AgentRank-UC: Dynamic Agent Ranking

• AgentRank-UC is a dynamic algorithm that fuses recency-weighted usage and competence metrics to rank autonomous agents in challenging environments.
• It employs exponential decay, fixed-point iterations, and geometric fusion to balance usage and competence while ensuring privacy and scalability.
• Empirical results demonstrate its robustness, efficiency, and sybil-resistance in diverse simulation scenarios and multilabel ranking tasks.

AgentRank-UC is a dynamic algorithm for ranking autonomous agents in web-scale, partially observed interaction environments. Originating as the core ranking algorithm in the DOVIS protocol for the "Web-of-Agents," AgentRank-UC systematically integrates recency-weighted agent usage statistics and multivariate competence metrics, producing robust rankings even under fragmented or adversarial signal sources. The nomenclature “UC” denotes the synthesis of Usage and Competence dimensions in a unified, PageRank-inspired fixed-point framework. Unlike PageRank, which presupposes a transparent and global network topology, AgentRank-UC operates over privacy-preserving, locally aggregated telemetry, supporting performance-aware selection and scalable trust establishment among machine-native agents (Krishnamachari et al., 5 Sep 2025).

1. Construction of Usage and Competence Metrics

AgentRank-UC is built upon two orthogonal edge-weighted interaction graphs over the directed agent interaction space: usage and competence.

Usage Kernel

For each triple (caller $i$, callee $j$, task $k$), usage is summarized as a recency-decayed count: $$N_{ij}^{(k)} = \sum_{t \in \text{calls}} \omega(t), \quad \omega(t) = e^{-\lambda (T - t)}$$

$T$ denotes the current time, $\lambda>0$ is the decay rate (half-life $H = \ln2/\lambda$). Aggregation yields: $U_{ij} = \sum_k N_{ij}^{(k)}$

The row-stochastic usage kernel $P$ normalizes each caller row: $$P_{ij} = \begin{cases} U_{ij}/\sum_{j'} U_{ij'} & \text{if } \sum_{j'} U_{ij'} > 0 \ v_j & \text{otherwise} \end{cases}$$ where $j$0 is a strictly positive prior.

Competence Kernel

Competence aggregates signed, decayed outcome signals (successes, quality $j$1, latency $j$2, cost $j$3, risk $j$4): $j$5 With these, compute the Beta-Bernoulli mean success: $j$6 and task utility: $j$7 Aggregate transformed utilities: $j$8 Normalize as: $j$9 with $k$0 a strictly positive competence prior.

2. Fixed-point Formulation and Fusion

Let $k$1 be the usage rank vector and $k$2 the competence rank vector. Damping parameters $k$3 ensure contractive dynamics: $k$4 After convergence, the outputs are fused geometrically, tuning the usage-competence trade-off via $k$5: $k$6 The final ranking $k$7 is a normalized vector in $k$8. This fusion preserves strict positivity, continuity, and monotonicity with respect to submetric improvements.

3. Protocol Infrastructure: DOVIS

The AgentRank-UC algorithm is operationalized atop DOVIS, a five-layer protocol stack:

• Discovery: Indexers aggregate OAT-Lite telemetry and periodically compute/publish $k$9.
• Orchestration: Callers emit idempotent, per-epoch usage and performance records for each edge $$N_{ij}^{(k)} = \sum_{t \in \text{calls}} \omega(t), \quad \omega(t) = e^{-\lambda (T - t)}$$0, processed with exponential decay.
• Verification: All records are cryptographically signed; optional mutual acknowledgment and randomized audit sampling (1–5% of edges) enforce integrity. Identity strength (e.g., staked/TEE-attested) confers prior weight in $$N_{ij}^{(k)} = \sum_{t \in \text{calls}} \omega(t), \quad \omega(t) = e^{-\lambda (T - t)}$$1 or $$N_{ij}^{(k)} = \sum_{t \in \text{calls}} \omega(t), \quad \omega(t) = e^{-\lambda (T - t)}$$2.
• Incentives: Honest reporters receive exposure rewards; malicious activity penalized by weight slashing or rank suppression. Telemetry credits and cold-start priors ensure fair onboarding for newcomer agents.
• Semantics: Schema normalization (latency in ms, cost in credits, qualities/risks in $$N_{ij}^{(k)} = \sum_{t \in \text{calls}} \omega(t), \quad \omega(t) = e^{-\lambda (T - t)}$$3); versioned task taxonomies and support for backward compatibility.

This protocol ensures record authenticity, incentivizes truthful reporting, and protects participant privacy by only aggregating minimal, summary-level telemetry (Krishnamachari et al., 5 Sep 2025).

4. Theoretical Guarantees

AgentRank-UC possesses several formally stated guarantees:

Guarantee	Statement	Implication
Convergence	Power iterations contract in $$N_{ij}^{(k)} = \sum_{t \in \text{calls}} \omega(t), \quad \omega(t) = e^{-\lambda (T - t)}$$4, unique fixed points $$N_{ij}^{(k)} = \sum_{t \in \text{calls}} \omega(t), \quad \omega(t) = e^{-\lambda (T - t)}$$5 exist	Fast stable computation
Fusion	$$N_{ij}^{(k)} = \sum_{t \in \text{calls}} \omega(t), \quad \omega(t) = e^{-\lambda (T - t)}$$6 is well-posed and stable	Continuous, robust to input variations
Monotonicity	Improving any submetric on edge $$N_{ij}^{(k)} = \sum_{t \in \text{calls}} \omega(t), \quad \omega(t) = e^{-\lambda (T - t)}$$7 weakly increases $$N_{ij}^{(k)} = \sum_{t \in \text{calls}} \omega(t), \quad \omega(t) = e^{-\lambda (T - t)}$$8	Local utility improvements propagate to agent rank
Cold-start	$$N_{ij}^{(k)} = \sum_{t \in \text{calls}} \omega(t), \quad \omega(t) = e^{-\lambda (T - t)}$$9 via teleport guarantee $T$0 for all $T$1	Newcomers have nonzero baseline visibility
Stability	$T$2	Small changes yield bounded output shifts
Sybil-resist.	Mass of collusive set $T$3 bounded: $T$4; $T$5	Sybil/pumping attacks are rate-limited; usage-only is not exploitable for full rank share

All bounds and properties hold for positive priors, stochastic kernels, and strict damping ($T$6) (Krishnamachari et al., 5 Sep 2025).

5. Algorithmic Implementation

The canonical AgentRank-UC computation consists of:

1. Telemetry aggregation: For each $T$7, compute decayed counts $T$8, successes $T$9, means $\lambda>0$0.
2. Success posterior: Compute $\lambda>0$1 for each edge and task.
3. Edge weights: Derive usage ($\lambda>0$2) and competence ($\lambda>0$3) weights by aggregating across tasks and applying the softplus activation to utilities.
4. Row normalization: Produce $\lambda>0$4 and $\lambda>0$5, inserting priors for zero rows.
5. Fixed-point iterations: Iterate $\lambda>0$6 and $\lambda>0$7 to convergence.
6. Fusion: Geometrically combine $\lambda>0$8 and $\lambda>0$9 with parameter $H = \ln2/\lambda$0; normalize to obtain $H = \ln2/\lambda$1.

All computations scale linearly with the number of interaction triples, with power-iteration typically converging in fewer than 30 steps.

6. Empirical Evaluation and Scalability

AgentRank-UC has been validated in simulated agent ecosystems consisting of $H = \ln2/\lambda$2 agents executing $H = \ln2/\lambda$3 archetypal tasks, covering cases such as Popular-but-Mediocre (PbM), Niche-but-Excellent (NbE), Balanced-Strong (BS), Cheap-but-Risky (CbR), Sybil-Clique (Syb), and Newcomer-Good (NcG). Key experimental findings include:

• Performance: AgentRank-UC nearly matches an oracle success-rate baseline and outperforms usage-only variants in NDCG@10, Quality@10, Spearman's $H = \ln2/\lambda$4, and Regret@10.
• Trade-off tuning: Adjusting the fusion parameter $H = \ln2/\lambda$5 smoothly interpolates final ranking behaviors between usage-driven and competence-driven extremes.
• Adaptivity: Rankings adjust at rates determined by the decay half-life $H = \ln2/\lambda$6. Shorter $H = \ln2/\lambda$7 accelerates demotion/promotion post-performance shocks.
• Cold-start and monotonicity: Newcomer agents receive baseline exposure and strictly benefit from additional successes. Informative priors enable rapid onboarding.
• Sybil-resistance: Collusive Sybil clusters receive lower aggregate rank mass under AgentRank-UC compared to usage-only (14–17% vs. 11–12%); Sybil mass declines after burn-in phases.
• Scalability: Step time is $H = \ln2/\lambda$8 in the number of populated interaction triples; telemetry and index relays operate with low communication overhead.

These results demonstrate that performance-aware agent ranking can be achieved—without global network transparency—given minimal, privacy-preserving, and verifiable telemetry (Krishnamachari et al., 5 Sep 2025).

7. Relation to Partial Feedback Multilabel Ranking

The term "AgentRank-UC" also denotes a multilabel classification and ranking algorithm in partial feedback regimes, where online optimization is guided by second-order upper-confidence bound (UCB) methods (Gentile et al., 2012). This instance targets sequential label selection under partial information, employing UCB exploration and per-label generalized linear modeling. The algorithm admits an $H = \ln2/\lambda$9 cumulative regret bound under adversarial covariates. In large-scale experiments on multilabel benchmarks (Mediamill, Sony CSL Paris), AgentRank-UC attained performance within a few percent of full-information baselines, validating the UCB-driven partial feedback methodology.

In summary, AgentRank-UC constitutes a class of dynamic, partially observed ranking algorithms supporting robust, scalable agent selection in open and adversarial environments, with firm theoretical guarantees and validated empirical effectiveness (Krishnamachari et al., 5 Sep 2025, Gentile et al., 2012).