Proxy Evaluation in Swarm Systems

• Proxy Evaluation in SWARM is a framework that uses surrogate metrics to summarize high-dimensional states for assessing multi-agent system performance and safety.
• It employs techniques like generalized moments, distributed consensus, and soft-label assessments to reduce communication load and achieve scalable evaluation.
• These methodologies enable efficient benchmarking, system governance, and optimization in settings where direct measurement is impractical.

Proxy evaluation in SWARM refers to systematically assessing multi-agent system performance, safety, or emergent behaviors by means of lower-dimensional, surrogate, or otherwise indirectly observed measurements rather than direct access to the full system state or final ground truth. Proxy evaluation frameworks in swarm and multi-agent systems span a spectrum: from distributed estimation of collective state via low-dimensional statistics, to continuous soft-proxy assessment of outcomes, to reputation-weighted aggregation in decentralized AI swarms. These methodologies share two foundational goals: reducing the dimensionality and communication costs of system-level evaluation, and enabling governance, benchmarking, or optimization in settings where ground truth is inaccessible or delayed.

1. Core Concepts: Proxy Metrics and Surrogates

Proxy evaluation centers on constructing and operationalizing metrics, models, or surrogate states that stand in for hard-to-observe or high-dimensional true system variables. In swarm robotics, generalized moments (GMs) serve as canonical proxies, capturing mean position, variance, or higher-order statistical summaries of agent configurations. Given agent positions $s^j \in \mathbb{R}^d$, a proxy GM is defined as $T^P(\mathbf{s}) = \frac{1}{N} \sum_{j=1}^N P(s^j)$ for polynomial $P$ (Yan et al., 2020). This reduces the $2N$-dimensional swarm state to a tractable low-dimensional vector $\boldsymbol{\eta}$ suitable for distributed monitoring.

In continuous performance assessment, scalar error metrics such as $$e_N^\delta(x_1,\ldots,x_N) = \int_\Omega |\rho_N^\delta(z) - \rho(z)| dz$$ are used as proxies for evaluating spatial coverage, with $\rho(z)$ a target density and $\rho_N^\delta$ a kernel density estimate of the swarm (Anderson et al., 2019). In multi-agent safety, the proxy may be a composite soft label $p = \sigma(k \hat v)$ indicating the estimated probability of safety or utility, rather than a binary outome (Aiersilan et al., 19 Mar 2026).

The unifying principle is that proxies are carefully chosen summaries, surrogates, or statistically constructed signals that uphold the monotonicity or sensitivity of evaluation with respect to the true target feature of interest.

2. Distributed Proxy Estimation and Consensus

Distributed proxy evaluation in swarm systems requires each agent to independently estimate global proxies using only local information and limited communication. The principal architecture for this is the combination of local denoising (Kalman filter) and dynamic consensus (e.g., asynchronous gossip), as formalized in the Generalized Moments Consensus Algorithm (GMCA) (Yan et al., 2020).

The prototypical workflow is:

• Each agent $j$ maintains a local state estimate $T^P(\mathbf{s}) = \frac{1}{N} \sum_{j=1}^N P(s^j)$0 using its own noisy observations and a standard discrete-time Kalman filter.
• After each update, the agent computes a proxy increment $T^P(\mathbf{s}) = \frac{1}{N} \sum_{j=1}^N P(s^j)$1, mapping its denoised state to the desired functional (moment) space.
• Swarm-wide, a randomized pair of neighbors exchange their current proxy estimates ($T^P(\mathbf{s}) = \frac{1}{N} \sum_{j=1}^N P(s^j)$2), averaging and incorporating local increments; all others apply updates with their own increments only.
• This dynamic couples classic consensus algebra with stochastic estimation, ensuring $T^P(\mathbf{s}) = \frac{1}{N} \sum_{j=1}^N P(s^j)$3 tracks the true moment $T^P(\mathbf{s}) = \frac{1}{N} \sum_{j=1}^N P(s^j)$4, up to quantifiable, closed-form error bounds.

A critical property established in (Yan et al., 2020) is that the mean consensus error is independent of the collective control input $T^P(\mathbf{s}) = \frac{1}{N} \sum_{j=1}^N P(s^j)$5, depending only on system size, consensus topology ($T^P(\mathbf{s}) = \frac{1}{N} \sum_{j=1}^N P(s^j)$6 of the gossip matrix), and individual agent maneuvering bounds. This enables proxy evaluation to track global features robustly, in parallel with arbitrary underlying multi-agent dynamics.

3. Soft-Label Proxy Evaluation and Safety Trade-offs

In system-wide risk assessment frameworks, such as SWARM (Aiersilan et al., 19 Mar 2026), proxies are directly mapped onto probability space: the outcome of each agent interaction is assigned a soft label $T^P(\mathbf{s}) = \frac{1}{N} \sum_{j=1}^N P(s^j)$7, indicating the posterior likelihood of a positive (safe, correct) result, computed via $T^P(\mathbf{s}) = \frac{1}{N} \sum_{j=1}^N P(s^j)$8, then passed through a sigmoid.

Governing system behavior under this regime involves:

• Continuous-valued payoffs: Expected surplus and harm are calculated under $T^P(\mathbf{s}) = \frac{1}{N} \sum_{j=1}^N P(s^j)$9, so agent utility and costs become $P$0-weighted expected values.
• Soft risk metrics: System-level toxicity is $P$1, while quality gap reflects selection-induced adverse effect: $P$2.
• Governance levers modulate cost terms or enforce additional acceptance restrictions contingent on the observed proxies, including taxes, reputation decay, circuit breakers, random audits, and harm internalization.

Quantitative experiments (Aiersilan et al., 19 Mar 2026) reveal inherent trade-offs: stricter governance (e.g., higher taxes, more aggressive harm internalization) reliably reduces aggregate social welfare but does not improve average toxicity, while only carefully tuned thresholds (e.g., circuit breaker setting $P$3) can approach Pareto-optimal safety-welfare frontiers. The adoption of soft proxies also enables detection of strategic proxy gaming, e.g., agents optimizing for threshold passing without improving true safety—a phenomenon binary evaluations fail to catch.

4. Proxy State-Based and Swarm Inference in LLM and AI Systems

Proxy evaluation extends to multi-agent LLM settings, where ground-truth knowledge or deterministic backends may be absent. Proxy state-based evaluation (Chuang et al., 18 Feb 2026) employs an LLM-driven state tracker that recursively infers a structured proxy state $P$4 from the complete dialog and tool-call trace, approximating the true effect of each interaction. This enables robust, scalable benchmarking of tool-using agents by evaluating whether the final proxy state matches scenario-specific targets.

Key features include:

• Structured proxies (JSON-like states) reflecting domain-relevant variables.
• Automated LLM judgments for goal completion and hallucination detection, benchmarked against human agreement.
• Metrics (goal-completion, error, hallucination rates) based exclusively on proxy state and judge output; no reliance on a deterministic database or direct replay.

By calibrating the proxy scenario specification and using robust LLM architectures for state tracking and judging, this approach yields stable, model-differentiating evaluation even in complex multi-turn, multi-tool settings.

In the "swarm inference" paradigm for decentralized AI (Larin et al., 27 Oct 2025), proxy evaluation is realized via peer-ranked consensus. Each node in a network—representing a distinct model or agent—generates both candidate responses and pairwise rankings of other nodes' outputs. Proxy quality is determined via a reputation-weighted Bradley–Terry aggregation of these rankings, yielding a global score for each answer. Critically, node influence (reputation) evolves based on demonstration of correctness and ranking reliability, and a proof-of-capability mechanism enforces Sybil resistance. This design demonstrably outperforms individual models and naive majority voting in hard AI benchmarks and maintains robustness under adversarial prompting.

5. Proxy Metrics in Swarm System Design and Optimization

Proxy evaluation is central to design iteration and optimization of swarm architectures. Harwell and Gini (Harwell et al., 2019) formalize three quantitative proxy metrics to guide algorithmic selection in large robot swarms:

• Scalability metric: Captures parallelism via the serial fraction $P$5, analogously to the Karp–Flatt metric in parallel computation, quantifying how efficiently performance scales with swarm size.
• Emergence/self-organization metric: Measures sublinear growth of interference loss with swarm size, with a high $P$6 indicating robust self-organization.
• Flexibility metrics: Reactivity $P$7 and adaptability $P$8, computed via DTW distances to idealized performance curves under environmental changes, formally connect dynamic responses to algorithmic hypotheses.

Iterative deployment of these proxies across increasing scales, environments, and control algorithms enables early detection of scalability bottlenecks or emergent coordination failures, informing controller and system design decisions.

In continuous-performance tasks such as coverage, the kernel-based error metric $P$9 (Anderson et al., 2019) provides an analytically tractable, implementation-agnostic proxy for spatial uniformity. Realizable bounds and sampling-distribution benchmarks support principled choices of swarm sizing and control law evaluation.

6. Proxy Models in Swarm-Based Optimization

Proxy evaluation also underpins optimization workflows involving swarm intelligence, such as particle swarm optimization (PSO) guided by physics-based surrogate models (Frerichs, 29 Aug 2025). In divertor-target design for fusion reactors, FLARE acts as a proxy evaluating solution candidates $2N$0 (angle and position) by rapidly simulating heat flux distributions. The PSO loop embeds this proxy at each iteration, minimizing an objective function $2N$1 with penalty terms reflecting design constraints.

Proxy fidelity (e.g., parameterizations encoding upstream vs. downstream plasma assumptions) directly sculpts the optimization landscape, determining feasible optima and robustness to noise. Evaluation cost and convergence properties reflect a balance between computational budget (proxy cost), proxy model noise (via Monte Carlo sampling), and optimization accuracy. The architecture demonstrates the utility of surrogates in large-scale, high-dimensional swarm optimization tasks, emphasizing the need for careful calibration and validation of proxy assumptions.

7. Limitations, Best Practices, and Comparative Summary

Proxy evaluation in SWARM and related multi-agent platforms provides tractable, scalable, and theoretically justified alternatives to direct observation or fully centralized monitoring. However, accuracy and robustness depend critically on:

• The fidelity of the proxy metric/model to the underlying variable or behavior of ultimate interest.
• Proper quantification of uncertainty and error bounds, as in consensus tracking or probabilistic safety metrics.
• Resistance to strategic manipulation or proxy gaming; soft proxies and continuous auditing offer superior detection of such effects.

Best practices synthesized from contemporary research include:

• Selecting proxy structures tailored to domain-relevant, observable aggregates (e.g., moments, structured states, pairwise judgments).
• Embedding proxies in distributed estimation frameworks with closed-form convergence or risk guarantees (Yan et al., 2020, Aiersilan et al., 19 Mar 2026).
• Incorporating robust benchmarking via scenario diversity, LLM judge calibration, and human supervision as practical in complex agentic applications (Chuang et al., 18 Feb 2026).
• Calibrating proxy penalties and governance parameters empirically to balance safety, welfare, and performance trade-offs (Aiersilan et al., 19 Mar 2026).
• Using statistical and sampling-distribution techniques to interpret observed proxy values and benchmark against randomized or theoretical maxima/minima (Anderson et al., 2019, Harwell et al., 2019).

Table: Representative Proxy Evaluation Approaches

Domain	Proxy/Surrogate	Aggregation/Consensus Method	Key Quantitative Guarantees
Swarm robotics	Generalized moments, $2N$2	Kalman + gossip consensus; kernel integration	Bounded error, CLT for coverage proxy
LLM agents	LLM-inferred proxy state	LLM judges, scenario completeness	~1–3% error rates, high human–LLM agreement
Decentralized AI	Peer ranking, response quality	Bradley–Terry, reputation weighting	+17–25% absolute perf. gains vs. majority
Multi-agent safety	Soft label $2N$3, continuous $2N$4	Modular governance, soft audits	Welfare–toxicity trade-offs; proxy-gaming detection

In summary, proxy evaluation frameworks are a foundational component of modern SWARM and multi-agent system design, facilitating scalable, distributed, and auditable assessment, enabling system-wide governance, and supporting robust, flexible architectures across robotics, language agents, and AI collectives (Yan et al., 2020, Aiersilan et al., 19 Mar 2026, Chuang et al., 18 Feb 2026, Larin et al., 27 Oct 2025, Frerichs, 29 Aug 2025, Harwell et al., 2019, Anderson et al., 2019).