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

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. \