The Agent Capability Problem: Predicting Solvability Through Information-Theoretic Bounds
This addresses the problem of resource allocation for autonomous agents, offering a generalizable framework that is incremental by linking existing principles through an information-theoretic lens.
The paper introduces the Agent Capability Problem (ACP), a framework for predicting if an agent can solve a task under resource constraints by modeling problem-solving as information acquisition, and shows that ACP predictions closely track actual agent performance, improving efficiency over greedy and random strategies.
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. \