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Why Keep Your Doubts to Yourself? Trading Visual Uncertainties in Multi-Agent Bandit Systems

Jusheng Zhang, Yijia Fan, Kaitong Cai, Jing Yang, Jiawei Yao, Jian Wang, Guanlong Qu, Ziliang Chen, Keze Wang

arXiv:2601.18735v1cs.AIcs.LG

TL;DR

Multi-agent VLM coordination faces economic and scalability challenges, while heuristic approaches ignore costs and uncertainty structure. Agora treats uncertainty as a tradable asset and coordinates agents through profitability-driven market mechanisms. Across five benchmarks, it reports accuracy gains with lower cost than competing approaches.

  • Problem

    Existing multi-agent coordination heuristics rely on proxies that ignore costs and fine-grained uncertainty structure, despite the economic challenges of scaling VLM systems.

    Source: §1 · pp. 1–2

  • Method

    Agora represents epistemic uncertainty as a structured, tradable asset and uses profitability-driven trading within a decentralized market coordinated by a market-aware Broker.

    Source: §3.1 · p. 5, §3.2 · p. 5, §5 · p. 9

  • Results

    Across five benchmarks, Agora reports gains of up to +8.5% accuracy at over 3× lower cost.

    Source: §5 · p. 10

  • Takeaways & Limitations

    The experiments establish market-based coordination as a principled approach to economically viable multi-agent visual intelligence systems.

    Source: §5 · p. 10

Abstract

from arXiv · show

Vision-Language Models (VLMs) enable powerful multi-agent systems, but scaling them is economically unsustainable: coordinating heterogeneous agents under information asymmetry often spirals costs. Existing paradigms, such as Mixture-of-Agents and knowledge-based routers, rely on heuristic proxies that ignore costs and collapse uncertainty structure, leading to provably suboptimal coordination. We introduce Agora, a framework that reframes coordination as a decentralized market for uncertainty. Agora formalizes epistemic uncertainty into a structured, tradable asset (perceptual, semantic, inferential), and enforces profitability-driven trading among agents based on rational economic rules. A market-aware broker, extending Thompson Sampling, initiates collaboration and guides the system toward cost-efficient equilibria. Experiments on five multimodal benchmarks (MMMU, MMBench, MathVision, InfoVQA, CC-OCR) show that Agora outperforms strong VLMs and heuristic multi-agent strategies, e.g., achieving +8.5% accuracy over the best baseline on MMMU while reducing cost by over 3x. These results establish market-based coordination as a principled and scalable paradigm for building economically viable multi-agent visual intelligence systems.

1 INTRODUCTION

Agora reframes multi-agent coordination as a decentralized market that treats uncertainty as a scarce, tradable resource. Its structured uncertainty model, profitability-driven trading, and market-aware broker target cost-effective coordination, and experiments report strong performance with improved cost-effectiveness.

1 INTRODUCTION

  • As VLM-based multi-agent systems scale, the paper identifies coordination under information asymmetry and bounded rationality, alongside spiraling operational costs, as challenges to economic viability.It frames intelligence as a scarce resource requiring principled management rather than a brute-force commodity.Source: §1 · p. 1
  • Existing approaches such as Mixture-of-Agents and KABB use proxies including consensus or semantic similarity rather than optimizing for cost and fine-grained uncertainty.The paper argues this makes them provably suboptimal and wasteful.Source: §1 · pp. 1–2
  • Agora recasts multi-agent coordination as a decentralized micro-economy in which agents trade quantifiable uncertainty using price signals and economic incentives.The framework aims to reveal private information and move the system toward a cost-effective equilibrium despite information asymmetry and bounded rationality.Source: §1 · p. 2
  • The methodology combines multidimensional uncertainty quantification, profitability-driven trading, and a market-aware Broker that initializes collaboration using a utility function.These components respectively target structure-aware allocation, economic rationality, and economically sound initialization.Source: §1 · p. 2
  • Across multiple visual-understanding benchmarks, Agora achieves state-of-the-art performance while improving cost-effectiveness.The introduction presents these results as support for scalable, economically viable multi-agent systems.Source: §1 · p. 2

2 PROBLEM FORMULATION

This section frames multi-agent coordination as a constrained economic optimization problem: reduce operational cost while resolving uncertainty to an acceptable level. It argues that common heuristic coordinators ignore essential cost or uncertainty structure, making them unreliable optimizers.

2 PROBLEM FORMULATION

  • Figure 1 contrasts heuristic coordination based on flawed proxies with Agora’s dynamic market, where emergent prices enable coordination.The section uses the comparison to motivate a shift from proxy-based coordination toward explicit economic reasoning.Source: Figure 1 · p. 2
  • The paper attributes the scalability bottleneck to soaring costs and redundant computation when uncertainty is handled without economic discipline.It frames the underlying challenge as treating intelligence as a scarce economic resource rather than a brute-force commodity.Source: §2 · pp. 2–3

2.1 THE ECONOMIC OBJECTIVE OF MULTI-AGENT COORDINATION

  • The coordination objective is to minimize expected operational cost while resolving final uncertainty to an acceptable level ϵ.The setup models heterogeneous agents by unit processing costs and expertise across perceptual, semantic, and inferential uncertainty.Source: §2.1 · p. 3

2.2 THE FAILURE OF HEURISTIC PROXIES FOR ECONOMIC RATIONALITY

  • Aggregation heuristics such as MoA equate consensus with truth, an assumption that breaks when agents share architectural biases and correlated errors.For ambiguous inputs, consensus can amplify shared hallucinations.Source: §2.2 · p. 3
  • KABB-style routing scores historical performance and semantic similarity but omits processing costs and collapses structured uncertainty into a scalar proxy.The paper links this structural ignorance to higher residual uncertainty than Agora, as illustrated in Figure 2.Source: §2.2 · p. 3, Figure 2 · p. 3

2.3 THE CORE CHALLENGE: A CALL FOR A NEW PARADIGM

  • A coordinator is agnostic when its selection process is invariant to agent costs and collapses the uncertainty vector into a scalar proxy.The paper identifies MoA and KABB as examples of these two forms of agnosticism.Source: §2.3 · p. 4
  • Agnostic coordination is not guaranteed to solve the stated objective and is provably suboptimal when the heuristically preferred agent is not the most cost-effective resolver.The section therefore calls for mechanisms that explicitly integrate cost and uncertainty.Source: §2.3 · p. 4

3 METHODOLOGY: THE AGORA MARKET FRAMEWORK

Agora addresses agnostic coordination by turning epistemic uncertainty into a structured asset and reallocating it through economically rational trades. A Thompson Sampling-based Broker initializes the market, which iteratively trades until no profitable feasible move remains.

3 METHODOLOGY: THE AGORA MARKET FRAMEWORK

  • Agora recasts coordination as a decentralized micro-economy that explicitly accounts for costs and uncertainty structure by making uncertainty a quantifiable, tradable asset.The framework is presented as a constructive solution to the optimization problem posed earlier.Source: §3 · p. 4

3.1 ESTABLISHING THE MARKET: FROM UNCERTAINTY TO TRADABLE ASSETS

  • Epistemic uncertainty is the reducible, tradable information gap, represented across perceptual, semantic, and inferential dimensions; aleatoric uncertainty is irreducible systemic risk.Each agent’s uncertainty portfolio combines self-generated uncertainty with uncertainty acquired through market trades, allowing distinct components to be priced and traded independently.Source: §3.1 · p. 5

3.2 THE CORE MECHANISM: A PROFITABILITY-DRIVEN TRADING PROTOCOL

  • The trading protocol evaluates the change in total cost from reallocating an uncertainty packet and executes a trade only when it is profitable and feasible for the receiving agent.The displayed cost-delta derivation compares costs before and after a transfer; admissibility requires ΔC < 0 and sufficient receiving-agent capacity.Source: §3.2 · p. 5

3.3 MARKET EXECUTION: THE BROKER AND THE AGORA ALGORITHM

  • A Thompson Sampling-based Broker selects an economically sound initial agent, then the market repeatedly applies trades until none remain, reaching a locally optimal cost-efficient equilibrium.The algorithm describes this as utility-maximizing initialization followed by iterative greedy cost descent.Source: §3.3 · pp. 5–6
  • Table 1 reports percentage scores across visual benchmarks, marks the best and second-best results, and gives Agora’s gains over the top baseline.Agora routes tasks within the baseline pool.Source: Table 1 · p. 6

4 EXPERIMENTS

Experiments evaluate Agora with five VLM agents across visual-understanding benchmarks and coordination strategies. Results report benchmark gains, a favorable accuracy–cost trade-off, and performance differences across broker and strategy ablations.

4.3 THE ROLE OF THE MARKET-AWARE MAB STRATEGY

  • 79.0% accuracy and 70.5 UAPS give market-aware MAB the top MMMU (Val) scores, beating KABB by 3.0% accuracy and 5.0 UAPS points.The comparison holds the uncertainty-trading protocol constant while replacing the selector.Source: Table 2 · p. 7, §4.3 · p. 8

4.1 COMPREHENSIVE VISUAL UNDERSTANDING PERFORMANCE

  • Agora posts +1.1–8.5% gains across benchmarks, reaches new SOTA on MMBench V11 Test, InfoVQA, and CC-OCR, and places second on MMMU and MathVision.The study uses five benchmarks and compares Agora with constituent models and external SOTA VLMs.Source: §4 · p. 6, §4.1 · p. 7

4.2 COMPARISON WITH ALTERNATIVE ROUTING AND MULTI-AGENT STRATEGIES

  • 89.50% accuracy gives Agora the highest MMBench score; KABB-VLM and MOA score 87.12% and 86.65% at 1.24× and 3.11× relative cost, respectively.Their COI values are 1.53 and 1.82, with residual uncertainty 0.21 and 0.25; cheaper routers reduce cost to 0.73–0.91 but lose 8–9.6 accuracy points and have uncertainty of 0.27–0.33.Source: §4.2 · p. 7, Figure 4 · p. 8

4.4 COST AND PERFORMANCE BALANCE ANALYSIS

  • As the pool grows, accuracy rises at sublinear cost; it peaks at 89.6% for N=8 and changes marginally at N=9.At N=1, Agora reaches 87.5% accuracy at a 0.02057 cost ratio; every N≥1 configuration has a better cost ratio than qwen-72b (0.05656) and KABB-VLM (0.05191).Source: Figure 5 · p. 8, §4.4 · pp. 8–9

4.5 MODULE AND STRATEGY ABLATION STUDIES

  • The full strategy leads the MMBench ablation with 89.50% accuracy, 0.16 final epistemic uncertainty, 1.25 COI, and 78.33% UAPS.Removing Strategic Uncertainty causes the largest reported degradation: accuracy -3.08%, Ufinal epis +0.07, UAPS -6.75 points, and cost +6%; removing Synergy, Task Match, or Time Decay also reduces performance, while Only Net Return performs substantially worse.Source: Table 3 · p. 9, §4.5 · p. 9

5 CONCLUSION

Agora coordinates multi-agent VLMs through a market-based framework that treats uncertainty as a tradable asset and uses a market-aware Thompson Sampling broker. Across five benchmarks, its profitability-driven trading protocol delivers accuracy gains at substantially lower cost.

5 CONCLUSION

  • Agora coordinates multi-agent VLMs by treating epistemic uncertainty as a structured, tradable asset across perceptual, semantic, and inferential dimensions.A market-aware Thompson Sampling broker guides collaboration.Source: §5 · p. 9
  • Across five benchmarks, Agora achieves gains of up to +8.5% accuracy at over 3× lower cost.The framework uses a profitability-driven protocol for rational uncertainty trading and cost-efficient equilibria.Source: §5 · p. 10

ETHICS STATEMENT

The study follows the ICLR Code of Ethics and uses publicly available vision-language benchmarks under their respective licenses and terms. It does not collect or distribute human data and does not intend the methods for sensitive or high-stakes deployment without additional safeguards.

ETHICS STATEMENT

  • The study reports no human-subjects research, collection of personally identifiable information, or annotation of sensitive attributes.It also states that it does not create or distribute new human data.Source: ETHICS STATEMENT · p. 10
  • Experiments use publicly available, widely used vision-language benchmarks under their respective licenses and terms of use..Source: ETHICS STATEMENT · p. 10
  • The methods are not intended for sensitive or high-stakes applications without additional safeguards.Source: ETHICS STATEMENT · p. 10

REPRODUCIBILITY STATEMENT

This section presents Agora’s market-based coordination framework and specifies how expertise, trading conditions, and cost-benefit thresholds govern uncertainty transfers. It formalizes when transfers may reduce system costs and total uncertainty.

C.1.2 MANAGEABILITY DIMENSIONS: EPISTEMIC UNCERTAINTY AND ALEATORIC UNCERTAINTY

  • Epistemic uncertainty is reducible through additional information or better models, whereas aleatoric uncertainty represents inherent, irreducible randomness or task ambiguity.The framework separates these manageability types to support targeted uncertainty trading.Source: A PRELIMINARY · p. 15, §C.1.2 · p. 19

B.2 UNCERTAINTY QUANTIFICATION AND MANAGEMENT

  • Agora replaces cost-agnostic heuristic coordination with profitability-driven trading of perceptual, semantic, and inferential uncertainty as structured assets.The framework uses a market-aware Broker extending Thompson Sampling to initiate collaborations and optimize coordination for cost.Source: A PRELIMINARY · p. 16, §B.2 · p. 17

C.1.1 FORMAL DEFINITION AND EXPANSION OF CORE UNCERTAINTY DIMENSIONS

  • Uncertainty is structured into perceptual, semantic, and inferential dimensions; inferential uncertainty combines confidence in the most likely outcome with the predictive distribution’s entropy.The balance between these two sources is controlled by γ.Source: §B.2 · p. 17, §C.1.1 · p. 18

B.3 MULTI-ARMED BANDITS AND DECISION-MAKING

  • The Broker extends multi-armed bandits with a market-aware utility integrating expected reward, explicit costs, task similarity, team synergy, and a Strategic Uncertainty Index.Agora bases collaboration on explicit cost-benefit analysis rather than heuristic rules.Source: §B.3 · p. 17

C.2.1 UNCERTAINTY FLOW EQUATION

  • Agent uncertainty comprises its base uncertainty plus multidimensional uncertainty transferred from other agents, enabling Agora to track uncertainty flows across the system.The transfer mechanism is introduced to actively manage uncertainty and optimize operating costs.Source: §C.2 · p. 19, §C.2.1 · p. 20

C.2.2 TREND OF CHANGE IN SYSTEM-TOTAL UNCERTAINTY: CONSERVATION/CONVERGENCE ANALYSIS

  • System uncertainty decreases when receiver expertise absorbs transferred uncertainty; ΔUsys=0 when ξ_l+κ=1, while typically κ≈1 and ξ_l>0 yields ΔUsys=−ξ_lT_kl.The analysis distinguishes effective resolution by a more suitable agent from uncertainty merely being redistributed.Source: §C.2.2 · p. 20
  • With receiver expertise above zero, transfers can reduce total system uncertainty, but convergence depends on base uncertainty generation and continued trading effectiveness.If base uncertainty tends to zero and transfers continue, total uncertainty may fall to zero; cost-optimized trading can instead yield a stable distribution where uncertainty continues to be processed.Source: §C.2.2 · p. 21

C.2.3 DEEPENING THE TRANSFER COST-BENEFIT ANALYSIS: CONSIDERING TOTAL TRANSFER AMOUNT AND EXPERT KNOWLEDGE

  • A trade reduces variable processing costs only when the sender’s unit cost exceeds the receiver’s expertise-adjusted unit cost, while execution must also account for fixed and transaction costs.The effective receiver cost is cj(1 − ξj); the transferred amount and receiver expertise determine the effective uncertainty added to the receiver.Source: §C.2.3 · pp. 21–22

C.3 UNCERTAINTY TRADING PROTOCOL

  • The protocol treats transferable epistemic uncertainty as a resource traded according to comparative advantage and cost-effectiveness to reduce system operating costs..Source: §C.3 · p. 22

C.3.1 PREREQUISITES FOR A TRADE

  • Trades require a sufficiently large uncertainty imbalance and must keep the receiver’s expertise-adjusted post-trade uncertainty within its processing capacity.These prerequisites aim to avoid ineffective trades and prevent the receiver from being overloaded.Source: §C.3.1 · p. 23

C.3.2 COST-BENEFIT ANALYSIS OF A TRADE

  • A trade must reduce variable processing costs, and its overall expected benefit must exceed a threshold after considering uncertainty, costs, and trade impacts.The comprehensive evaluation accounts for fixed-cost effects and implicit transaction costs or risks, not just marginal processing-cost savings.Source: §C.3.2 · p. 24

C.3.3 MARKET EQUILIBRIUM ANALYSIS - BRIEF THEORETICAL PERSPECTIVE

Agora’s market reaches a local equilibrium when no bilateral trade satisfies all protocol conditions; the appendix connects this trading framework to comparative advantage and an uncertainty-aware broker. It also describes the broker’s strategic uncertainty index, convergence conditions, and the agent-pool evaluation setup.

C.3.3 MARKET EQUILIBRIUM ANALYSIS - BRIEF THEORETICAL PERSPECTIVE

  • Trading terminates at a local equilibrium under finite tradable uncertainty or a positive minimum trade volume, strictly decreasing bounded-below system cost, and no remaining eligible trades.Each trade reduces system cost by more than δmin; the proof therefore establishes finite convergence under the stated assumptions.Source: §C.3.3 · p. 24

C.3.4 APPLICATION OF COMPARATIVE ADVANTAGE THEORY

  • Comparative advantage favors assigning each uncertainty type to the agent with the lowest opportunity cost, even without an absolute cost advantage across all dimensions.Agora’s local effective-cost trades can align the uncertainty distribution with comparative advantage when agent costs and expertise reflect their dimension-specific efficiencies.Source: §C.3.4 · p. 25

C.4 UNCERTAINTY-AWARE MAB SELECTION STRATEGY

  • The uncertainty-aware MAB broker scores agents using expected reward net of cost alongside task match, recency, team synergy, and strategic uncertainty value.The strategic factor favors agents expected to contribute system-level cost savings through market participation.Source: §C.4 · p. 26

C.4.1 THEORETICAL GUARANTEES: REGRET & CONVERGENCE

  • Classic O(log T) or O(T) regret bounds are difficult to prove; under a stationary context, selection is designed to converge to the best expected-value agent.In non-stationary contexts, tracking performance depends on contextual-change speed and predictability and on factor-estimate accuracy and adaptation speed.Source: §C.4.1 · p. 27

C.4.2 MATHEMATICAL DECONSTRUCTION OF STRATEGIC UNCERTAINTY INDEX (USTRATEGIC(S))

  • The strategic uncertainty index estimates an agent’s expected net system-cost savings across eligible future trades, extending MAB utility from local rewards to market-wide benefits.The expectation covers future market states, other agents’ behavior, and trade volumes.Source: §C.4.2 · pp. 27–28

D IMPACT OF AGENT POOL CONFIGURATION ON AGORA

  • The agent-pool study varies heterogeneity, specialization, and pool size on 100 sampled tasks each from MMMU (Val) and MMBench V11 Test, averaging results over five runs.Metrics include accuracy, inference time, trading frequency, uncertainty reduction, normalized operational cost, and complex-task failure rate.Source: D IMPACT OF AGENT POOL CONFIGURATION… · p. 28, §D.1 · pp. 28–29

D.1 EXPERIMENTAL SETUP

  • The setup contrasts diverse and homogeneous pools, general-purpose and uncertainty-specialized agents, and pool sizes N = 2, 3, 5, 10, and 15.The homogeneous pool uses five instances of one model with varied initialization seeds; larger pools add duplicates and distinct models.Source: §D.1 · p. 29

D.2 RESULTS AND ANALYSIS

Pool configuration affects Agora’s accuracy, uncertainty reduction, cost, and failure rates, while the accompanying FLOPs experiment evaluates uncertainty-based dispatch against fixed and heuristic routing strategies.

D.2 RESULTS AND ANALYSIS

  • 79.2% MMMU accuracy and 89.5% MMBench accuracy in heterogeneous pools exceed homogeneous-pool results of 74.5% and 86.3%.Heterogeneous pools also show more trades per task (0.8 vs. 0.3), greater uncertainty reduction (25.4% vs. 20.1%), and lower complex-task failure (5.2% vs. 8.7%).Source: §D.2 · p. 29
  • 80.8% MMMU accuracy and 90.2% MMBench accuracy accompany high specialization, versus 79.2% and 89.5% for low specialization.Uncertainty reduction is 30.1% versus 25.4%, while inference time and normalized cost rise slightly (2.6s vs. 2.5s; 1.12 vs. 1.10).Source: §D.2 · pp. 29–30
  • Accuracy and uncertainty reduction improve through N = 10, reaching 80.1% MMMU accuracy and a trade frequency of 1.0; at N = 15, MMMU gains only +0.4% as cost reaches 1.30 and time 3.5s.The passage attributes diminishing returns to increased selection and communication complexity; N = 2 has a 10.5% complex-task failure rate.Source: §D.2 · p. 30

E.1 EXPERIMENT SETUP

  • The simulated agents are assigned approximate per-token costs of 1.4 TFLOPs for a 7-billion-parameter small model, 2.8 TFLOPs for a 14-billion-parameter medium model, and 15.6 TFLOPs for a 78-billion-parameter large model.The estimates assume FLOPs are roughly proportional to parameter count.Source: §E.1 · p. 30

E FLOPS COMPARISON AND COMPUTATIONAL EFFICIENCY

  • The FLOPs comparison simulates 100 tasks averaging 20 output tokens across small, medium, and large agents, comparing static assignment, random routing, Top-2 routing, tiered cascade, and uncertainty-aware dispatch.In Agora’s simulation, tasks start with the small agent and escalate when estimated uncertainty or resolution cost exceeds a threshold.Source: §E.1 · p. 30

E.2 EXPERIMENTAL RESULTS AND DISCUSSION

Agora’s uncertainty-aware dispatch balances accuracy and computational cost in the simulated comparison. It approaches the large-only strategy’s accuracy with substantially lower FLOPs and a more favorable cost-performance ratio than the other dynamic approaches described.

E.2 EXPERIMENTAL RESULTS AND DISCUSSION

  • 5.54 PFLOPs gives Agora 88.7% accuracy, close to Large-only’s 89.2%, while using 82.2% fewer FLOPs than its 31.2 PFLOPs.The reported cost-performance ratio is 0.0625 for Agora, versus 0.3496 for Large-only, 0.0789 for Top-2 Routing, and 0.0910 for Tiered Cascade; Figure 6 plots accuracy against cost-performance ratio.Source: §E.2 · p. 31, Figure 6 · p. 31
  • Agora’s 0.0625 cost-performance ratio is lower than Top-2 Routing’s 0.0789 and Tiered Cascade’s 0.0910, while their respective accuracies are 86.1% and 86.8%.Small-only has a lower ratio of 0.0389 but 72.0% accuracy.Source: §E.2 · p. 31
  • Figure 6 compares routing strategies by accuracy and cost-performance ratio, with lower ratios indicating better performance on that cost measure.The passage describes Agora’s uncertainty-aware strategy as balancing accuracy and cost efficiency.Source: Figure 6 · p. 31, §E.2 · p. 31

F SUPPLEMENTARY CORE COMPONENT ABLATION DISCUSSION

The supplementary ablations examine Agora’s uncertainty dimensions, the distinction between epistemic and aleatoric uncertainty, trading parameters, and MAB hyperparameters. Results support multidimensional uncertainty assessment and selective trading of epistemic uncertainty, while showing trade-offs at parameter extremes.

F SUPPLEMENTARY CORE COMPONENT ABLATION DISCUSSION

F.1 IMPACT OF UNCERTAINTY DIMENSIONS

  • Removing perceptual uncertainty produces the largest reported dimensional-ablation penalty: MMBench accuracy falls to 85.37% and UAPS to 70.59%.Removing any one of the three dimensions degrades performance and raises residual uncertainty and collaboration overhead; single-dimension configurations perform worse across the reported metrics.Source: §F.1 · pp. 32–33, Figure 7 · p. 32

F.2 VALIDATION OF EPISTEMIC-ALEATORIC DISTINCTION IN UNCERTAINTY TRADING

  • Trading only epistemic uncertainty preserves stronger performance than adding aleatoric uncertainty: trading 10% Ualea yields 88.17% accuracy, while undifferentiated trading yields 84.66%.Undifferentiated trading also yields a 67.92% UAPS; the reported degradation is consistent with aleatoric uncertainty being irreducible by reallocating it among agents.Source: Figure 7 · p. 32, §F.2 · p. 33

F.3 ROBUSTNESS AND BOUNDARY ANALYSIS OF TRADING PROTOCOL PARAMETERS

  • Extreme trading thresholds can reduce efficacy: τtrade = 0.05 increases trading to 5.8 trades and COI to 1.36, while τtrade = 0.25 cuts trading to 1.9 trades.A low τbenefit of 0.02 encourages 4.7 trades and may increase overhead; a high value of 0.16 reduces trading to 2.3 and may forgo gains.Source: §F.3 · p. 34
  • Relaxed receiver capacity reaches 89.63% accuracy and 78.71% UAPS, with slightly higher collaboration overhead and cost than stricter capacity.Strict capacity marginally constrains performance; the passage says sufficient receiver bandwidth is necessary for effective market operation.Source: §F.3 · p. 34

G.1 ABLATION ON UCB1 EXPLORATION CONSTANT C

  • The UCB1 exploration-constant passage reports that performance tends to degrade when C is too low or too high, but labels its default C = 1.0 hypothetical.The referenced Table 5 is identified as an ablation on MMBench V11 Test.Source: §G.1 · p. 34, Table 5 · p. 34

G.2 ABLATION ON MAB LEARNING RATE α

  • The learning-rate passage labels its default α = 0.1 hypothetical and says lower values can slow adaptation while higher values may cause instability.The referenced Table 6 is an ablation on MMBench V11 Test.Source: §G.2 · p. 35, Table 6 · p. 35

G.3 ABLATION ON TIME DECAY FACTOR λ∆t

The appendix evaluates Agora’s time-decay setting and documents the configurations used for the framework, comparison strategies, and model inference, alongside runtime-analysis setup.

G.3 ABLATION ON TIME DECAY FACTOR λ∆t

  • With λ∆t = 0.99, the ablation reports slightly reduced performance without decay and cautions that rapid decay may discard useful history prematurely.The passage describes the default as effective and says larger deviations can negatively affect performance.Source: §G.3 · p. 35, Table 7 · p. 35

H.1 AGORA FRAMEWORK PARAMETERS

  • Agora’s full-strategy settings include time-decay base 0.99, task-match weight 0.2, synergy exponent 0.8, strategic-uncertainty exponent 1.2, and uniform Beta priors.Additional settings weight perceptual, semantic, and inferential uncertainty at 0.4, 0.3, and 0.3; the agent pool varies by experiment section.Source: §H.1 · p. 36

H.2 HYPERPARAMETERS FOR COMPARATIVE MODELS AND STRATEGIES

  • Comparative strategies were adapted to the VLM setting, using Agora’s base agent pool where applicable and hyperparameters from original formulations, standard practices, or task-specific tuning.The appendix lists configurations for no-trading Agora, KABB, RL-based selectors, and alternative routing strategies.Source: §H.2 · pp. 36–37

H.3 MODEL INFERENCE PARAMETERS

  • Across VLMs and external comparators, inference used OpenRouter, greedy decoding, and a 2,048-token maximum unless otherwise specified.Source: §H.3 · p. 37

I RUNTIME ANALYSIS

  • Runtime analysis measures average per-question inference time across 1, 3, 5, 7, and 10 rounds on 500 MMBench V11 Test questions using an NVIDIA A100.The stated operational aim is to keep average inference time below approximately 30 seconds.Source: I RUNTIME ANALYSIS · pp. 37–38

I.1 RESULTS AND DISCUSSION

On MMBench V11 Test, inference time rises with processing rounds, with 3–7 rounds within the stated latency target. The appendix also describes prompt design and illustrative expert personas.

I.1 RESULTS AND DISCUSSION

  • 8.73 seconds for one round, 14.29 for three, 22.86 for five, 28.51 for seven, and 36.17 for ten; the 10-round setting exceeds the 30-second guideline.The authors describe 3–7 rounds as a practical balance and suggest configurations beyond approximately 7–8 rounds may be less suitable for real-time use without optimization or intensive task needs.Source: Table 8 · p. 38, §I.1 · p. 38

J PROMPT SETTING STATEMENT

  • Prompt configurations combine general agent personas with task-specific templates, using structured reasoning, evidence requirements, role specialization, and uncertainty awareness.The authors report iterative prompt refinement improved benchmark accuracy by 1–8% and cost-efficiency by focusing agents on high-confidence domains.Source: J PROMPT SETTING STATEMENT · pp. 38–39

J.1 GENERAL PROMPTS FOR EXPERT ROLES AND THE AGGREGATOR

  • Illustrative analysis and strategy personas emphasize logical decomposition and practical relevance, respectively, with the accompanying discussion linking them to reasoning-heavy tasks and cost reduction.Source: §J.1 · pp. 39–40

J.2 PROMPTS FOR VLM EXPERTS IN BENCHMARK EVALUATIONS

This appendix documents the prompts and configurations used for VLM experts in Agora experiments, including its distinction among perceptual, semantic, and inferential uncertainty. It also describes expert organization for multimodal case analysis and mechanisms for updating agent selection and checking capacity during uncertainty trades.

J.2 PROMPTS FOR VLM EXPERTS IN BENCHMARK EVALUATIONS

  • CoT prompt elements boost performance by 2-5% on reasoning metrics.The prompts were optimized for visual-language tasks and incorporate evidence citation to mitigate bias and improve factual accuracy.Source: §J.2 · p. 40

J.2.1 BASE EXPERT PROMPTS

  • Specialist prompts cover logical reasoning, scene description, context, visual attributes, and action inference, using evidence-based CoT tailored to each task.The logical-reasoning prompt targets inference tasks such as MMMU; scene description supports spatially grounded MVBench tasks, while the other prompts address context-dependent, attribute-based, and action-oriented tasks.Source: §J.2.1 · pp. 40, 42, 43, 44
  • Object-recognition prompting improves accuracy by 3-4% on MMBench for object-heavy queries.It asks experts to list significant objects, describe their appearance and location, and cite visual evidence.Source: §J.2.1 · p. 40
  • The Wise Integrator resolves contradictions and synthesizes expert inputs, reducing final epistemic uncertainty by up to 10%.Its instructions emphasize relevance, accuracy, and clear, actionable responses.Source: §J.2.1 · p. 41

K.1 AGORA FRAMEWORK PARAMETERS

  • Agora uses extended Thompson Sampling with uncertainty weights of 0.4, 0.3, and 0.3, trading thresholds of 0.15 and 0.08, and an agent pool sized by experiment.The pool uses 5 agents in Section 4.1, varies from 1 to 9 for Section 4.4, and is fixed at 6 in Sections 4.2, 4.3, and 4.5.Source: §K.1 · pp. 44–45

K.2 HYPERPARAMETERS FOR COMPARATIVE MODELS AND STRATEGIES

  • Comparative strategies use Agora’s base pool where applicable, while VLM inference uses greedy decoding and a 2048-token maximum.The comparative configurations include no-trading Agora, KABB and RL-based selectors, and alternative routing strategies; inference uses OpenRouter with default API settings unless specified.Source: §K.2 · p. 45, §K.3 · p. 46

L.2 UNCERTAINTY QUANTIFICATION AND ESTIMATION

  • Agora quantifies uncertainty as perceptual, semantic, and inferential rather than as a single scalar.Perceptual uncertainty concerns confidence in recognizing visual signals, semantic uncertainty captures ambiguity among scene interpretations, and inferential uncertainty combines top-outcome confidence with predictive-distribution entropy; a table centralizes core variable definitions.Source: §L.2 · pp. 46–47, §L.1 · p. 46

L.3 EXPLANATION OF KEY ELEMENTS IN FIGURE 3

  • The appendix identifies the “Value Model” and “Too Many?” label in Figure 3 as architectural elements needing clarification.It states that these components are clarified but does not provide their definitions in this passage.Source: §L.3 · p. 47
  • Agora’s Value Model scores the selected agents’ final output and returns a quantitative Policy Selection Reward to the MAB.The reward may come from comparison with a ground-truth answer or a pretrained reward model.Source: §L.3 · p. 47
  • The MAB uses the Policy Selection Reward to update its selection policy under the Thompson Sampling rule and improve future agent selection.The passage identifies this feedback as essential to the MAB’s learning process.Source: §L.3 · p. 47
  • Before a trade, the “Too Many?” check rejects uncertainty packets that would exceed the receiver’s capacity, enforcing Uj(t) + Tij(t) ≤ Cj(t).This admission control is described as maintaining system stability and agent effectiveness.Source: §L.3 · p. 47

M CASE ANALYSIS

  • The case studies include two successful and two unsuccessful examples, with object-recognition, scene-description, and text/OCR experts analyzing images.Each expert’s analysis and uncertainty score are reported; colored underlines highlight key excerpts.Source: M CASE ANALYSIS · p. 48

M.1 SUCCESSFUL CASE

  • The successful-case passage credits role-specialized experts with improving factual accuracy, contextual completeness, and logical consistency across diverse questions and input formats.It also characterizes the architecture as enhancing robustness, interpretability, and stability.Source: §M.1 · p. 48
  • The successful-case tables illustrate how distinct expert roles cover multiple modalities and semantic dimensions, while uncertainty estimates let the system prioritize contributions by reliability.The roles are object recognition, scene understanding, and text/OCR analysis.Source: §M.1 · p. 48

M.2 UNSUCCESSFUL CASE

The unsuccessful cases expose limits in spatial judgments and cross-modal reasoning when conclusions require geometric inference or knowledge unavailable in the image and extracted text. The paper also states that LLM assistance was limited to literature review and manuscript editing.

M.2 UNSUCCESSFUL CASE

  • The system incorrectly judged two sliders to be the same size despite unresolved visual uncertainty, revealing difficulty with spatial ambiguity in 2D depictions of 3D objects.The authors identify missing geometric-perspective reasoning and inadequate use of uncertainty to qualify conclusions when evidence is inconclusive or conflicting.Source: §M.2 · p. 48
  • The system’s ammonia example exposes difficulty linking recognized objects to scientific properties that cannot be inferred from image or OCR evidence.The authors identify absent external knowledge or verification as a design limitation and call for knowledge-grounded reasoning or factual verification.Source: §M.2 · p. 49

STATEMENT ON THE USE OF AI ASSISTANCE

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