Training-Free Group Relative Policy Optimization

## Abstract

Abstract Recent advances in Large Language Model (LLM) agents have demonstrated their promising general capabilities. However, their performance in specialized real-world domains often degrades due to challenges in effectively integrating external tools and specific prompting strategies. While methods like agentic reinforcement learning have been proposed to address this, they typically rely on costly parameter updates, for example, through a process that uses Supervised Fine-Tuning (SFT) followed by a Reinforcement Learning (RL) phase with Group Relative Policy Optimization (GRPO) to alter the output distribution. However, we argue that LLMs can achieve a similar effect on the output distribution by learning experiential knowledge as a token prior, which is a far more lightweight approach that not only addresses practical data scarcity but also avoids the common issue of overfitting. To this end, we propose Training-Free Group Relative Policy Optimization (Training-Free GRPO), a cost-effective solution that enhances LLM agent performance without any parameter updates.
Our method leverages the group relative semantic advantage instead of numerical ones within each group of rollouts, iteratively distilling high-quality experiential knowledge during multi-epoch learning on a minimal ground-truth data. Such knowledge serves as the learned token prior, which is seamlessly integrated during LLM API calls to guide model behavior. Experiments on mathematical reasoning and web searching tasks demonstrate that Training-Free GRPO, when applied to DeepSeek-V3.1-Terminus, significantly improves out-of-domain performance.
With just a few dozen training samples, Training-Free GRPO outperforms fine-tuned small LLMs with marginal training data and cost.

## 1 Introduction

Large Language Models (LLMs) are emerging as powerful general-purpose agents capable of interacting with complex, real-world environments.
They have shown remarkable capabilities across a wide range of tasks, including complex problem-solving [4, 5, 6], advanced web research [7, 8, 9, 10], code generation and debugging [11, 12], and proficient computer use [13, 14, 15].
Despite their impressive capabilities, LLM agents often underperform in specialized, real-world domains.
These scenarios typically demand the integration of external tools (e.g., calculators, APIs, databases), along with domain-specific task definitions and prompting strategies.
Deploying a general-purpose agent out-of-the-box in such settings often results in suboptimal performance due to limited familiarity with domain-specific requirements or insufficient exposure to necessary tools.

To bridge this gap, agentic training has emerged as a promising strategy to facilitate the adaptation of LLM agents to specific domains and their associated tools [4, 7, 8, 16].
Recent advancements in agentic reinforcement learning (Agentic RL) approaches have employed Group Relative Policy Optimization (GRPO) [17] and its variants [18, 19, 20] to align model behaviors in the parameter space.
Although these methods effectively enhance task-specific capabilities, their reliance on tuning LLM parameters poses several practical challenges:

- •
Computational Cost: Even for smaller models, fine-tuning demands substantial computational resources, making it both costly and environmentally unsustainable. For larger models, the costs become prohibitive. Furthermore, fine-tuned models require dedicated deployment and are often limited to specific applications, rendering them inefficient for low-frequency use cases compared to more versatile general-purpose models.
- •
Poor Generalization: Models optimized via parameter tuning often suffer from unsatisfactory cross-domain generalization, limiting their applicability to narrow tasks. Consequently, multiple specialized models must be deployed to handle a comprehensive set of tasks, significantly increasing system complexity and maintenance overhead.
- •
Data Scarcity: Fine-tuning LLMs typically necessitates large volumes of high-quality, carefully annotated data, which are often scarce and prohibitively expensive to obtain in specialized domains.
Additionally, with limited samples, models are highly susceptible to overfitting, leading to poor generalization.
- •
Diminishing Returns: The prohibitive training costs usually compel existing approaches to fine-tune smaller LLMs with fewer than 32 billion parameters, due to resource constraints rather than optimal design choices.
While larger models would be preferred, the computational expense of fine-tuning necessitates this compromise. Paradoxically, API-based or open-source larger LLMs often deliver better cost-performance ratios through scalability and continuous model updates. However, these general-purpose models underperform in specialized domains where fine-tuning is necessary, creating a cost-performance dilemma.

Such limitations inherent in parameter tuning motivate a fundamental research question: Is applying RL in parametric space the only viable approach? Can we enhance LLM agent performance in a non-parametric way with lower data and computational costs?

We answer this question affirmatively by proposing Training-Free Group Relative Policy Optimization (Training-Free GRPO), a novel and efficient method that improves LLM agent behavior in a manner similar to vanilla GRPO, while preserving the original model parameters unchanged.
Our approach is motivated by the insight that LLMs already possess the fundamental capability to adapt to new scenarios, requiring only minimal practice through limited samples to achieve strong performance. Thus, instead of adapting their output distribution through parameter tuning, in-context learning [21] that leverages a lightweight token prior can also encapsulate experiential knowledge learned from a minimal training dataset.

Training-Free GRPO retains the multi-epoch learning mechanism of vanilla GRPO.
In each epoch, multiple outputs are generated to deliver a group of rollouts for every query, which helps to explore the policy space and evaluate potential strategies. While vanilla GRPO relies on gradient-based parameter updates to iteratively improve policy performance, Training-Free GRPO eliminates this requirement by employing inference-only operations using LLMs.
At each optimization step, rather than calculating a numerical advantage for gradient ascent within each group of rollouts, our method leverages LLMs to introspect on each group and distill a semantic advantage.
Such advantage refines external experiential knowledge and guide policy outputs based on evolving contextual priors, thereby achieving policy optimization effects without modifying any model parameters.

By evaluating challenging mathematical reasoning and interactive web searching tasks, we demonstrate that our method significantly enhances the performance of frozen policy models such as DeepSeek-V3.1-Terminus [3] with only dozens of training samples.
It surpasses fine-tuned 32B models in performance while requiring only a fraction of the computational resources, offering a simple and much more efficient alternative to traditional fine-tuning techniques.

Our principal contributions are threefold:

- •
A New Training-Free RL Paradigm: We introduce Training-Free GRPO, which shifts policy optimization from the parameter space to the context space by leveraging evolving experiential knowledge as token priors without gradient updates.
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Semantic Group Advantage: We replace numerical group advantage in vanilla GRPO with semantic group advantage, enabling LLMs to introspect their own rollouts and continuously updating experiential knowledge at multiple optimization steps.
- •
Data and Computational Efficiency: Experiments confirm that Training-Free GRPO effectively enhances the performance of a frozen policy with minimal training samples, offering a practical and cost-effective alternative across different domains.
- •
Superior Generalization: By leaving model parameters frozen and plugging in different token priors, our approach fully preserves the generalization power, eliminating the cost and complexity of deploying multiple fine-tuned specialists.

## 2 Training-Free GRPO

Figure: Figure 2: Comparison of vanilla GRPO and Training-Free GRPO.
Refer to caption: figures/training-free_GRPO.png

Figure: Figure 3: Example of a Training-Free GRPO learning step.
Refer to caption: figures/case.png

In this section, we introduce our Training-Free GRPO, a method designed to replicate the alignment benefits of the GRPO algorithm without performing any gradient-based updates to the policy model’s parameters.

Vanilla GRPO.
As shown in Figure [2](https://arxiv.org/html/2510.08191v1#S2.F2), the vanilla GRPO procedure operates by first generating a group of $G$ outputs $\{o_{1},o_{2},\dots,o_{G}\}$ for a given query $q$ using the current policy LLM $\pi_{\theta}$, i.e., $\pi_{\theta}(o_{i}\mid q)$. Each output $o_{i}$ is then independently scored with a reward model $\mathcal{R}$.
Subsequently, with rewards $\mathbf{r}=\{r_{1},\dots,r_{G}\}$, it calculates a group-relative advantage $\hat{A}_{i}=\frac{r_{i}-\text{mean}(\mathbf{r})}{\text{std}(\mathbf{r})}$ for each output $o_{i}$.
By combining a KL-divergence penalty against a reference model, it constructs a PPO-clipped objective function $\mathcal{J}_{\text{GRPO}}(\theta)$, which is then maximized to update the LLM parameters $\theta$.

Training-Free GRPO repurposes the core logic of this group-based relative evaluation but translates it into a non-parametric, inference-time process.
Instead of updating the parameters $\theta$, we leave $\theta$ permanently frozen and maintain an external experiential knowledge $\mathcal{E}$, which is initialized to $\emptyset$.

Rollout and Reward.
As shown in Figure [2](https://arxiv.org/html/2510.08191v1#S2.F2), our rollout and reward process mirrors that of GRPO exactly.
Given a query $q$, we perform a parallel rollout to generate a group of $G$ outputs $\{o_{1},o_{2},\dots,o_{G}\}$ using the LLM.
Notably, while GRPO uses the current trainable policy $\pi_{\theta}$, our policy conditions on the experiential knowledge, $\pi_{\theta}(o_{i}|q,\mathcal{E})$.
Identical to the standard GRPO setup, we score each output $o_{i}$ by the reward model $\mathcal{R}$ to obtain a scalar reward $r_{i}=\mathcal{R}(q,o_{i})$.

Group Advantage Computation.
To provide an optimization direction for policy parameters, vanilla GRPO computes a numerical advantage $\hat{A}_{i}$ that quantifies each output $o_{i}$’s relative quality within its group.
Similarly, Training-Free GRPO performs an analogous comparison within each group but produces a group relative semantic advantage in the form of natural language experience, as shown in Figure [3](https://arxiv.org/html/2510.08191v1#S2.F3).
Since $\hat{A}_{i}=0$ when all $G$ outputs receive identical rewards (i.e., $\text{std}(\mathbf{r})=0$) in vanilla GRPO, we generate such semantic advantages only for groups with both clear winners and losers.
Specifically, for each output $o_{i}$, we first ask the same LLM $\mathcal{M}$ to provide a corresponding summary $s_{i}=\mathcal{M}(p_{\text{summary}},q,o_{i})$ separately, where $p_{\text{summary}}$ is a prompt template that incorporates the query $q$ and output $o_{i}$ to form a structured summarization request.
Given the summaries $\{s_{1},s_{2},\dots,s_{G}\}$ and the current experiential knowledge $\mathcal{E}$, the LLM $\mathcal{M}$ articulates the reasons for the relative success or failure of the outputs, followed by extracting a concise natural language experience $A_{\text{text}}=\mathcal{M}({p_{\text{extract}}},q,s_{i},\mathcal{E})$, where $p_{\text{extract}}$ is another prompt template for experience extraction.
This natural language experience $A_{\text{text}}$ serves as our semantic advantage, functionally equivalent to vanilla GRPO’s $\hat{A}_{i}$, encoding the critical experiential knowledge of what actions lead to high rewards.

Optimization.
Whereas vanilla GRPO updates its model parameters $\theta$ via gradient ascent on $\mathcal{J}_{\text{GRPO}}(\theta)$ computed by all advantages in a single batch, we update our experience library $\mathcal{E}$ using all semantic advantages $A_{\text{text}}$ from the current batch.
Specifically, given the existing experiences library $\mathcal{E}$, we prompt the LLM to generate a list of operations based on all these $A_{\text{text}}$, where each operation could be:

- •
Add: Directly append the experience described in $A_{\text{text}}$ to the experience library $\mathcal{E}$.
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Delete: Based on $A_{\text{text}}$, remove a low-quality experience from the experience library $\mathcal{E}$.
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Modify: Refine or improve an existing experience in the experience library $\mathcal{E}$ based on insights from $A_{\text{text}}$.
- •
Keep: The experience library $\mathcal{E}$ remains unchanged.

After updating the experience library $\mathcal{E}$, the conditioned policy $\pi_{\theta}(y|q,\mathcal{E})$ produces a shifted output distribution in subsequent batches or epochs. This mirrors the effect of a GRPO policy update by steering the model towards higher-reward outputs, but achieves this by altering the context rather than the model’s fundamental parameters. The frozen base model $\pi_{\theta}$ acts as a strong prior, ensuring output coherence and providing a built-in stability analogous to the KL-divergence constraint in GRPO that prevents the policy from deviating excessively from $\pi_{\text{ref}}$.

## 3 Evalution

To compare Training-Free GRPO with competitive baselines, we conduct comprehensive experiments on both mathematical reasoning and web searching benchmarks.

### 3.1 Mathematical Reasoning

Benchmarks.
We conduct our evaluation on the challenging AIME24 and AIME25 benchmarks [2], which are representative of complex, out-of-domain mathematical reasoning challenges. To ensure robust and statistically reliable results, we evaluate each problem with 32 independent runs and report the average Pass@1 score, which we denote as Mean@32.

Setup.
We primarily focus on large powerful LLMs that are usually hard and expensive to be fine-tuned in real-world applications, such as DeepSeek-V3.1-Terminus [3].
We include two basic configurations: (1) Direct Prompting without tool use (a text-only input/output process), and (2) ReAct [1] with a code interpreter (CI) tool.
To apply Training-Free GRPO experiments, we randomly sample 100 problems from the DAPO-Math-17K dataset [19], denoted as DAPO-100. We run the learning process for 3 epochs with a single batch per epoch (i.e., 3 steps), using a temperature of $0.7$ and a group size of $5$ during the learning phase.
For out-of-domain evaluation on AIME 2024 and 2025 benchmarks, we use a temperature of $0.3$.

**Table 1: Mean@32 on AIME 2024 and AIME 2025 benchmarks (%).**
| Method | Learning Cost | Training Set | Model | Tool | AIME24 | AIME25 |
| --- | --- | --- | --- | --- | --- | --- |
| Direct | - | - | DeepSeek-V3.1-Terminus | - | 68.6 | 52.9 |
| + Training-Free GRPO | $\approx\mathdollar 8$ | DAPO-100 | DeepSeek-V3.1-Terminus | - | 72.6 ($\uparrow$4.0) | 54.0 ($\uparrow$1.1) |
| ReAct [1] | - | - | DeepSeek-V3.1-Terminus | CI | 80.0 | 67.9 |
| + Training-Free GRPO | $\approx\mathdollar 18$ | DAPO-100 | DeepSeek-V3.1-Terminus | CI | 82.7 ($\uparrow$2.7) | 73.3 ($\uparrow$ 5.4) |
| ReAct [1] | - | - | DeepSeek-V3.2-Exp | CI | 71.0 | 61.8 |
| + Training-Free GRPO | $\approx\mathdollar 8$ | DAPO-100 | DeepSeek-V3.2-Exp | CI | 73.1 ($\uparrow$2.1) | 63.2 ($\uparrow$1.4) |

Figure: Figure 4: Statistics at each Training-Free GRPO step with tool use and DeepSeek-V3.1-Terminus.
Refer to caption: x1.png

Main Results.
As illustrated in Table [3](https://arxiv.org/html/2510.08191v1#S3.T3), Training-Free GRPO achieves substantial gains in mathematical reasoning, showing a clear advantage in performance across both the tool-use and non-tool-use scenarios. The strong baseline established by DeepSeek-V3.1-Terminus with ReAct [1] yields scores of $80.0\%$ on AIME24 and $67.9\%$ on AIME25. Critically, applying Training-Free GRPO to the frozen DeepSeek-V3.1-Terminus elevates its performance significantly, reaching $82.7\%$ on AIME24 and $73.3\%$ on AIME25. This represents a substantial absolute gain of $+2.7\%$ and $+5.4\%$, respectively, which is achieved with only $100$ out-of-domain training examples and zero gradient updates.
This performance surpasses various state-of-the-art RL methods like ReTool [4] and AFM [16] trained on 32B LLMs (see Table [3](https://arxiv.org/html/2510.08191v1#S3.T3)), which typically require thousands of training examples and incur costs exceeding $\mathdollar 10,000$. In contrast, Training-Free GRPO utilizes only $100$ data points with an approximate cost of $\mathdollar 18$.
Such outcome suggests that in real-world applications, guiding a powerful but frozen model through context-space optimization is more effective and efficient than exhaustively fine-tuning a less capable model in parameter space.
For quantitative evaluation and learned experiences of Training-Free GRPO, please refer to Appendices [A](https://arxiv.org/html/2510.08191v1#A1) and [C](https://arxiv.org/html/2510.08191v1#A3), respectively.

Learning Dynamics. As shown in Figure [4](https://arxiv.org/html/2510.08191v1#S3.F4), during the 3-step learning process, we observe a steady and significant improvement in Mean@5 on the training set.
Concurrently, the Mean@32 performance on both AIME24 and AIME25 also improves with each step, demonstrating that the learned experiences from only $100$ problems generalize effectively and the necessity of multi-step learning.
Also, the average number of tool calls decreases during both training and out-of-domain evaluation on AIME benchmarks.
This suggests that Training-Free GRPO not only encourages correct reasoning and action, but also teaches the agent to use tools more efficiently and judiciously.
The learned experiential knowledge helps the agent to discover some shortcuts and avoid erroneous or redundant tool calls, validating the effectiveness of our semantic advantage guided optimization.

**Table 2: Ablation study on DeepSeek-V3.1-Terminus (Mean@32, %).**
| Method | Training Set | AIME24 | AIME25 |
| --- | --- | --- | --- |
| ReAct [1] | - | 80.0 | 67.9 |
| ReAct [1] + Directly Generated Experiences | - | 79.8 | 67.3 |
| ReAct [1] + Training-Free GRPO (w/o ground truths) | DAPO-100 | 80.7 | 68.9 |
| ReAct [1] + Training-Free GRPO (w/o group computation) | DAPO-100 | 80.4 | 69.3 |
| ReAct [1] + Training-Free GRPO | DAPO-100 | 82.7 | 73.3 |

**Table 3: Mean@32 with smaller LLMs on AIME 2024 and AIME 2025 benchmarks (%).**
| Method | Learning Cost | Model | Tool | AIME24 | AIME25 |
| --- | --- | --- | --- | --- | --- |
| ReAct [1] | - | Qwen2.5-32B-Instruct | CI | 29.6 | 23.1 |
| ZeroTIR [5] | $\approx\mathdollar 20,000$ | Qwen2.5-32B-Instruct | CI | 56.7 | 33.3 |
| SimpleTIR [6] | $\approx\mathdollar 20,000$ | Qwen2.5-32B-Instruct | CI | 59.9 | 49.2 |
| ReTool [4] | $\approx\mathdollar 10,000$ | Qwen2.5-32B-Instruct | CI | 67.0 | 49.3 |
| AFM [16] | $\approx\mathdollar 10,000$ | Qwen2.5-32B-Instruct | CI | 66.7 | 59.8 |
| ReAct [1] | - | Qwen3-32B (Non-Thinking) | CI | 29.1 | 19.5 |
| + Training-Free GRPO | $\approx\mathdollar 4$ | Qwen3-32B (Non-Thinking) | CI | 33.5 ($\uparrow$4.4) | 25.4 ($\uparrow$5.9) |
| ReAct [1] | - | Qwen2.5-72B-Instruct | CI | 13.5 | 9.6 |
| + Training-Free GRPO | $\approx\mathdollar 3$ | Qwen2.5-72B-Instruct | CI | 14.9 ($\uparrow$1.4) | 11.4 ($\uparrow$1.8) |
| ReAct [1] | - | DeepSeek-V3.1-Terminus | CI | 80.0 | 67.9 |
| + Training-Free GRPO | $\approx\mathdollar 18$ | DeepSeek-V3.1-Terminus | CI | 82.7 ($\uparrow$2.7) | 73.3 ($\uparrow$ 5.4) |

Effectiveness of Learned Experiences. In Table [2](https://arxiv.org/html/2510.08191v1#S3.T2), we also include the ReAct enhanced with the experiences directly generated by DeepSeek-V3.1-Terminus, matching the quantity learned from Training-Free GRPO.
However, such directly generated experiences fail to improve the performance, highlighting the effectiveness of learned experiential knowledge from Training-Free GRPO.

Robustness to Reward Signal. Table [2](https://arxiv.org/html/2510.08191v1#S3.T2) also presents a variant of Training-Free GRPO, where the ground truth answers are not provided during learning process. In such cases, the semantic advantage is directly obtained by comparing the rollouts within each group, where the LLM can only rely on implicit majority voting, self-discrimination and self-reflection to optimize the experiences. Although it does not surpass the default version with ground truths, Training-Free GRPO still achieves an impressive results of 80.7% on AIME24 and 68.9% on AIME25. It shows the robustness and applicability to domains where ground truths are scarce or unavailable, further broadening its practical utility.

Removing Group Computation. We also remove the group computation by setting the group size of $1$ in Training-Free GRPO, where the LLM can only distill semantic advantage from the single rollout of each query. The results in Table [2](https://arxiv.org/html/2510.08191v1#S3.T2) show that it significantly harm the performance comparing with the default group size of $5$. It confirms the necessity of group relative computation, which enables the LLM to compare different trajectories within each group for better semantic advantage and experience optimization.

Applicability to Different Model Sizes.
By applying Training-Free GRPO on smaller LLMs, specifically Qwen3-32B [22] and Qwen2.5-72B-Instruct [23] with DAPO-100 dataset, we observe consistent improvements on the out-of-domain AIME benchmarks in Table [3](https://arxiv.org/html/2510.08191v1#S3.T3). Training-Free GRPO requires significantly fewer data and much lower learning cost, contrasting sharply with recent RL methods like ZeroTIR [5], SimpleTIR [6], ReTool [4], and AFM [16], which often necessitate thousands of data points and substantial computational resources for parameter tuning. Furthermore, powered by larger models like DeepSeek-V3.1-Terminus, our approach achieves much higher Mean@32 on AIME benchmarks than all RL-trained models, while only incurring about $\mathdollar 18$ for the learning process.

### 3.2 Web Searching

**Table 4: Pass@1 on WebWalkerQA (%).**
| Method | Training Set | Model | pass@1 |
| --- | --- | --- | --- |
| ReAct [1] | - | DeepSeek-V3.1-Terminus | 63.2 |
| + Training-Free GRPO | AFM-100 | DeepSeek-V3.1-Terminus | 67.8 ($\uparrow$4.6) |

In this section, we evaluate the effectiveness of Training-Free GRPO in addressing web searching tasks by leveraging minimal experiential data to enhance agent behavior.

Datasets.
For training, we constructed a minimal training set by randomly sampling 100 queries from the AFM (Chain-of-Agents) web interaction RL dataset [16], denoted as AFM-100. AFM provides high-quality, multi-turn interactions between agents and web environments, collected via reinforcement learning in realistic browsing scenarios. For evaluation, we employ WebWalkerQA benchmark [24], a widely-used dataset for assessing web agent performance. Its tasks require understanding both natural language instructions and complex web page structures, making it a rigorous evaluation framework for generalist agents.

Methods.
Our proposed Training-Free GRPO is applied to DeepSeek-V3.1-Terminus without any gradient-based updates. We perform 3 epochs of training-free optimization with a group size of $G=3$. The temperature settings follow those used in prior mathematical experiments.

Main Results.
We evaluate the effectiveness of our proposed Training-Free GRPO method on the WebWalkerQA benchmark. As shown in Table [4](https://arxiv.org/html/2510.08191v1#S3.T4), our method achieves a pass@1 score of 67.8% using DeepSeek-V3.1-Terminus, a significant improvement over the baseline of 63.2%. This result indicates that our approach effectively steers model behavior by leveraging learned experiential knowledge, surpassing the capabilities of static prompting ReAct strategy.

**Table 5: Ablation results on WebWalkerQA subset (%).**
| Method | Training Set | Model | pass@1 | pass@3 |
| --- | --- | --- | --- | --- |
| ReAct [1] | - | QwQ-32B | 27.5 | 43.1 |
| ReAct [1] + Training-Free GRPO | AFM-100 | QwQ-32B | 25.5 | 45.1 |
| ReAct [1] | - | DeepSeek-V3.1-Terminus | 66.7 | 74.5 |
| ReAct [1] + Directly Generated Experiences | AFM-100 | DeepSeek-V3.1-Terminus | 64.7 | 76.5 |
| ReAct [1] + Training-Free GRPO (w/o ground truths) | AFM-100 | DeepSeek-V3.1-Terminus | 66.7 | 78.4 |
| ReAct [1] + Training-Free GRPO | AFM-100 | DeepSeek-V3.1-Terminus | 68.6 | 78.4 |

Ablation.
We conduct ablation studies on a stratified random sample of 51 instances from the WebWalkerQA test set, where the sampling is proportionally stratified by difficulty level to ensure balanced representation across different levels of complexity. All ablated models are evaluated after 2 epochs of experience optimization. The results are summarized in Table [5](https://arxiv.org/html/2510.08191v1#S3.T5).

Using directly generated experiences slightly degrades over ReAct (64.7% vs. 66.7% pass@1), confirming that mere in-context examples without proper optimization may not yield gains. Training-Free GRPO without ground truth maintains the same pass@1 as ReAct (66.7%) but improves pass@3 to 78.4%, demonstrating that relative reward evaluation can enhance consistency even without ground truth. The full Training-Free GRPO achieves the best performance (68.6% pass@1 and 78.4% pass@3), highlighting the importance of combining ground truth guidance with semantic advantage and experience optimization.

Applying Training-Free GRPO to QwQ-32B [25] yields only 25.5% pass@1, significantly lower than the 66.7% achieved with DeepSeek-V3.1-Terminus, and even under performing its own ReAct baseline (27.5%). This may suggest that the effectiveness of our method is dependent on the underlying model’s reasoning and tool-use capabilities in complex tool use scenarios, indicating that model capability is a prerequisite for effective experience-based optimization.

## 4 Comparing RL Learning on Context Space and Parameter Space

### 4.1 Cross-domain Transfer Analysis

**Table 6: Cross-domain transferability (Averaged pass@1, %).**
| Method | Learned Domain | Math Reasoning | Web Searching |  |
| --- | --- | --- | --- | --- |
| AIME24 | AIME25 | WebWalker |  |  |
| ReAct [1] (Qwen2.5-32B-Instruct) | - | 29.6 | 23.1 | 31.9 |
| ReTool [4] (Qwen2.5-32B-Instruct) | Math | 67.0 | 49.3 | 18.3 |
| MiroThinker [10] (Qwen3-32B) | Web | 43.5 | 36.8 | 53.6 |
| Training-Free GRPO (DeepSeek-V3.1-Terminus) | Math / Web | 82.7 | 73.3 | 67.8 |

A critical strength of Training-Free GRPO lies in its ability to achieve strong performance across diverse domains without suffering from the domain specialization trade-off observed in parameter-tuned methods. As demonstrated in Table [6](https://arxiv.org/html/2510.08191v1#S4.T6), we observe the unsatisfactory performance when domain-specialized models are transferred to different domains. For instance, ReTool [4] specifically trained on mathematical reasoning tasks, achieves competitive performance on AIME24 and AIME25 within its specialized domain. However, when transferred to web searching tasks on WebWalker, its performance drops dramatically to only $18.3\%$, which is much lower than ReAct [1] without fine-tuning. Similarly, though optimized for web interactions, MiroThinker [10] significantly underperforms ReTool that is trained in the math domain on the AIME benchmarks. Such phenomenon highlights that parameter-based specialization narrows the model’s capabilities to excel in the training domain at the expense of generalizability. In contrast, Training-Free GRPO applied to the frozen LLM achieves state-of-the-art performance in both domains simultaneously by simply plugging in domain-specific learned experiences.
Such cross-domain robustness makes Training-Free GRPO particularly valuable for real-world applications where agents must operate in multifaceted environments with diverse requirements.

### 4.2 Computational Costs

As shown in Figure [1](https://arxiv.org/html/2510.08191v1#S0.F1), we further analyze the economic benefits of Training-Free GRPO by comparing its computational costs with a vanilla RL training approach, specifically ReTool [4], on mathematical problem-solving tasks. This comparison highlights the practical benefits of our method in scenarios characterized by limited data, constrained budgets, or volatile inference demand.

Training Cost.
By replicating the training process of ReTool [4] on Qwen2.5-32B-Instruct [23], we find that it requires approximately 20,000 $\times$ GPU hours with the rental price of $0.5 per GPU hour, resulting in the total training expense amounts to roughly $10,000. In contrast, Training-Free GRPO, when applied to DeepSeek-V3.1-Terminus, achieves superior performance on the AIME benchmarks (Table [3](https://arxiv.org/html/2510.08191v1#S3.T3)) while requiring only minimal costs.
It requires only $3$ training steps over $100$ samples completed within $6$ hours, which consumes 38M input tokens and 6.6M output tokens, amounting to a total cost of approximately $18 based on the official DeepSeek AI pricing(^1^11[https://api-docs.deepseek.com/quick_start/pricing](https://api-docs.deepseek.com/quick_start/pricing). Most of the input tokens qualify for the lower cache hit pricing with ReAct framework, as each processing step typically involves reusing extensive prior context.). The drastic reduction in training cost by over two orders of magnitude makes our approach especially cost-effective.

Inference Cost.
Deploying a trained model like ReTool-32B entails significant fixed infrastructure costs. In a typical serving setup with 4 $\times$ GPUs at the price of $0.5 per GPU-hour, vLLM-based batching requests can process about 400 problems per hour from the AIME benchmarks. The inference cost per problem averages $0.005. While this per-instance cost is relatively low, it presupposes continuous GPU availability, which becomes inefficient under fluctuating or low request volumes. In contrast, Training-Free GRPO incurs a token-based cost.
On average, each request consumes 60K input tokens and 8K output tokens, totaling about $0.02 per problem with cache hit pricing for reused contexts.
Although per-query inference with a large API-based model is more expensive than with a dedicated small model, many real-world applications, particularly specialized or low-traffic services, experience irregular and modest usage patterns. In such cases, maintaining a dedicated GPU cluster is economically unjustifiable. By leveraging the shared, on-demand infrastructure of large model services like DeepSeek, Training-Free GRPO eliminates fixed serving overhead and aligns costs directly with actual usage. This pay-as-you-go model is distinctly advantageous in settings where demand is unpredictable or sparse.

## 5 Related Work

LLM Agents.
By leveraging external tools, Large Language Models (LLMs) can overcome inherent limitations, such as lacking real-time knowledge and precise computation. This has spurred the development of LLM agents that interleave reasoning with actions. Foundational frameworks like ReAct [1] prompt LLMs to generate explicit chain-of-thought (CoT) and actionable steps, enabling dynamic planning through tool use. Furthermore, Toolformer [26] demonstrates that LLMs can learn to self-supervise the invocation of APIs via parameter fine-tuning. Building on these principles, subsequent research has produced sophisticated single- and multi-agent systems, such as MetaGPT [27], CodeAct [28], and OWL [29], which significantly enhance the quality of planning, action execution, and tool integration.

Reinforcement Learning.
Reinforcement learning (RL) has proven highly effective for aligning LLMs with complex and long-horizon goals. Foundational algorithms like Proximal Policy Optimization (PPO) [30] employ a policy model for generation and a separate critic model to estimate token-level value. Group Relative Policy Optimization (GRPO) [17] eliminates the need for a critic by estimating advantages directly from groups of responses. Recent research try to apply RL to transform LLMs from passive generators into autonomous agents that learn through environmental interaction. GiGPO [31] implements a two-level grouping mechanism for trajectories, enabling precise credit assignment at both the episode and individual step levels. ReTool [4] uses PPO to train an agent to interleave natural language with code execution for mathematical reasoning. Chain-of-Agents [16] facilitates multi-agent collaboration within a single model by using dynamic, context-aware activation of specialized tool and role-playing agents. Furthermore, Tongyi Deep Research [7] introduces synthetic data generation pipeline and conduct customized on-policy agentic RL framework.
However, such parameter-updating approaches result in prohibitive computational cost, which typically restricts application to LLMs with fewer than 32B parameters. Moreover, they only achieve diminishing returns compared to simply using larger, more powerful frozen LLMs. In contrast, our proposed Training-Free GRPO method seeks to achieve comparable or even better performance on state-of-the-art LLMs without any parameter updates, drastically reducing both data and computational requirements.

Training-Free Methods.
A parallel line of research aims to improve LLM behavior at inference time without updating model weights. The general approach is in-context learning (ICL) [21], which leverages external or self-generated demonstrations within a prompt to induce desired behaviors. More recent methods introduce iterative refinement mechanisms. Self-Refine [32] generates an initial output and then uses the same LLM to provide verbal feedback for subsequent revisions. Similarly, Reflexion [33] incorporates an external feedback signal to prompt the model for reflection and a new attempt. In-context reinforcement learning (ICRL) [34, 35] demonstrates that LLMs can learn from scalar reward signals by receiving prompts containing their past outputs and associated feedback. TextGrad [15] proposes a more general framework, treating optimization as a process of back-propagating textual feedback through a structured computation graph. A key characteristic of these methods is their focus on iterative, within-sample improvement for a single query. In contrast, our Training-Free GRPO more closely mirrors traditional RL by learning from a separate dataset across multiple epochs to iteratively refine a shared, high-quality experience library for out-of-domain queries. Furthermore, given each query, unlike self-critique or context updates for a single trajectory, our method explicitly compares multiple rollouts per query for a semantic advantage to compare different trajectories in each group, which has been confirmed effective in Section [3.1](https://arxiv.org/html/2510.08191v1#S3.SS1).
Specifically in the context for optimizing agent systems, Agent KB [36] constructs a shared, hierarchical knowledge base to enable the reuse of problem-solving experiences across tasks. Unlike the complex reason-retrieve-refine process of Agent KB, Training-Free GRPO simply injects the learned experiences into the prompt.
Moreover, Agent KB relies on hand-crafted examples and employs an off-policy learning paradigm only once by collecting trajectories in the different way of online inference.
In contrast, our Training-Free GRPO uses a consistent pipeline and more closely mirrors on-policy RL with multi-epoch learning.

## 6 Conclusion

In this paper, we introduced Training-Free GRPO, a novel paradigm that shifts RL policy optimization from the parameter space to the context space. By leveraging group-based rollouts to iteratively distill a semantic advantage into an evolving experiential knowledge which serves as the token prior, our method successfully steers the output distribution of a frozen LLM agent, achieving significant performance gains in specialized domains. Experiments demonstrate that Training-Free GRPO not only surmounts the practical challenges of data scarcity and high computational cost but also outperforms traditional parameter-tuning methods. Our work establishes a new, highly efficient pathway for adapting powerful LLM agents, making advanced agentic capabilities more accessible and practical for real-world applications.

## Contributions

Authors  Yuzheng Cai^1,2*  Siqi Cai^1* Yuchen Shi^1* Zihan Xu^1*  Lichao Chen^1,3  Yulei Qin^1  Xiaoyu Tan^1 Gang Li^1  Zongyi Li^1  Haojia Lin^1  Yong Mao^1  Ke Li^1Q  Xing Sun^1

Affiliations  ^1Tencent Youtu Lab ^2Fudan University ^3Xiamen University

*Equal Contributions  Yuzheng Cai  Siqi Cai  Yuchen Shi  Zihan Xu

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## Appendix A Case Study

On math reasoning and web searching scenarios, we provide examples illustrating how Training-Free GRPO enhances ReAct [1] with DeepSeek-V3.1-Terminus and corresponding tools.

### A.1 Experience-Guided Tool-Integrated Math Reasoning

We consider a geometric configuration with two rectangles $ABCD$ and $EFGH$ where $D,E,C,F$ are collinear in that order, and $A,D,H,G$ are concyclic. Given $BC=16$, $AB=107$, $FG=17$, $EF=184$, the task is to determine $CE$.

Figure: Figure 5: Example trajectory without experience in Math Reasoning.

Baseline (without experiences).
As shown in Figure [5](https://arxiv.org/html/2510.08191v1#A1.F5), the unassisted agent initializes a coordinate system with $D=(0,0)$ and models $ABCD$ as axis-aligned. For $EFGH$, it places $E=(x_{f}-184,0)$, $F=(x_{f},0)$ and, critically, sets $G=(x_{f},\,+17)$, $H=(x_{f}-184,\,+17)$, i.e., with a positive vertical orientation for the short side. It then enforces the four-point concyclicity of $A(0,16)$, $D(0,0)$, $G$, $H$ via a determinant condition and solves for $x_{f}$, yielding $x_{f}\approx 184.092$ and consequently $x_{e}=x_{f}-184\approx 0.092$. From this, it reports $CE\approx 106.9076$ and an “exact” expression $199-\sqrt{8481}$.

This trajectory exhibits three systemic issues: (i) misinterpretation of the vertical orientation (wrong sign for the $y$-coordinates of $G,H$), (ii) inconsistent handling of the order $D$–$E$–$C$–$F$ and the lack of a unified parameterization for segment relations, and (iii) absence of systematic, comprehensive post-solution verification—i.e., no integrated check that the final coordinates simultaneously satisfy rectangle dimensions. These issues lead to an incorrect cyclic constraint (e.g., an intermediate relation of the form $x(x+184)=17$) and acceptance of a spurious solution without full geometric verification. Note that although $CE\approx 106.91$ lies within $0<CE<107$, this alone does not validate the solution; the critical failure was the lack of holistic consistency checks across all problem constraints.

Figure: Figure 6: Example trajectory with experiences in Math Reasoning.

Enhanced (With Experiences).
Refer to Figure [6](https://arxiv.org/html/2510.08191v1#A1.F6), with a curated experience pool, the agent follows a structured pipeline:

- •
Directional ordering ([29]) and boundedness validation ([1]): It fixes the order $D$–$E$–$C$–$F$ on a line and sets $CE=x$ with $0<x<107$, ensuring $E$ lies on segment $DC$ and $F$ lies beyond $C$.
- •
Segment-addition parameterization ([37]): It uses $DE+EC=DC=AB=107$ and $EC+CF=EF=184$ to obtain $DE=107-x$, $CF=184-x$, and places $D=(0,0)$, $E=(107-x,0)$, $C=(107,0)$, $F=(291-x,0)$.
- •
Consistent vertical orientation and cyclic modeling: Noting $A=(0,16)$, $D=(0,0)$, it orients the short side downward ($FG=17$) so $H=(107-x,-17)$, $G=(291-x,-17)$. Using the circle equation $x^{2}+y^{2}+Dx+Ey+F=0$ with $A$ and $D$ yields $F=0$, $E=-16$. Substituting $H$ and $G$, subtracting the two equations gives $D=2x-398$; back-substitution reduces to the quadratic$x^{2}-398x+30576=0$, with discriminant $398^{2}-4\cdot 30576=36100=190^{2}$ and roots $x=104,\,294$.
- •
Root selection and full verification ([1], [7]): Applying $0<x<107$ filters out $x=294$, selecting $x=104$. The agent then verifies all constraints: $DE=107-104=3$, $CF=184-104=80$, $EF=184$, $FG=17$, and confirms that the circle $x^{2}+y^{2}-190x-16y=0$ passes through $A=(0,16)$, $D=(0,0)$, $H=(3,-17)$, $G=(187,-17)$.

Comparative Analysis.
This case reveals a clear causal link between experience-guided behaviors and correctness. Experience [29] eliminates directional ambiguity and enforces the correct collinearity order, directly addressing the baseline’s misplacement of $G,H$. Experience [37] induces a clean single-variable parameterization ($DE=107-x$, $CF=184-x$), which simplifies the cyclic constraint to a solvable quadratic. Experience [1] imposes a necessary boundedness filter ($0<x<107$) to discard extraneous roots. Finally, experience [7] mandates comprehensive post-solution verification (rectangle dimensions, collinearity, concyclicity), preventing acceptance of spurious solutions.

Compared to the unassisted trajectory, the experience-informed reasoning corrects the vertical orientation, resolves ordering and parameterization inconsistencies, and installs principled validation gates. This case demonstrates the positive impact of integrating domain-specific experiences on reliability and accuracy in tool-integrated mathematical reasoning.

### A.2 Experience-Guided Web Searching

We consider a web searching task from WebWalkerQA: quantify 2024 rewards for (i) creators in the Creator Program (weekly amount), and (ii) players in the Play-2-Airdrop during Private Beta 4 (total pool and duration).

Baseline (without experiences).
As summarized in Figure [7](https://arxiv.org/html/2510.08191v1#A1.F7), the unassisted agent issues multiple broad searches and relies heavily on result snippets and third-party summaries, delaying clicks into authoritative pages. It eventually opens the PB4 registration post to confirm “Play-2-Airdrop Campaign: 200,000 ILV over six months,” but continues to scan snippets for the Creator Program value without opening the relevant official post. Connection errors to one official page cause the agent to revert to broad searches rather than alternative primary-source strategies (e.g., site-specific queries or adjacent official posts). The trajectory remains incomplete: it reports the Play-2-Airdrop figure but fails to confirm the Creator Program’s “100 ILV weekly” from an official source, yielding an incorrect/incomplete answer.

Enhanced (With Experiences).
Refer to Figure [8](https://arxiv.org/html/2510.08191v1#A1.F8). With a curated experience pool, the agent follows a disciplined pipeline: (1) prioritize official sources ([14], [4]) and open the PB4 overview and registration posts to extract the “200,000 ILV over six months” and Testnet/Mainnet allocation structure; (2) refine search terms to target formal titles ([2], [12], [1]) and open “The Illuvium Creator Program Is Getting An Upgrade!”; (3) extract the exact line “The prize pool of 100 ILV tokens awaits participating Creators each week,” and (4) synthesize both verified statements into a complete answer aligned with the question requirements ([25]). This results in the correct, fully supported output: creators earn 100 ILV weekly; players have a 200,000 ILV pool distributed over six months in PB4’s Play-2-Airdrop.

Figure: Figure 7: Example trajectory without experiences in Web Searching.

Figure: Figure 8: Example trajectory with experiences in Web Searching.

Comparative Analysis.
Experience-guided behaviors directly address baseline deficiencies: primary source prioritization ([14], [4]) removes reliance on snippets and third-party coverage; document identification ([1]) and iterative refinement ([2], [12]) ensure the agent locates and opens the exact Creator Program post; partial match evaluation ([25]) steers the agent to confirm numerical claims at their authoritative origin. In contrast, the baseline wastes context on searches without content acquisition, leaves critical values unverified, and produces an incomplete answer.

## Appendix B Prompts

In this appendix, we provide the prompts used in math reasoning tasks.
Figures [9](https://arxiv.org/html/2510.08191v1#A2.F9) and [10](https://arxiv.org/html/2510.08191v1#A2.F10) present the prompts for solving math tasks.
Figures [11](https://arxiv.org/html/2510.08191v1#A2.F11) and [12](https://arxiv.org/html/2510.08191v1#A2.F12) are used in group relative semantic advantage.
Figure [13](https://arxiv.org/html/2510.08191v1#A2.F13) works for optimizing the experiential knowledge $\mathcal{E}$.

Figure: Figure 9: System prompt for ReAct framework in Math Reasoning.

Figure: Figure 10: Prompt for supplementing math problems with experiential knowledge $\mathcal{E}$.

Figure: Figure 11: Prompt for summarizing each trajectory in Math Reasoning.

Figure: Figure 12: Prompt for group advantage computation in Math Reasoning.

Figure: Figure 13: Prompt for optimizing experiential knowledge $\mathcal{E}$ based on group advantages in the same batch in Math Reasoning.

## Appendix C Examples of Learned Experiences

In this appendix, we provide some examples in Figure [14](https://arxiv.org/html/2510.08191v1#A3.F14), which are extracted from 48 learned experiences by Training-Free GRPO with tool use in Math Reasoning.

Figure: Figure 14: Example of learned experiences from Training-Free GRPO with tool use in Math Reasoning.

## Peer Reviews

confidence: 4
contribution: 2
initial_rating: 2
presentation: 3
questions: See weaknesses
soundness: 2
strengths: The paper presents a decent idea with their aggregation mechanism for rationales and incorporates a self judging mechanism with the same LLM that seems to be fairly simple and efficient to implement. The presentation and plots in the paper a nice making it easy to read and understand. Overall I think the papers overall presentation and method are sound.
summary: This work introduces training-free GRPO a method that mimics the traditional gradient updates of GRPO with contextual aggregation of trials.
weaknesses: With the strengths being said, I think the paper has significant weaknesses that I think prevent me from recommending its acceptance. First, the marketing of the paper I have fundamental problems with, it is written in a way that makes it seem like through simple pseudo-prompting one can learn new things similar to what could be learnt through RL. I believe this to be simply not true, as if there are problems the model cannot solve (i.e the answer is not in its support) no amount of reasonable prompting (except maybe leaking the answer) should be able to obtain this sample. Now test-time scaling/online ICL does work, but I am reluctant to draw an equivalence between it and RL. 

With that said,  I think the paper suffers from further technical weaknesses. It is a bit weird to be that training-free GRPO is implemented for Deepseek V1 but RL is not implemented for the same model, only for Qwen 32b. Since this is ultimately a psu-prompting work I would expect more complex agentic pipelines being compared, I am unfamiliar with that side of the literature but something akin to [1].

Multiple random seeds and multiple models are also missing. Overall I think the work lacks significant polishing. 


[1] https://arxiv.org/abs/2509.26626

---

confidence: 5
contribution: 2
initial_rating: 4
presentation: 3
questions: 1. The paper states that semantic advantages are generated only for groups with "clear winners and losers" (line 189). Could you please precisely define this condition? Is it based on the variance of rewards, or is there another mechanism at play? How does your method handle the common scenario where all trajectories in a group fail and receive an identical low reward?
2. Could you justify the experimental design choice of not including direct comparisons on the same base model? Specifically, why was a traditional fine-tuning method like GRPO not applied to DeepSeek-V3.1, and why were results for Training-free GRPO on Qwen2.5-32B not reported? Is the observed performance advantage primarily due to the strength of the base model?
3. Could you clarify the conceptual framing of your method? Specifically, please justify the name "Training-free GRPO" given that no policy parameters are updated, and explain why it is classified as "RL" rather than an advanced form of prompt engineering, especially since other iterative methods like ReAct are categorized as "Prompt". Additionally, could you confirm whether the "reward model" is a fixed, deterministic function rather than a learned model?
4. Regarding the cross-domain analysis, would you consider running a more stringent experiment where the experience library learned on the math tasks is directly applied to the web navigation tasks without modification? This would provide a much clearer assessment of the generalizability of the learned "experiential knowledge".
5. The reference section contains several critical errors (e.g., the DeepSeek AI reference cites dates in 2025, the Li et al., 2025a and 2025b citations appear identical). We strongly urge the authors to perform a thorough revision of the bibliography. Could you confirm that these will be corrected?
6. Please describe the differences and connections between your proposed method and the ReasonFlux series of papers.
https://arxiv.org/pdf/2502.06772, https://arxiv.org/pdf/2506.18896, https://arxiv.org/pdf/2506.03136
soundness: 2
strengths: 1. The central idea of shifting policy optimization from the parameter space to the context space is a practical concept. It presents a compelling alternative to traditional fine-tuning, directly addressing critical challenges such as prohibitive computational costs, data scarcity, and potential catastrophic forgetting associated with parameter updates.
2. The paper demonstrates the effectiveness of the proposed method with good empirical results on challenging and well-recognized benchmarks for mathematical reasoning (AIME24/25) and web navigation (WebWalkerQA). The application to a capable frozen model (DeepSeek-V3.1) shows significant performance gains, highlighting the practical utility of the approach.
3. The concept is explained with a helpful analogy to vanilla GRPO, and the inclusion of a concrete example in Figure 3 effectively illustrates the core mechanism of generating and applying "semantic advantage". This aids in understanding the intuition behind the method.
summary: This paper introduces Training-free Group Relative Policy Optimization (Training-free GRPO), a method for enhancing LLM agent performance without updating model parameters. The approach leverages group-based rollouts to distill a natural language "semantic advantage" from successful and failed attempts, which is then used to iteratively build and refine an external "experience library". This library is provided as context (a "token prior") to a frozen LLM, effectively steering its output distribution towards higher-reward behaviors in a data- and compute-efficient manner.
weaknesses: 1. The experimental evaluation suffers from a lack of direct, controlled comparisons, making it difficult to isolate the true contribution of the proposed method. The primary results in Table 1 compare Training-free GRPO on the powerful DeepSeek-V3.1 model against RL baselines fine-tuned on the weaker Qwen2.5-32B model. To make a convincing claim, the paper should have included results for Training-free GRPO on Qwen2.5-32B and, more importantly, a traditional GRPO fine-tuning baseline on DeepSeek-V3.1. Without these crucial control experiments, the observed performance gap could be attributed more to the superior base model than to the merits of the training-free optimization technique.
2. The conceptual framing and terminology used in the paper are potentially misleading. The name "Training-free GRPO" is an oxymoron, as GRPO is fundamentally a training algorithm that updates policy parameters, which this method explicitly avoids. Furthermore, classifying the method as "RL" in Table 1 is questionable. Since the model parameters are frozen and improvement comes from engineering the context, the method is mechanistically closer to iterative prompt optimization or in-context learning rather than reinforcement learning in the traditional sense. This framing creates confusion and potentially overstates the connection to established RL algorithms.
3. The cross-domain transfer analysis in Section 4.1 is not designed as a fair comparison. The experiment shows that specialized fine-tuned models (ReTool, MiroThinker) perform poorly when transferred to a new domain, which is a well-known limitation. However, the Training-free GRPO method is evaluated by providing it with a domain-specific experience library for each task. A more rigorous test of transferability would involve using the experiences learned from the math domain to evaluate performance on the web search domain, which would properly assess how the learned knowledge generalizes, rather than just showing the flexibility of swapping context.
4. The ablation studies could be more comprehensive and the methodology more clearly defined. The paper states that semantic advantage is generated only for groups with "clear winners and losers," but this critical condition is not formally defined. The sensitivity to key hyperparameters, such as the group size $G$, is not explored. Furthermore, the term "reward model" used in Figure 2 is ambiguous; for verifiable tasks like math, this is typically a deterministic reward function, and using the word "model" incorrectly implies a learned, parameterized critic.
5. The important negative result on the weaker QwQ-32B model, where the method underperforms its own ReAct baseline, is a significant finding that is not sufficiently discussed as a core limitation. This suggests that the effectiveness of Training-free GRPO is highly dependent on the advanced reasoning and introspection capabilities of the underlying base model, which should be stated more explicitly as a prerequisite for the method's success.

---

confidence: 3
contribution: 3
initial_rating: 6
presentation: 2
questions: - When generating $A_{\text{text}_i}$, does the LLM have access to other summaries in the group? From line 194 it seems not, but if so, how can it compute a relative semantic advantage?

- How are “self-generated experiences” produced. Do they follow the same group-comparison pipeline but skip the experience refinement stage?

- In Figure 4, AIME24 and AIME25 show opposite trends in Pass@32 performance across steps. What might explain this behavior?

- What happens if the optimization runs for more than three epochs (e.g., 5 or 10)? Would the experience library become more specialized, or would overfitting occur?
soundness: 3
strengths: The paper explores the idea of iterative prompt optimization as an alternative to RL-based fine-tuning, aiming to reduce the need for costly online samples. The motivation is clear, and the comparison between parameter-space and context-space optimization is conceptually interesting. The experimental setup spans multiple domains and shows consistent improvements across tasks, demonstrating the method’s practicality. The overall structure and writing make the paper easy to follow, although some implementation details are missing.
summary: The paper proposes Training-free GRPO, an iterative method that builds an experience library by comparing outputs of a base model against each other. Instead of updating model parameters, it refines behavior through accumulated experiential knowledge, offering a lightweight alternative to RL-based fine-tuning. The approach is well-motivated and demonstrates how iterative prompt optimization can achieve competitive results with lower computational cost.
weaknesses: ### Major comments:

- The method appears heavily dependent on the underlying model’s inherent reasoning strength. For instance, results on Qwen2.5-32B-Instruct are missing in Table 1 but appear in Table 4 (WebWalkerQA), where they show minimal improvement. While the authors briefly acknowledge this at the end of Section 3, it should be emphasized further and discussed in more depth.

- From Table 2, access to ground-truth results seems quite important for the improvements. It would benefit readers to explicitly explain how the ground truth is integrated into the offline dataset in Section 2.

- Table 5 can be misleading: since the base models differ, cross-model comparisons are not meaningful. The relevant comparison should be across domains rather than models. Moreover, Training-free GRPO leverages specialized experience libraries, making the claim of “cross-domain generalization” less convincing. A more rigorous evaluation (e.g., testing experience libraries trained on one domain and applied to another) is needed to support such claims.

### Minor comments:

- Since the optimization happens on the prompt level rather than the policy (usually refered to the base model) itself, the name “GRPO” may not be the most precise.

- How does the base model retrieve relevant experiences from the library? In Figure 6 it appears that the full library is appended to the prompt, whereas in Figure 11 each agent trajectory uses specific experiences. Clarifying this mechanism in Section 2 would make the method much clearer.

- Related work is missing prior studies on offline experience or guideline construction, such as:

[1] Fu et al., AutoGuide: Automated Generation and Selection of Context-Aware Guidelines for Large Language Model Agents;

[2] Wang et al., Agent Workflow Memory.

- It’s reasonable that ablations on WebWalkerQA are done on a subset of tasks, but it is unclear why they are performed after only two epochs of experience optimization. This choice should be justified.

---

confidence: 4
contribution: 2
initial_rating: 2
presentation: 2
questions: [Q1] Comparison in Table 1 is improper, you are not doing your method on Qwen2.5-32B-Instruct, but why you put those results and compare with your method on DeepSeek-V3.1?

[Q2] Comparison in Table 5 is also unfair, please avoid comparing your method towards the other methods on different base models. Make sure they are trained on the same base model with the same training dataset configuration.

[Q3] How would it work on smaller model? Please report training result over model less than 10B.

Please also addresses the concerns in weakness part.
soundness: 2
strengths: - The idea is clear and could work under specific model setups.

- The overall paper is well written, with clear motivation and rationale.

- The method is practical and can be replicated by the community.
summary: This work proposes Training-free GRPO, a method that keeps model weights fixed while introducing an external experience library to update experiences. In each round, groups of rollouts per query are sampled, and the LLM summarizes winners and losers to extract a natural-language “semantic” advantage. This information is then used to update an external experience library, which is later fed back as a token prior in subsequent API calls. Essentially, the authors introduce a way to build an internal RAG system via prompt engineering and demonstrate that such an internal RAG can improve model performance on AIME and WebWalkerQA.
weaknesses: - Please reconsider how you classify your method. Labeling it as "RL" is misleading, given that the model parameters remain frozen and the reward mechanism is not clearly defined. A more appropriate framing would be under prompt-based RAG or inference-time memory optimization. Additionally, since there is no performance comparison with RL baselines, labeling your method as "RL" in all tables is inappropriate. Finally, emphasizing only the training cost savings without comparing performance against GRPO is insufficient and could weaken the overall claim.

- The experience may accumulate over time, eventually exceeding the model's context window, which suggests that this method does not scale well. Moreover, the proposed framework appears unsuitable for training smaller models with limited context and rollout lengths; for example, Qwen-Math with only a 4K context window.

- Only a limited set of baselines is compared, as ReAct is the only method evaluated under the same base model and training configuration. Moreover, the results presentation and comparisons are **improper and unfair** (see Q1 and Q2 for details).

- There is a limitation in the benchmarking setup, as only one benchmark from the math domain (AIME) and one from the web domain are presented. This does not sufficiently support the paper’s claims or demonstrate the effectiveness of the proposed method through empirical evidence. It is recommended to include results on at least two classic math benchmarks, such as **AMC23**, **Minerva**, or **Olympiads**, to strengthen the evaluation. Additionally, regarding the web domain, it would be helpful to clarify whether your method can be applied to more actual, real-world web tasks such as **WebArena** or **WebShop**, as WebWalkerQA is quite limited to reflect the actual web browsing & exploring ability.

- The idea and framework is similar to previous work such as Reflexion and Self-Refine, even though it's discussed.


Decision: Reject