The Agent Capability Problem: Predicting Solvability Through Information-Theoretic Bounds

2025-12-08

AI Summary

This paper introduces the Agent Capability Problem (ACP) framework to predict the feasibility of task solving by intelligent agents under resource constraints. Method: Departing from conventional heuristic strategies, ACP models task solving as an information acquisition process from an information-theoretic perspective. It defines an effective cost $ C_{ ext{eff}} $ as a unified predictive metric for resource requirements, and derives its theoretical lower bound and probabilistic upper bound—providing rigorous criteria for task solvability. Integrating principles from active learning, Bayesian optimization, and reinforcement learning, ACP quantifies search cost via total information content $ I_{ ext{total}} $ and per-step information gain $ I_{ ext{step}} $. Results: Experiments demonstrate that ACP significantly outperforms greedy and random baselines in LLM-driven agents, accurately estimating actual search overhead, effectively characterizing task difficulty, and improving resource utilization efficiency.

Technology Category

Constraint Satisfaction and Optimization: Constraint Learning and AcquisitionSearch and Optimization: Learning to SearchMultiagent Systems: Distributed Problem Solving

Application Category

Search and Retrieval-Augmented AI: Agentic searchEconomics, Online Markets and Human Computation: Cost models of using LLMs in production systemsSemantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

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. ",提出智能体能力问题(ACP)框架，通过信息量理论预测智能体在资源约束下能否解决问题，计算解决所需信息量及每步成本，实验证明该方法优于贪婪和随机策略。,,2025-12-08,2025.0,,https://arxiv.org/pdf/2512.07631,0,0,2026-01-21 17:08:43,2026-01-21 17:08:43 https://arxiv.org/abs/2512.07629,Sustainable Exploitation Equilibria for Dynamic Games,"We introduce the Sustainable Exploitation Equilibrium (SEE), a refinement of Markov Perfect Equilibrium (MPE) for dynamic games with an exploiter-exploitee structure. SEE imposes two additional discipline conditions: (i) viability, requiring state trajectories to remain inside a sustainability set; and (ii) renegotiation-proofness with exploiter-optimal selection, to retain only those viable equilibria that are immune to Pareto-improving renegotiations, with ties resolved in favor of the exploiter. In our base formulation the exploitee cannot exit the relationship (no outside option), but retains a strategic effort margin that affects dynamics and payoffs. We establish existence under appropriate conditions and illustrate SEE in a hegemon-client model of foreign politics, where tribute demands trade off against the client's governance effort.

Problem

• Predicting agent solvability under resource constraints
• Framing problem-solving as information acquisition process
• Generalizing across LLM-based and agentic workflows

Innovation

• Information-theoretic bounds predict agent solvability
• Unified framework links active learning and reinforcement learning
• Cost-effective resource estimation before search execution