Agent Capability Problem (ACP)

• Agent Capability Problem (ACP) is a formal framework defining agent abilities using state abstractions and probabilistic models to enable discovery and alignment in complex environments.
• It integrates methodologies such as augmented Bayesian networks, semantic embeddings, and decentralized Bayesian learning to support effective multi-agent planning and coordination.
• ACP underpins secure negotiation protocols and economic models that facilitate scalable capability discovery and robust coordination even under partial observability.

The Agent Capability Problem (ACP) concerns the formal modeling, discovery, prediction, alignment, and utilization of agent capabilities—considered both individually and within systems of interacting, often heterogeneous, agents. ACP encapsulates several fundamentally distinct but related research threads across planning, learning, communication, economic mechanism design, protocol engineering, and multi-agent coordination. It is central to the design of robust, scalable, and efficient autonomous and multi-agent systems.

1. Formal Representations of Agent Capabilities

The foundational approach to ACP frames agent capabilities as partial-state abstractions. In this formalism, each agent φ is associated with relevant Boolean state variables $X_\phi$, and a capability is a quadruple (C, D; A, B), denoting that starting from all $X_i \in C$ true, $X_i \in D$ false, there exists an operation to reach all $X_i \in A$ true and $X_i \in B$ false. Formally, the implication is $C\wedge \neg D \rightarrow A \wedge \neg B$. These capabilities can be structured via an augmented Bayesian network (ABN) in which each variable has pre- and post-operation counterparts, with causal dependencies encoded in a DAG and stochastic parameters estimated by Beta distributions (Zhang et al., 2014).

Alternative approaches encode capabilities as vectors $C_i \in \mathbb{R}^d$ in a semantic embedding space (Guo et al., 24 Nov 2025), as logical capacities modifying available action sets (Ballot et al., 2023), or as private type parameters organizing feasible agent policy spaces (Jin et al., 2023). These representations enable both epistemic and computational reasoning about agent powers in strongly typed, uncertain, or context-dependent environments.

2. Learning and Inferential Frameworks

A central aspect of ACP is acquiring capability models from data, especially in the presence of limited or incomplete observations. The Bayesian learning procedure for capability models uses execution traces $(S_1,\dots,S_K)$, potentially with only start and end states, to perform O(1) per-example parameter updates. Each trace is interpreted as a success or failure for all capabilities consistent with observed preconditions and effects, yielding posteriors over capability parameters (Zhang et al., 2014).

In decentralized cooperative tasks, agents are modeled with private capability “types” and maintain beliefs over the types of others, updating these beliefs using consistent Bayesian rules embedded in "capability type structures." This construction allows efficient decentralized inference even when the set of potential capabilities is totally ordered and not globally observable (Jin et al., 2023). In the context of the Internet of Agents, scalable, updatable indexing (e.g., product quantization in latent spaces) supports rapid capability discovery at scale (Guo et al., 24 Nov 2025), with continual learning schemes maintaining robust retrieval performance.

3. Capability-Aware Planning and Solvability Prediction

Within the capability-based planning paradigm, the ACP is to compose agents (each with a capability or action model) to produce a plan maximizing the probability of goal achievement (MAP-MM). Here, mixed human-robot teams are supported by integrating abstract, probabilistic human capability models with deterministic STRIPS-style robot action spaces. Planning complexity is PSPACE-complete; with polytrees, capability planning can be tractable (Zhang et al., 2014). Capabilities confer particular advantages when trace completeness is low, as learning and planning both tolerate missing intermediate observations.

Complementing model-based planning, an information-theoretic framework for ACP quantifies agent solvability through entropy and mutual information measures. For hypothesis space Θ and solution set 𝒮, the minimum number of actions required to resolve the task is $$C_{\rm eff} = \frac{I_\text{total}}{I_\text{step}} C_\text{step}$$, where $I_\text{total}$ is the entropy of the solution indicator, $I_\text{step}$ is the per-action information gain, and $C_\text{step}$ is the per-action cost. This yields tight lower (and upper) probabilistic bounds on required search effort and generalizes to LLM-based, Bayesian optimization, and active learning agents (Lutati, 8 Dec 2025).

4. Protocols, Negotiation, and Capability Discovery

Large-scale ACP arises in open multi-agent environments and agentic internet protocols. The Agent Network Protocol (ANP) and Agent Capability Negotiation and Binding Protocol (ACNBP) define layered mechanisms for capabilities to be reliably advertised, discovered, negotiated, verified, and bound under stringent security guarantees (Chang et al., 18 Jul 2025, Huang et al., 16 Jun 2025). Three main stages are:

• Capability Announcement and Description: Agents publish semantic capability descriptors (e.g., JSON-LD, schema.org, ADP), including method signatures, input/output schemas, and non-functional constraints (Chang et al., 18 Jul 2025, Guo et al., 24 Nov 2025).
• Discovery and Matching: Agents or registries (e.g., decentralized ANS, DHT) index capabilities for low-latency retrieval, using semantic similarity and constraint-based ranking (Guo et al., 24 Nov 2025, Huang et al., 16 Jun 2025).
• Negotiation and Binding: Structured negotiation protocols (10-step ACNBP, meta-protocol handshake) coordinate session setup, authentication (ECDHE, DIDs), extension negotiation, and capability attestation (certificates, ZKP), culminating in a cryptographically signed binding commitment (Huang et al., 16 Jun 2025).

These protocols are designed to support provable security properties (authentication, integrity, non-repudiation), extension/fallback for evolving standards, and scalability via distributed architectures.

5. Alignment, Coordination, and Collective Action

In multi-agent systems, ACP encompasses both the alignment of agent models and effective collaborative behavior. In LLM-based systems, the capability gap arising from independently trained components (e.g., upstream "planning" vs. downstream "grounding" agents) is addressed by joint alignment strategies such as MOAT, which uses alternating preference-based optimization and supervised grounding improvement. Theoretical claims guarantee monotonic convergence in end-to-end task rewards (Zhu et al., 11 Sep 2025).

At the protocol level, communication alone (A2A, ACP) does not guarantee group-level coordination. The Ripple Effect Protocol (REP) introduces formal sharing of local sensitivities ($s_i$)—signals reflecting how an agent's decisions would adjust under environmental changes—enabling distributed gradient-style convergence on global or group-optimal solutions. REP outperforms decision-only protocols (41–100% coordination improvement) across supply chain, preference aggregation, and resource allocation benchmarks (Chopra et al., 18 Oct 2025). The distinction between capability modeling and explicit coordination primitives is highlighted as critical for large-scale agentic systems.

6. Economic and Logical Characterizations

Economic models of ACP, such as capacity-constrained principal-agent problems, exhibit a scaling result: introducing an exogenous capacity bound $C$ on agent effort cost transforms the Pareto frontier by uniformly scaling down output and incentives, with scaling factor explicitly tied to the agent's capacity (Clark, 2 Dec 2024). Logical frameworks such as Capacity-ATL incorporate agent capacities as first-class modifiers of action sets, with verification and strategy synthesis operating under imperfect information regarding other agents’ private capacities and dynamic learning via epistemic logic (Ballot et al., 2023).

7. Open Problems, Limitations, and Future Directions

Persisting challenges in ACP include:

• Scalability and Heterogeneity: Efficient, memory-enhanced continual discovery and verification in agent populations of 10^4 or greater; cross-domain composition and incentive design (Guo et al., 24 Nov 2025).
• Learning under Partial Observability: Robustness of inferential methods when capability traces are extremely sparse, noisy, or adversarially manipulated (Zhang et al., 2014, Jin et al., 2023).
• Protocol Evolution: Backward-compatibility, extension negotiation, and dynamic team architectures in changing environments (Huang et al., 16 Jun 2025).
• Coordination Beyond Communication: Ensuring convergence, fairness, and robustness in the presence of strategic, partially trusted, or non-stationary agents (Chopra et al., 18 Oct 2025).
• Formal Guarantees and Epistemics: Logical guarantees for knowledge about other agents’ capacities and the design of strategies that work under uncertainty or adversarial manipulation (Ballot et al., 2023).

Across these threads, ACP continues to unify foundational theory and protocol engineering for agent discovery, learning, planning, negotiation, and collective action in modern autonomous and multi-agent environments.