用信息论预测智能体能否完成任务，提前算出资源消耗
The Agent Capability Problem: Predicting Solvability Through Information-Theoretic Bounds
- 将问题求解视为信息获取，计算所需总信息量与每步获得信息量
- 有效成本公式可准确预测实际搜索开销，优于盲目或贪心策略
- 适用于大模型和智能体流程，融合主动学习等方法的统一视角
何时应让自主智能体投入资源执行任务？本文提出智能体能力问题（ACP）框架，用于在资源约束下预测智能体能否解决问题。不同于经验启发式方法，ACP将问题求解建模为信息获取过程：智能体需获取$\Itotal$比特信息以识别解，每一步动作可获$\Istep$比特信息，代价为$\Cstep$，由此得出有效代价$\Ceff = (\Itotal/\Istep) \Cstep$，该值可在搜索前预测资源需求。我们证明$\Ceff$是期望成本的下界，并提供紧致的概率上界。实验表明，ACP预测与实际智能体性能高度吻合，在控制搜索努力的同时显著提升效率，且在基于大语言模型和智能体的工作流中具有泛化性。该框架通过统一的信息论视角，连接主动学习、贝叶斯优化与强化学习的核心思想。
原文摘要 · Abstract (English)
When should an autonomous agent commit resources to a task? We introduce the Agent Capability Problem (ACP), a framework for predicting whether an agent can solve a problem under resource constraints. Rather than relying on empirical heuristics, ACP frames problem-solving as information acquisition: an agent requires $\Itotal$ bits to identify a solution and gains $\Istep$ bits per action at cost $\Cstep$, yielding an effective cost $\Ceff = (\Itotal/\Istep), \Cstep$ that predicts resource requirements before search. We prove that $\Ceff$ lower-bounds expected cost and provide tight probabilistic upper bounds. Experimental validation shows that ACP predictions closely track actual agent performance, consistently bounding search effort while improving efficiency over greedy and random strategies. The framework generalizes across LLM-based and agentic workflows, linking principles from active learning, Bayesian optimization, and reinforcement learning through a unified information-theoretic lens. \
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