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A Theory of Information Architecture for Networked Decisions: Freshness, Locality, and Coordination

Scott Moeller, Bhaskar Krishnamachari

arXiv:2609.06351v1eess.SYcs.NIcs.SYmath.OC

TL;DR

Networked decisions trade the coordination value of broad information against the freshness lost while it is gathered and shared. The paper analyzes fixed architectures through prediction of the full-information decision, deriving a fresh-local versus stale-global crossover and an optimal synchronized-snapshot radius.

  • Problem

    Networked agents make coupled decisions from information distributed across space and changing over time, creating a design tradeoff between broad coordination and freshness.

    Source: §1 · p. 1

  • Method

    The paper uses a fixed-information static-team framework for quadratic costs, treating architecture regret as the Q-weighted projection error in reproducing the full-information action while varying scope and age.

    Source: §1 · p. 2

  • Results

    The theory derives a fresh-local versus stale-global crossover and characterizes the optimal synchronized-snapshot radius by marginal balance, with a closed-form scaling law for the canonical model.

    Source: §1 · pp. 2–3, §8 · p. 39

  • Takeaways & Limitations

    Architecture design should track predictability of the full-information decision rather than raw state predictability, since decision sensitivity and coupling shape which uncertainty matters.

    Source: §8 · p. 39

    The analysis is a static-team baseline with exogenous state; its radius family uses synchronized snapshots, and history sufficiency is specific to the common-rate Gaussian model.

    Source: §2.2 · p. 7, §8 · p. 39

Abstract

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Networked systems face a tradeoff between the scope of the information behind a decision and its freshness: a broader view of the system supports better coordination, but assembling and communicating it takes time, so it arrives older. We study this tradeoff for a team of agents that repeatedly choose actions to minimize a shared quadratic cost driven by an environment that evolves on its own, unaffected by the agents' actions. An information architecture specifies what each agent observes, from where, and with what delay; we measure an architecture by the cost it loses relative to a decision made with complete, current information. We first compare fresh local observations with a complete but delayed global view. When every component of the environment decorrelates at a common exponential rate, this comparison reduces to a closed-form threshold on the ratio of delay to coherence time. We then study intermediate architectures in which each agent acts on a time-aligned, and therefore older, snapshot of a wider neighborhood. The optimal neighborhood radius occurs where the marginal value of added scope equals the marginal cost of lost freshness. In a canonical spatial model, this radius is set by the spatial-correlation, decision-relevance, and temporal-propagation lengths. Throughout, architecture performance is governed by the predictability of the optimal decision rather than of the raw state.

1 Introduction

Networked decisions trade the coordination value of broader information against the loss of freshness while it is collected and communicated. The paper evaluates architectures by how well they predict the full-information decision, deriving crossover and optimal-radius results for this scope–age tradeoff.

1 Introduction

  • The analysis treats a shared quadratic-cost team in an exogenous environment and reduces each fixed architecture’s optimization to a Q-orthogonal projection of the full-information action.The outer design problem varies information scope and age jointly.Source: §1 · p. 2
  • Fresh-local information is preferred when stale-global prediction loss exceeds the locally uncaptured share of decision-relevant variation; stronger coupling increases the staleness worth tolerating for global coordination.The endpoint comparison concerns current local observations versus delayed access to the complete state.Source: §1 · pp. 2–3
  • The baseline assumes static information structures: current actions do not alter the environment’s future law or what other agents later observe.Controlled queueing and decentralized Markov decision processes lie beyond this baseline.Source: §1 · p. 3
  • For synchronized neighborhood snapshots, the optimal radius balances spatial-information gain against freshness loss, with a canonical scaling law set by spatial-correlation, decision-relevance, and temporal-propagation lengths.Increasing radius broadens the snapshot but increases its age.Source: §1 · p. 3
  • Architecture performance is governed by predictability of the full-information decision, not raw state predictability, because decision sensitivity and coupling determine which uncertainties matter.A hard-to-predict remote component may be architecturally unimportant if it has little influence on the desired action.Source: §1 · pp. 2, 4
  • The contribution is an exogenous-environment, stagewise team decision valued by prediction error of the full-information decision, yielding scope–age results beyond prior scope-dependent-delay work.The framework complements distributed optimization that specifies communication structure first and freshness metrics that value updates primarily by age.Source: §1 · pp. 3–4

2 Networked Decisions and Information Architectures

The framework separates network geometry, decision coupling, and information architecture to study how information limits affect networked decisions. For quadratic costs, architecture regret is the weighted error in reproducing the full-information decision.

2.1 Network, Environment, and Decision Model

  • The environment evolves exogenously, and agents choose actions to minimize a shared quadratic cost based on its state.The basic results require stationarity and square integrability, but not independence, Gaussianity, or a Markov process.Source: §2 · p. 4, §2.1 · p. 5

2 Networked Decisions and Information Architectures

  • The framework distinguishes network proximity from decision coupling: the graph governs information proximity, while Q and b(·) determine which states and actions interact.These structures need not coincide; strongly coupled agents may be far apart in the information graph.Source: §2.1 · p. 5

2.2 Information Architectures

  • A synchronized-snapshot architecture trades scope for freshness: broader neighborhoods replace narrower, fresher snapshots with older ones.At the graph diameter, the family provides a delayed global snapshot, not the complete delayed global history.Source: §2.2 · pp. 6–7

2.3 Architecture Regret

  • Architecture regret is the optimized expected performance gap from full information; this measure does not separately charge for communication, sensing, or computation.The physical cost of broader information enters through feasible architectures, especially the scope–latency relation.Source: §2.3 · p. 7

2.4 Fixed-Architecture Quadratic Projection

  • Under the quadratic model, the optimal policy for a fixed architecture is the Q-orthogonal projection of the full-information policy onto the admissible policy space.Consequently, regret is exactly the Q-weighted squared error in reproducing the full-information action.Source: §2.1 · p. 6, §2.4 · pp. 8–9

3 Fresh-Local versus Stale-Global Information

This section compares fresh local information with a complete but delayed global view, measuring both against the current full-information decision. Its crossover depends on temporal predictability and how much decision-relevant variation local information captures.

3.1 The Two Architectures

  • The paper compares two pure regimes: current local state for each agent, versus complete system information delayed by τ.A system free to combine the two sources weakly dominates either pure regime.Source: §3 · p. 10

3.2 General Predictability Characterization

  • Staleness matters only insofar as older information fails to predict the current full-information decision; the comparison is between temporal unpredictability and the decision-relevant information missing locally.Fresh-local regret is independent of the global delay, while stale-global regret is governed by prediction error for the current decision.Source: §3.1 · p. 10, §3.2 · pp. 11–12

3.3 Gauss–Markov Temporal Model

  • With common exponential temporal decay, stale-global regret rises from zero toward open-loop regret as the delay grows relative to coherence time T.For fixed positive delay, it approaches open-loop regret as T decreases and zero as T increases.Source: §3.3 · p. 13

3.4 Fresh-Local versus Stale-Global Crossover

  • Fresh-local information beats stale-global information precisely when the temporal loss from delay exceeds the decision-relevant variation omitted locally.Under common-rate Gauss–Markov dynamics and an affine decision, the crossover is expressed as a threshold on the dimensionless delay-to-coherence-time ratio; if local information captures all decision variation, it never strictly wins at finite delay.Source: §3.4 · pp. 13–14

3.5 Role of Decision Coupling

  • In the shared-resource model, stronger coordination coupling increases the locally omitted decision share and moves the crossover toward tolerating greater delay relative to T.With no coupling, current local information suffices, so any positive global delay favors fresh-local information.Source: §3.5 · pp. 15–16
  • The endpoint comparison motivates the broader design problem: choosing an intermediate information radius balances added spatial scope against the delay it requires.The paper next lets the information radius vary rather than restricting the choice to local or global information.Source: §3.5 · p. 16

4 Spatial and Temporal Predictability

Intermediate-radius architectures depend on how well nearby information predicts the optimal decision across both space and time. Under common-rate Gaussian-affine assumptions, spatial omission and temporal staleness combine in an exact composition law.

4.1 Spatial Structure of the Environment

  • Raw spatial correlation alone does not determine architecture regret; the relevant spatial predictability must account for how state uncertainty affects the desired decision.The decision-relevant measure combines spatial statistics, decision sensitivity, and information geometry.Source: §4.1 · p. 17, §4.4 · p. 20

4.2 Temporal Structure

  • The exact composition results use a common temporal decay rate and separable space-time covariance; with nonseparable covariance, the factorization generally does not remain exact.The framework can instead use a joint prediction-error function for more general covariance models.Source: §4.2 · p. 17

4.3 Joint Spatio-Temporal Information

  • Under a common temporal rate and Gaussian assumptions, neighborhood histories can be replaced by current neighborhood snapshots without increasing quadratic team cost for affine decisions.Heterogeneous temporal rates and nonseparable space-time processes need not have this sufficiency property.Source: §4.3 · p. 19

4.4 Decision-Relevant Smoothness

  • The spatial omission function reflects decision-relevant uncertainty, not merely how well nearby observations predict remote states.State modes with little influence on the full-information decision can have little decision value even when they are spatially unpredictable.Source: §4.4 · p. 20
  • The composition law separates temporal innovation from the temporally predictable decision fraction that radius-r information can reconstruct.Spatial information helps only with the portion of the current decision that remains predictable when the snapshot arrives.Source: §4.4 · pp. 20–21

5 Optimal Coordination Scale

The section characterizes how decision-relevant spatial information and the delay needed to obtain it determine the best information radius. In the canonical model, the radius has a closed-form rule and becomes positive only beyond a propagation-versus-correlation threshold.

5.1 Radius-Dependent Information Architectures

  • The general radius family assigns each agent a synchronized neighborhood snapshot delayed according to a nondecreasing information-propagation law.On finite graphs, radii are integer-valued; rounding a continuous optimum is justified only when the interpolated regret curve is unimodal.Source: §5 · p. 21, §5.1 · p. 22
  • A strict interior optimum requires a non-nested information family: broader synchronized snapshots replace narrower, fresher views with older ones.With nested information sets and no explicit acquisition cost, a strict interior minimum cannot occur.Source: §5.1 · p. 22
  • On finite graphs, adding one hop helps precisely when its proportional gain in decision-relevant spatial information exceeds the freshness loss.The exact optimizer is found by minimizing over admissible integer radii.Source: §5 · p. 21, §5.1 · p. 22

5.2 Spatial-Omission versus Temporal-Staleness Tradeoff

  • The continuous optimum balances marginal spatial-information gain against marginal freshness loss, with uniqueness requiring the theorem’s single-crossing conditions.Without those conditions, including under some concave aggregation laws, multiple crossings or boundary optima cannot be excluded.Source: §5.2 · pp. 23–24

5.3 An Exponential Spatial-Predictability Regime

  • Under exponential spatial predictability, optimal scope depends on the fraction of decision variation unavailable locally and on the ratio of temporal propagation length to decision-relevance length.The supplied result expresses this dependence through η0 and LT/ℓc.Source: §5.3 · p. 25

5.4 A Canonical Spatio-Temporal Field Model

  • In the canonical spatio-temporal field model, spatial roughness and long-range decision dependence increase the value of nonlocal information.When decisions are local or the state is nearly constant over space, local observations suffice to predict remote state and spatial omission falls toward zero.Source: §5.4 · pp. 26–27

5.5 Main Result: Closed-Form Optimal Coordination Radius

  • Within the interior regime, the optimal radius increases with temporal coherence, information-propagation speed, and decision-relevance length.The canonical result also identifies LT = vT as the temporal propagation length.Source: §5.5 · p. 28
  • In the canonical line model, the optimal radius is positive exactly when the temporal propagation length exceeds twice the spatial correlation length.The threshold is LT > 2ℓs; beyond it, the preferred radius grows with the excess propagation horizon and decision-relevance length.Source: §5.5 · pp. 27–28

6 Numerical Consistency Checks and Finite-Graph Illustrations

The numerical checks evaluate architecture regret under the corresponding information structures, testing the temporal law, endpoint crossover, and radius tradeoff. Further checks vary decision relevance and graph geometry to examine how preferred radii change.

6.1 Numerical Methodology and Synthetic Environments

  • The numerical methodology evaluates regret using each analytical counterpart’s information structure in an exogenous common-rate Gaussian-affine environment.Experiments 1–2 use exact OU pairs and paired fresh-local/open-loop draws; later checks use scalar composition or Gaussian conditional variances, with 95% confidence intervals for Monte Carlo means.Source: §6 · p. 29, §6.1 · p. 29, Table 2 · p. 29

6.2 Temporal Scaling and the Local–Global Crossover

  • The largest absolute normalized deviation from the exact temporal law was 0.0155, and the root-mean-square deviation was 0.00471 across four stationary common-rate systems.The test varied system dimensions, spatial covariances, objective matrices, and decision operators.Source: §6.2 · p. 30, Figure 1 · p. 30
  • At n = 5 and γ/q = 10, the exact fresh-local–stale-global threshold is 0.109 below the large-system limit; as n grows, it approaches 1/2 log(1+γ/q).The mean absolute boundary error is 0.00111 and the maximum is 0.00557.Source: §6.2 · p. 31, Figure 2 · p. 31

6.3 Emergence of an Optimal Coordination Radius

  • The capped radius minima were 0, 0.626, and 2 for the local, interior, and maximum-radius regimes, respectively.The interior grid and analytical minima were 0.626 and 0.62638; at the cap, ηS(D) remains positive, so decision-relevant state is still omitted.Source: §6.3 · p. 31, Figure 3 · p. 32

6.4 Scaling Laws and Regime Map

  • The mean absolute grid-versus-closed-form radius error was 2.25 × 10−4, below the 0.0016 grid step; the four predicted comparative statics were monotone in the tested range.The preferred radius increased with T, v, and ℓc, and decreased with ℓs; five zero/positive classifications disagreed adjacent to the threshold.Source: §6.4 · p. 32, Figure 4 · p. 33

6.5 State Predictability versus Decision-Relevant Predictability

  • With the graph and state covariance fixed, increasing decision-relevance range moved the discrete optimum from 1 to 2 to 5 hops, despite identical raw state correlation.ηS(0) increased from 0.0460 to 0.258 to 0.572; conditioning checks differed from exact omission by at most 2.39 × 10−3.Source: §6.5 · pp. 32–33, Figure 5 · p. 34

6.6 Finite Graphs beyond the Canonical Geometry

  • Under the reference setting, exact integer optima were 2, 2, 3, and 2 hops for the path, ring, grid, and geometric graph instances.Across these four instances, increasing T changed optima from 1 to 3 hops on path, ring, and geometric graphs, and from 1 to 4 on the grid; increasing per-hop latency weakly decreased the optimum.Source: §6.6 · pp. 33–34, Figure 6 · p. 35

7 Related Work

The related work spans static teams, distributed computation and control, freshness metrics, organizational design, and spatial statistics. The paper distinguishes its focus on exogenous stage decisions valued by prediction error for the full-information action, with spatial scope coupled to information age.

7.1 Static Team Decision Theory

  • Static-team theory supplies the fixed-information decision framework; this paper specializes it to quadratic teams, where the policy is a Q-orthogonal projection of the full-information action.Related work also studies information value, delayed information, and organizational networks; the distinctive object here couples spatial scope to delay through τ(r).Source: §7.1 · p. 36

7.2 Distributed Optimization, Communication Constraints, and Scope

  • Distributed optimization constrains iterative computation, while this paper takes the current full-information decision as a benchmark and designs what agents know when deciding.The contrast with networked control is that prior work optimizes feedback for controlled plants, whereas this setting predicts decisions in an exogenous environment.Source: §7.2 · p. 37

7.3 Freshness and Age of Information

  • Age of Information measures update timeliness, while task-aware freshness work values inference or decision loss; this paper chooses a decentralized team’s spatial scope and information age jointly.Because broader scope incurs greater acquisition delay, spatial omission and temporal staleness are coupled.Source: §7.3 · pp. 37–38

7.4 Centralization, Delegation, and Organizational Economics

  • Organizational-economics work studies information, communication, authority, and coordination; this paper abstracts from incentive conflicts and endogenous information acquisition.Its tradeoff is between broader synchronized snapshots that can improve coordination and their greater age.Source: §7.4 · p. 38

7.5 Spatial Statistics and Graph Signal Processing

  • Spatial statistics and graph signal processing provide covariance and graph-spectral context, but this paper values neighborhoods by their effect on reproducing the full-information decision, not on reconstructing the raw state.Graph-smooth modes matter only insofar as they are decision-relevant, while increasing radius also increases information age.Source: §7.5 · pp. 38–39

8 Discussion and Conclusions

Architecture regret measures the cost of acting with constrained information against the full-information decision, and its design depends on predicting that decision rather than reconstructing raw state. The theory balances broader scope against freshness within an exogenous-state, static-team baseline.

8 Discussion and Conclusions

  • Architecture regret is the loss relative to the full-information decision after optimizing over policies implementable under an architecture.Broader information can improve coordination but loses predictive value while collected and disseminated.Source: §8 · p. 39
  • Theorem 3 characterizes fresh-local versus stale-global endpoints, Theorem 5 identifies the optimal synchronized-snapshot radius by marginal balance, and Theorem 6 gives its canonical-model scaling law.Normalization by open-loop regret separates decision-problem scale from the fraction of decision-relevant variation preserved by an architecture.Source: §8 · p. 39
  • Predictability of the full-information decision, not raw state predictability, governs regret; physical distance can omit remote modes with high decision value.Decision sensitivity and coupling determine whether uncertain state changes the desired joint action.Source: §8 · p. 39
  • The exact projection benchmark assumes exogenous state evolution and static-team decisions; explicit laws additionally rely on quadratic costs and specified Gaussian, affine, or spatial assumptions.The explicit stale-global and composition laws require affine decisions and common-rate Gaussian or Gauss–Markov evolution; the canonical radius formula uses a separable homogeneous field and linear propagation delay.Source: §8 · pp. 39–40
  • Experiments leave temporal-rate heterogeneity, nonseparable covariance, non-Gaussian evolution, nonlinear decisions, and mixed-age architectures untested.Source: §8 · p. 40
  • With heterogeneous temporal modes, the scalar composition law generally becomes a joint spatio-temporal decision-prediction error, with no universal bias direction under a common-rate approximation.Bias direction depends on mode weights and how an effective coherence time is selected.Source: §8 · p. 40
  • Further work includes explicit information-acquisition costs, online adaptation to unknown or nonstationary statistics, and action-dependent dynamic teams where control and signaling interact.In dynamic teams, the fixed-subspace projection characterization generally no longer solves the problem, as Witsenhausen’s counterexample illustrates.Source: §8 · p. 40
  • Expand information scope while the marginal decision value of broader information exceeds the predictive value lost in obtaining it.Source: §8 · p. 40
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