22	1.07	$\downarrow$ 51.6%
2WikiMQA	29.5	78.5	$\uparrow$ 166%	7.45	3.67	$\downarrow$ 50.8%	21.5	77.5	$\uparrow$ 260%	2.02	0.57	$\downarrow$ 72.0%
HotpotQA	39.0	76.5	$\uparrow$ 96.2%	7.71	7.13	$\downarrow$ 7.5%	33.0	76.5	$\uparrow$ 132%	2.52	1.20	$\downarrow$ 52.2%
MBPP+	56.5	82.5	$\uparrow$ 46.0%	2.16	1.89	$\downarrow$ 12.3%	69.5	80.5	$\uparrow$ 15.8%	1.79	1.37	$\downarrow$ 23.7%
SQuAD2	57.5	74.0	$\uparrow$ 28.7%	0.29	0.11	$\downarrow$ 61.5%	74.0	70.5	$\downarrow$ 4.7%	0.37	0.16	$\downarrow$ 57.9%

Appendix

Table 12: Full per-benchmark cross-model transfer results. For each benchmark, the Strategist -discovered strategy and the strongest leaderboard baseline workflow are both re-executed on the new backend;

\Delta

Acc and

\Delta

Cost compare them on the same backend. 200 deterministic samples per cell. BL

and Ours

are total USD across all 200 samples, computed at the official list prices published on the OpenAI (GPT-5) and Google (Gemini-2.5) websites; the same per-token rates are applied to baseline and Strategist strategies.

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