Ensemble Learning-Based Prompt Optimization

• ELPO is a framework that aggregates diverse prompt outputs using ensemble learning techniques to mitigate individual prompt biases and improve model robustness.
• It employs advanced methods such as Bayesian optimization, Shapley value attribution, and boosting strategies to select and weight prompts effectively.
• Empirical studies demonstrate that ELPO significantly boosts accuracy, F₁ scores, and transferability across NLP, few-shot, and vision-related tasks.

Ensemble Learning based Prompt Optimization (ELPO) refers to a family of principled algorithms and frameworks that aggregate and optimize over sets of prompts—rather than relying on a single prompt—to improve the performance, reliability, and adaptivity of large pre-trained models, especially LLMs and vision-LLMs (VLMs). ELPO leverages ensemble learning theory, voting schemes, adaptive weighting, and complementary generation or transfer mechanisms to address intrinsic issues in prompt engineering, notably sensitivity to prompt formulation, sample diversity, and task generalization. Recent works have formalized ELPO in several modalities, introduced rigorous statistical attribution and optimization tools, and empirically demonstrated superior performance over single- or naively-ensembled prompt methods.

1. Theoretical Foundations of ELPO

The core principle of ELPO is that prompts can be viewed analogously to weak learners in classical ensemble learning. Each prompt elicits a prediction from the model, and ensemble aggregation mitigates individual prompt biases and exploits complementary strengths. The key mathematical framework is as follows:

• Let $P = \{p_1, ..., p_n\}$ be a pool of candidate prompts, and $M$ the LLM or VLM.
• For any subset $S \subseteq P$, an aggregation rule (e.g., majority voting, weighted voting, or logit-space ensembling) is applied over model outputs.
• The overall utility of a prompt coalition $U(S)$ is a task-specific metric (e.g., accuracy, BLEU, F₁).
• Prompts are valued and selected based on their marginal contributions, diversity, and stability within the ensemble.

A rigorous formalization employs the Shapley value from cooperative game theory to quantify each prompt’s fair credit in the ensemble:

$$\phi_i = \sum_{S \subseteq P \setminus \{p_i\}} \frac{|S|!\,(n-|S|-1)!}{n!}\,\big(U(S \cup \{p_i\}) - U(S)\big)$$

This approach ensures balanced, symmetric, and additive attribution, and provides actionable guidance for prompt pruning and weighting (Liu et al., 2023).

2. ELPO Architectures and Optimization Algorithms

Various ELPO instantiations differ in (a) prompt generation/diversification, (b) ensemble weighting, and (c) optimization backends. Major frameworks include:

• ELPO for LLMs (ELPO Framework): Combines multiple prompt-generation strategies—bad-case reflection, evolutionary reflection, and hard-case tracking—to build a diverse prompt pool. Prompt search is conducted using Bayesian optimization (Gaussian Process–based Expected Improvement) and Multi-Armed Bandit (MAB) search with K-means clustering and Upper Confidence Bound allocation. After selection, top prompts are ensembled via weighted voting, with weights optimized for macro-F₁ and $\ell_2$ regularization to avoid prompt collapse (Zhang et al., 20 Nov 2025).
• Shapley-guided ELPO: Computes per-prompt Shapley values for a prompt pool, enabling pruning of detrimental prompts (with $\phi_i \leq 0$) and weighting beneficial ones, leading to smaller, stronger ensembles (Liu et al., 2023).
• Boosting-style ELPO (PREFER): Iteratively constructs prompt ensembles via boosting, with each prompt as a weak learner. Misclassified (“hard”) examples feed back into prompt synthesis, generating new prompts that specifically address model blind spots. Bagging with bilateral confidence checks stabilizes individual prompt predictions (Zhang et al., 2023).
• Sample-specific Ensemble (SESoM): In few-shot settings, learns sample-conditional attention weights over source prompt-tuned models, combining their outputs with an adaptive network, and outperforming static prompt fusion (Peng et al., 2022).

Typical pseudocode for ensemble voting aggregation, as used in (Zhang et al., 20 Nov 2025), is:

$$\hat{y}(x) = \arg\max_{y \in \mathcal{Y}} \sum_{j=1}^M w_j \cdot \mathbb{1}\{f_j(x) = y\}$$

subject to $\sum_j w_j = 1, \; w_j \geq w_{\text{min}}$

ELPO architectures fundamentally combine prompt generation/search and robust, differentiable ensembling.

3. ELPO in Multi-Source and Vision-Language Settings

In visual and vision-language settings, ELPO extends beyond textual prompts, addressing domain transfer, multi-modal fusion, and cross-domain generalization:

• HGPrompt: For multi-source visual prompt transfer, defines the ensemble prompt as $P_T = \sum_i \alpha_i P_i$, learning the simplex-constrained weights $\boldsymbol\alpha$ by maximizing a feature-level information-theoretic H-score for transferability, while minimizing a novel gradient alignment loss to prevent mutual interference between source prompts. This yields stable, coherent transfer of knowledge and state-of-the-art results on VTAB (Zhang et al., 9 Apr 2025).
• ConPE: Constructs domain-factor–specialized visual prompts for embodied agents and ensembles their CLIP-based encodings with a guided attention mechanism. Prompts are contrastively trained to be invariant to specific factors, and the downstream policy jointly learns the optimal prompt-mixing for robust adaptation (Choi et al., 16 Dec 2024).
• CAPEL: For few-shot VLM adaptation, generates class- and cluster-specific sub-prompts and performs logit-space ensembling with an adaptive weighting matrix. A cluster-preserving entropy regularizer forces specialization across sub-prompts, preventing representational collapse and boosting generalization (Chen et al., 10 Oct 2025).

A representative example is the joint optimization for visual prompt ensembling (Zhang et al., 9 Apr 2025):

$$\min_{\boldsymbol\alpha \in \Delta} -H(\boldsymbol\alpha) + \lambda\,\mathcal{L}_{\text{align}}(\boldsymbol\alpha)\quad\text{s.t.}\;\boldsymbol\alpha \in \Delta$$

where $H$ captures transferability and $\mathcal{L}_{\text{align}}$ penalizes gradient conflict.

4. Empirical Results and Benchmarks

Empirical studies across NLP, few-shot, vision, and clinical NER tasks show ELPO frameworks consistently surpass single-prompt and naïve ensemble baselines in accuracy, F₁, and robustness.

• NLP Benchmarks (LLMs): On ArSarcasm, LIAR, BBH-navigate, and other tasks, ELPO outperforms state-of-the-art methods (e.g., ProTeGi, OPRO, GPO), e.g., on ArSarcasm F₁: 92.3 (ELPO) vs. 84.7 (prior best), and on LIAR: 72.1 (ELPO) vs. 60.3 (prior best) (Zhang et al., 20 Nov 2025).
• Few-Shot Prompt Transfer: SESoM achieves gains of 6–10 points over ATTEMPT, SPoT-t, and fixed ensemble baselines, and even surpasses larger-model fine-tuned baselines on multiple GLUE/SuperGLUE tasks in the 32-shot regime (Peng et al., 2022).
• Visual Transfer (VTAB): ELPO (HGPrompt) sets a new accuracy record at 59.6% on VTAB (ViT-B/16 backbone), surpassing SPoT (58.5), PANDA (58.7), and classic fusion approaches, with pronounced gains in fine-grained and geometric benchmarks (Zhang et al., 9 Apr 2025).
• Reinforcement Learning: ConPE improves zero-shot adaptation success rates by 5–21 percentage points over single-prompt baselines and achieves up to 50% gains in sample efficiency (Choi et al., 16 Dec 2024).
• Medical NER: Ensemble prompt aggregation lifts F₁ and recall by 1–2 points over strongest single-prompt designs, resulting in GPT-4o F₁/recall of 0.95/0.98 for EHR entity recognition (Islam et al., 13 May 2025).

Ablations throughout these works consistently show that ensemble diversity, adaptive weighting, and joint optimization are essential for realizing gains, while naive averaging or clustering can underperform or even degrade results.

5. ELPO Workflow Components and Practical Guidelines

The general ELPO workflow comprises:

• Prompt Pool Generation: Combine diverse generation strategies (reflection, mutation, cluster specialization); utilize both LLM-driven and manual prompt design.
• Search and Pruning: Employ sample-efficient search (Bayesian, MAB) and data-driven selection (Shapley value, attention weights, ablation).
• Aggregation and Weighting: Use majority voting, weighted-aggregation, logit-space mixing, or guided soft attention mechanisms depending on task structure.
• Regularization: Apply conditional entropy (e.g., in CAPEL), gradient alignment (HGPrompt), or L₂-weight regularization to prevent mode collapse or overfitting.
• Optimization: Maximize predictive utility (e.g., F₁, accuracy, BLEU, H-score) under constraints derived from validation splits, often with convex or projected gradient methods.

Recommended practical settings include Shapley thresholding at $\phi_i \leq 0$, prompt-pool sizes $K \sim 10$–$50$, validation-tuned regularizer weights, and ensemble pruning based on interpretability or domain diversity (Liu et al., 2023, Zhang et al., 20 Nov 2025, Chen et al., 10 Oct 2025).

6. Open Problems, Limitations, and Future Directions

Emerging directions and unresolved considerations in ELPO research include:

• Adaptive and Sample-Specific Weighting: Further improvements may arise from hierarchical gating, joint prompt-and-weight learning, or probabilistic attention over prompts, as suggested by sample-conditional ensemble methods (Peng et al., 2022).
• Representation Collapse: Naive prompt aggregation can cause feature or logit collapse, underlining the need for diversity-preserving regularization (e.g., prototype competition loss in CAPEL) (Chen et al., 10 Oct 2025).
• Computational Complexity: Full Shapley value computation remains combinatorially hard; efficient approximations (e.g., truncated Monte Carlo, greedy search) are necessary for large prompt pools (Liu et al., 2023).
• Domain Adaptation and Policy Transfer: In vision and RL, attention-based mixture and contrastive prompt specialization yield transferability but may depend on careful factor identification and annotation (Choi et al., 16 Dec 2024).
• Prompt Market and Valuation: The attribution scores (e.g., Shapley value) facilitate prompt markets and data exchanges, informing prompt pricing and intellectual property management (Liu et al., 2023).

A plausible implication is that as LLMs and VLMs are increasingly deployed in high-stakes, diverse, or under-resourced domains, ELPO will become the de facto paradigm for prompt engineering, combining interpretability, robustness, and state-of-the-art generalization.

7. Representative ELPO Frameworks: Summary Table

Framework / Paper	Domain	ELPO Key Feature(s)
ELPO (Zhang et al., 20 Nov 2025)	LLM (NLP/Reasoning)	Multi-generator ensemble, weighted voting, Bayesian/MAB search
Shapley-Value ELPO (Liu et al., 2023)	LLM (NLP/Gen/MT)	Shapley attribution, pruning, confidence weighting
PREFER (Zhang et al., 2023)	LLM (NLU/Classification)	Boosting, feedback-reflect-refine, bilateral bagging
SESoM (Peng et al., 2022)	LLM (Few-shot tuning)	Sample-specific attention, expert gating ensemble
HGPrompt (Zhang et al., 9 Apr 2025)	VLM (Vision Transfer)	Information-theoretic transferability, gradient alignment
CAPEL (Chen et al., 10 Oct 2025)	VLM (Few-shot/Zero-shot)	Logit-space cluster-ensemble, adaptive weighting, entropy reg.
ConPE (Choi et al., 16 Dec 2024)	Embodied RL/Vision	Attention ensemble of factor-specialized prompts, contrastive learning
EHR NER (Islam et al., 13 May 2025)	Medical LLM/NLP	Semantic clustering, prompt-format diversity, voting

These frameworks cover the spectrum of application modalities and technical innovations underpinning modern ELPO. Each incorporates ensemble learning principles tailored to the demands and structure of prompt-based optimization within pre-trained large models.