Rethinking the Role of Entropy in Optimizing Tool-Use Behaviors for Large Language Model Agents

1. Problem Statement

Large Language Model (LLM) agents excel at complex tasks like mathematical reasoning and multi-hop question answering by interleaving natural language reasoning with external tool calls (e.g., code execution, web search). However, in long-horizon reasoning trajectories, agents often suffer from:

• Excessive Tool Invocation: Triggering unnecessary or low-quality tool calls.
• Performance Degradation: Increased latency, higher computation costs, and reasoning derailment.
• Lack of Fine-Grained Supervision: Existing reinforcement learning (RL) methods often rely solely on outcome rewards (final answer correctness), which provide only endpoint feedback. This fails to guide the agent on when and how to invoke tools during the reasoning process. Conversely, process rewards often rely on hand-crafted rules or external evaluators, which are difficult to design for complex, open-ended tasks.

The core challenge is finding a principled, lightweight, and model-agnostic signal to evaluate tool-call quality during long-horizon reasoning without requiring external annotations.

2. Key Insight: Entropy Reduction

The authors hypothesize that model uncertainty, quantified by entropy, serves as a proxy for tool effectiveness.

• Observation: Through pilot experiments, they observed a strong positive correlation between entropy reduction and high-quality tool calls.
• Mechanism: High-quality tool calls provide relevant information that reduces the model's uncertainty about the next steps (lowering entropy). Conversely, low-quality calls introduce noise or irrelevant information, increasing uncertainty (raising entropy).
• Metric: They define Delta Segment Entropy ($\Delta H_k$) as the difference in entropy between the reasoning segment generated after a tool call ($r_k$) and the segment generated before it ($r_{k-1}$).
  • $\Delta H_k < 0$: Indicates the tool call reduced uncertainty (High Quality).
  • $\Delta H_k > 0$: Indicates the tool call increased uncertainty (Low Quality).

3. Methodology: TEPO Framework

Based on the entropy insight, the authors propose Tool-enhanced Entropy-guided Policy Optimization (TEPO), which integrates entropy reduction signals into the GRPO (Group Relative Policy Optimization) framework via two distinct reward strategies:

A. TEPO-sparse (Efficiency-Focused)

• Goal: Improve tool-use efficiency by reducing the total number of tool calls while maintaining accuracy.
• Reward Design: A sparse outcome reward.
  • The reward is calculated based on the final answer's correctness (F1-score) modulated by the proportion of entropy-reducing tool calls ($m/n$) in the trajectory.
  • Formula: $R_{sparse} = \text{F1} \times \frac{m}{n}$, where $m$ is the count of entropy-reducing calls and $n$ is the total calls.
• Effect: This creates a global incentive for the agent to achieve the correct answer with fewer calls, as increasing $n$ (without increasing $m$) dilutes the reward.

B. TEPO-dense (Performance-Focused)

• Goal: Enhance reasoning performance by optimizing the quality of every individual tool interaction.
• Reward Design: A dense process reward.
  • Every tool call that successfully reduces entropy receives an immediate bonus.
  • Formula: $R_{tool} = \text{F1} \times (1 + \alpha \cdot \mathbb{I}_{entropy\_reduction})$.
  • The advantage is assigned at the tool-level and propagated to the reasoning tokens preceding the tool call.
• Effect: This provides fine-grained, step-by-step supervision, encouraging the agent to internalize the behavior of making only high-quality, uncertainty-reducing tool calls.

4. Experimental Results

The authors evaluated TEPO on diverse domains: Mathematical Reasoning (AIME), Knowledge-Intensive QA (HotPotQA, 2Wiki, Musique), and Deep Search (GAIA, WebWalker, HLE).

• Efficiency (TEPO-sparse):
  • Reduced the average number of tool calls by 72.07% compared to baseline averages.
  • Maintained comparable accuracy to baselines, demonstrating that agents can solve complex tasks with significantly fewer interactions.
• Performance (TEPO-dense):
  • Achieved an average performance improvement of 22.27% over baselines.
  • Outperformed state-of-the-art methods (e.g., ARPO, AEPO, OTC-GRPO) in reasoning accuracy across multiple datasets.
• Scalability:
  • Both methods showed strong scaling laws, with performance improving as model size increased from 1.7B to 14B parameters.
• Delta Entropy Analysis:
  • Post-training analysis confirmed that both TEPO variants significantly increased the proportion of tool calls that resulted in entropy reduction compared to standard SFT models.

5. Key Contributions

1. Empirical Discovery: Identified that entropy reduction is a reliable, model-agnostic indicator of tool-call quality across diverse reasoning domains.
2. Novel Reward Mechanisms: Proposed TEPO, introducing two distinct reward designs:
   • Sparse: Optimizes for efficiency by penalizing excessive tool usage.
   • Dense: Optimizes for performance by rewarding step-wise uncertainty reduction.
3. Lightweight Supervision: Demonstrated that entropy reduction can serve as a self-supervised signal, eliminating the need for hand-crafted rules or external process reward models.
4. Comprehensive Validation: Validated the approach across mathematical, knowledge, and deep search tasks, showing significant gains in both efficiency and accuracy.

6. Significance

This work fundamentally shifts the paradigm of optimizing tool-using agents. Instead of relying on external evaluators or final-answer-only feedback, it leverages the intrinsic uncertainty of the LLM itself as a supervisory signal.

• Adaptability: The method allows agents to adapt to real-world scenarios where defining "correct" intermediate steps is difficult.
• Efficiency vs. Performance Trade-off: By offering two distinct reward strategies, TEPO allows practitioners to choose between optimizing for cost/latency (Sparse) or maximum reasoning capability (Dense).
• Future Direction: It opens a new avenue for using information-theoretic metrics (entropy) not just for exploration, but as a direct reward signal for refining agent behavior in complex, long-horizon tasks.