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Receiver-Specific Interventional Valuation of Semantic Atoms for Budget-Constrained Multi-Agent Communication

Danial Dehghani, Maximilian Lübke, Friedemann Laue, Zahra Seifaei, Norman Franchi

arXiv:2610.21504v1eess.SP

TL;DR

A transmitter in cooperative multi-agent communication must decide which semantic content to send to each receiver under limited link budgets. This paper values independently selectable content for each receiver using prospective randomized delivery and transmitter-side estimates. On the intersection benchmark, receiver-specific selection outperforms shared and random alternatives, while exhaustive subset selection can outperform sending the full payload.

  • Problem

    A transmitter must choose content for each receiver under a limited link budget because agents can have different information needs despite sharing one source observation.

    Source: §I · p. 1

  • Method

    The framework identifies receiver-specific controlled-delivery utility through prospective randomized payload delivery before the receiver acts, then estimates it from transmitter-available information to compute signed atom values.

    Source: B. Semantic Atoms, Payloads, and… · p. 3, B. Prospective Utility Identification… · p. 4, §VI · p. 6

  • Results

    On MRIR, receiver-specific selection outperformed shared and random alternatives, and exhaustive subset selection exceeded full-payload transmission at full affordability.

    Source: §VI · p. 6

  • Takeaways & Limitations

    Transmitting all available content need not maximize utility, and receiver-specific semantic valuation can support budget-constrained communication despite imperfect estimates.

    Source: §VI · p. 6

    Practical surrogate training requires a simulator or equivalent reward-evaluation and receiver-feedback mechanism, because labels require privileged offline access.

    Source: B. Prospective Logging and Surrogate… · p. 5

Abstract

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Cooperative multi-agent semantic communication requires deciding not only how a transmitter encodes its observation, but also which resulting semantic content should be delivered to each receiver under a limited link budget. We introduce an encoder-agnostic transmitter-side framework for receiver-specific valuation of independently selectable semantic units, termed semantic atoms. Each atom is assigned a signed value that quantifies whether delivering it is expected to improve or degrade the intended receiver's downstream decision. We formulate this effect through a controlled-delivery utility and identify it via prospective randomized payload delivery before the receiver acts. A shadow receiver estimates this utility using only transmitter-available information, from which receiver-specific leave-one-out (LOO) and Shapley atom values are computed. Experiments on a four-receiver intersection benchmark show 68.4% accuracy in recovering the sign of non-negligible LOO atom effects and a Spearman correlation of 0.302 between estimated and reference LOO values. Under limited budgets, we show that receiver-specific selection consistently outperforms shared and random alternatives, demonstrating the benefit of adapting semantic ranking to the intended receiver. At full affordability, exhaustive subset selection also outperforms full-payload transmission, showing that transmitting all available content need not maximize receiver utility. Overall, our results show that receiver-specific semantic valuation can support effective budget-constrained communication despite imperfect atom-value estimation.

I. INTRODUCTION

The paper addresses how a transmitter should choose semantic content for each receiver when agents have heterogeneous information needs and links are budget-limited. It frames communication as a single pre-action round in a cooperative team, with receiver policies held fixed while payloads are optimized.

I. INTRODUCTION

  • Different routes, local observations, and decision states mean receivers can need different parts of the same observation, while a shared subset may not fit those needs.Sending the full representation to every agent can spend limited per-link budgets on redundant information.Source: §I · p. 1
  • Prior semantic and task-oriented communication work guides representation, transmission, or resource allocation, but does not directly assign selectable content to individual receivers under budgets.The proposed framework evaluates content for the intended receiver and supports different payloads from the same observation.Source: §I · pp. 1–2

A. Cooperative Multi-Agent Communication Setting

  • The system is a cooperative Dec-POMDP in which scheduled agents communicate in one simultaneous, error-free round before acting.Scheduling, relaying, and shared-budget optimization are outside the scope; receiver policies are pretrained and fixed while payloads are optimized.Source: A. Cooperative Multi-Agent… · p. 2

B. Semantic Atoms, Payloads, and Receiver-Specific Utility

The system represents an observation as a common set of independently selectable semantic atoms, then constructs a separate payload for each receiver. Receiver-specific utility measures the expected task contribution of the receiver’s post-communication action under forced delivery, conditioned on transmitter-available context.

B. Semantic Atoms, Payloads, and Receiver-Specific Utility

  • A semantic atom is an operationally minimal encoded component that the selection layer can deliver or withhold independently to each receiver.Atom extraction is modeled as a fixed upstream mapping; its design and training are outside the work’s scope.Source: B. Semantic Atoms, Payloads, and… · p. 2
  • The extracted candidate set is common across receivers, but each receiver’s payload is a separately selected subset of that set.Atom identity is preserved by its index.Source: B. Semantic Atoms, Payloads, and… · p. 2
  • The utility measures the incremental task contribution of the receiver’s post-communication action relative to its no-current-payload behavior, holding other agents’ actions fixed.Source: B. Semantic Atoms, Payloads, and… · p. 2
  • Controlled-delivery utility is the expected receiver-attributed task contribution when a payload is forced onto the focal link before the receiver acts.It averages over the receiver’s private decision state and remaining randomness, conditioning only on transmitter-available context and candidate atoms; nonfocal links retain their joint conditional distribution.Source: B. Semantic Atoms, Payloads, and… · pp. 2–3

C. Communication Cost and Budgeted Payload Selection

The transmitter selects a payload for each active link to maximize receiver-specific utility subject to a link budget. Because atom interactions can make utility nonadditive or nonmonotone, selecting all affordable content need not be optimal.

C. Communication Cost and Budgeted Payload Selection

  • Each independently packetized atom has a known positive bit cost, and a payload is feasible when its total cost does not exceed the link’s assigned budget.Source: C. Communication Cost and Budgeted… · p. 3
  • The selection problem maximizes receiver-specific payload utility under the per-link budget and is solved myopically and independently for each active link.The empty payload is feasible; scheduling, joint-link optimization, and shared budgets are outside the scope.Source: C. Communication Cost and Budgeted… · p. 3
  • Redundancy, complementarity, or harmful atoms can make utility nonadditive or nonmonotone, so score ranking may not capture the best subset.Even when all atoms are affordable, transmitting them all need not be optimal; under modular utility, selection reduces to an additive knapsack.Source: C. Communication Cost and Budgeted… · p. 3

III. SEMANTIC ATOM VALUATION AND SELECTION

The method derives signed atom values from receiver-specific controlled-delivery utility, using leave-one-out and Shapley attributions to define atom values for selection. The sign matters: an atom can reduce expected utility, so an affordable full payload is not always optimal.

III. SEMANTIC ATOM VALUATION AND SELECTION

  • The framework derives signed atom-level values from controlled-delivery utility because payload construction requires estimating each atom’s contribution.An atom’s marginal effect can depend on the other atoms in the reference payload, so the method specifies a reference-payload rule.Source: A. Signed Interventional Atom Values · p. 3

A. Signed Interventional Atom Values

  • LOO measures an atom’s marginal effect relative to the full payload, while Shapley averages its marginal effect over coalition backgrounds.Source: A. Signed Interventional Atom Values · p. 3
  • Shapley values decompose the total utility gain, but do not make additive selection optimal when atom interactions make utility nonadditive.With positive additive costs, if the full payload is affordable, every subset is feasible; monotone utility then makes the full payload optimal.Source: A. Signed Interventional Atom Values · pp. 3–4
  • A negative LOO value means that removing the atom from the full payload increases receiver utility, making an affordable full payload strictly suboptimal.Source: A. Signed Interventional Atom Values · p. 3

B. Prospective Utility Identification and Surrogate Estimation

The framework identifies receiver-specific controlled-delivery utility from randomized payloads delivered before the receiver acts, then uses a transmitter-side surrogate to estimate atom values.

B. Prospective Utility Identification and Surrogate Estimation

  • Prospective logging randomizes and applies payload masks before the receiver acts, so outcomes reflect the information actually delivered rather than post-action masking.Retrospective logging assigns masks after action, while retrospective occlusion changes only surrogate input.Source: B. Prospective Utility Identification… · p. 4
  • Utility identification requires consistency, conditional randomization given context and candidate atoms, and positive assignment probability for every queried payload.Under these conditions, the conditional mean logged outcome for a payload equals its controlled-delivery utility.Source: B. Prospective Utility Identification… · p. 4
  • A scalar shadow-receiver surrogate estimates utility from transmitter-available context, candidate atoms, and delivered-subset inputs, excluding the receiver’s private decision state.It estimates utility for payloads supported by the randomized design.Source: B. Prospective Utility Identification… · p. 4
  • The surrogate’s full-payload and atom-withheld predictions produce plug-in LOO scores, while Shapley scores use predictions over the required coalition masks.At deployment, score computation does not require the receiver’s private state, realized outcome, or an environment rollout.Source: B. Prospective Utility Identification… · p. 4

C. Budgeted Payload Construction

The framework constructs a separate budget-feasible payload for each active receiver link by selecting atoms with positive estimated value.

C. Budgeted Payload Construction

  • Atoms with nonpositive estimated scores are excluded, and remaining atoms are selected with a 0–1 knapsack problem under the link budget.With uniform costs, selection takes the largest positive scores up to affordable cardinality; heterogeneous integer costs use exact dynamic programming.Source: C. Budgeted Payload Construction · p. 4
  • LOO scoring needs M + 1 surrogate queries per receiver, and knapsack dynamic programming costs O(MB) in integer cost units.For R receivers, LOO uses R(M + 1) queries.Source: C. Budgeted Payload Construction · p. 4
  • Additive selection is exact with exact atom values and modular utility, but learned scores or nonmodular utility make it approximate.Experiments evaluate selected payloads with an evaluation-only reference utility estimate unavailable at deployment.Source: C. Budgeted Payload Construction · p. 4

IV. EXPERIMENTAL SETUP

The experiments use the Multi-Receiver Intersection Response benchmark to evaluate valuation fidelity and budgeted payload selection.

IV. EXPERIMENTAL SETUP

  • The Multi-Receiver Intersection Response benchmark instantiates the framework for evaluation of valuation fidelity and budgeted payload selection.Source: §IV · p. 4

A. MRIR System Instantiation

The MRIR setup models one roadside transmitter communicating with four receivers facing three hazards, and evaluates a frozen receiver policy using prospective randomized payloads. Valuation labels require privileged offline information, while deployment inputs are restricted to transmitter-available features.

A. MRIR System Instantiation

  • MRIR models one roadside transmitter, four scheduled receivers, and three hazards in a single pre-action communication round.Receivers choose among five actions, and receiver-local rewards distinguish safe/efficient, over-conservative, inefficient, and unsafe behavior.Source: A. MRIR System Instantiation · p. 4
  • Semantic extraction is fixed rather than trained or evaluated, producing 8–10 atoms across content categories with receiver-independent confidence and age metadata.The receiver policy is trained on 40,000 randomized partial-payload instances and then frozen; its validation accuracy is 39.2% without current payload, 58.4% with randomized payloads, and 67.2% with full payload.Source: A. MRIR System Instantiation · p. 5

B. Prospective Logging and Surrogate Training

  • Prospective logging randomizes payload delivery before receiver action, with a fixed mixture of LOO-targeted, permutation-prefix, and independent Bernoulli masks.The Bernoulli masks use p = 0.5; logging uses 25,000 training and 6,000 validation instances.Source: B. Prospective Logging and Surrogate… · p. 5
  • Valuation labels require privileged offline access and are not assumed locally observable at the roadside transmitter.Practical training requires a simulator or an equivalent reward-evaluation and receiver-feedback mechanism.Source: B. Prospective Logging and Surrogate… · p. 5
  • The shadow receiver is a permutation-invariant DeepSets regressor, while deployment uses only transmitter-available context, candidate atoms, and delivery mask.Private receiver state, realized actions or outcomes, and true utility are never surrogate inputs.Source: B. Prospective Logging and Surrogate… · p. 5

C. Evaluation Protocol and Result Definitions

The evaluation measures fidelity of receiver-specific LOO atom values and tests whether those estimates produce useful budget-feasible payloads. It compares matched-budget selection methods using independently evaluated controlled utility.

C. Evaluation Protocol and Result Definitions

  • 2,000 held-out instances across four receivers yield 8,000 receiver cells per seed for valuation-fidelity evaluation across five seeds.Fig. 1 reports LOO fidelity on 8,000 cells, using δ0 = 0.02 and Spearman ρ with 95% CIs.Source: C. Evaluation Protocol and Result… · p. 5, Figure 1 · p. 6
  • Reference utility for each queried payload forces its delivery and averages receiver outcomes over βj,t and ωt using 1,408 conditional draws and exact expectation over five receiver actions.Common draws are used across payloads.Source: C. Evaluation Protocol and Result… · p. 5
  • Estimated LOO effects compare predicted utility for the full payload with predicted utility after removing atom m.The protocol reports MAE, sign accuracy for non-negligible reference effects, and within-cell Spearman ρ.Source: C. Evaluation Protocol and Result… · p. 5
  • Budget evaluation uses a disjoint set of 1,000 instances across four receivers, evaluates every subset per cell, and tests α values from 0 to 1.Intermediate budgets are mapped to integer cost units, and candidate payloads are evaluated with reference utility.Source: C. Evaluation Protocol and Result… · p. 5
  • Matched-budget comparators include random feasible selection, shared LOO, receiver-specific Shapley, full payload when feasible, and evaluation-only OracleSubset.Primary comparisons are paired across seeds, instances, and receivers; 10,000 hierarchical-bootstrap replicates provide 95% percentile CIs.Source: C. Evaluation Protocol and Result… · pp. 5–6

V. RESULTS

Receiver-specific valuation provides useful but imperfect atom rankings, and receiver-specific LOO selection outperforms shared and random alternatives at interior budgets. At full affordability, exhaustive subset selection also exceeds full-payload transmission.

A. Semantic Atom Valuation Fidelity

  • MAE is 0.0496 for P, 0.0503 for RO, and 0.0528 for R, so magnitude error alone weakly separates logging designs.P changes the payload before the receiver acts and targets controlled utility, whereas RO and R use retrospective comparisons.Source: A. Semantic Atom Valuation Fidelity · p. 6
  • 68.4% sign accuracy for P exceeds 63.8% for RO and 50.3% for R among non-negligible effects.The threshold is δ0 = 0.02.Source: A. Semantic Atom Valuation Fidelity · p. 6
  • ρ = 0.302 for P, with 95% CI [0.291, 0.312], versus 0.256 for RO and 0.008 for R.R's interval crosses zero, while P preserves a consistent but moderate ordering.Source: A. Semantic Atom Valuation Fidelity · p. 6

B. Budgeted Controlled Utility

  • Receiver-specific LOO exceeds Shared LOO and Random Feasible across interior budgets, with the gap most visible under tight budgets.Utility generally rises with α as larger budgets admit more useful atoms.Source: B. Budgeted Controlled Utility · p. 6
  • At α = 1, Full payload yields 0.3739 versus OracleSubset's 0.4653, about 24% higher for OracleSubset.OracleSubset is an evaluation-only exhaustive reference.Source: Figure 2 · p. 6, B. Budgeted Controlled Utility · p. 6

C. Scope and Outlook

The conclusion reports benefits from receiver-specific selection on MRIR and argues that useful payload decisions remain possible with imperfect atom values. It also bounds the study to fixed, myopic settings and identifies directions for extending the framework.

C. Scope and Outlook

  • MRIR evaluates receiver-specific selection in a controlled, single-round setting with fixed policies; larger candidate sets can use LOO or permutation-sampled Shapley, with batching and caching reducing overhead.Source: C. Scope and Outlook · p. 6
  • Future work targets heterogeneous packet costs, learned semantic representations, channel-aware valuation, and updating surrogates as policies or context distributions change.Source: C. Scope and Outlook · p. 6

VI. CONCLUSION

  • The study values post-encoding semantic content per receiver using prospective randomized delivery to estimate signed LOO and Shapley values at the transmitter without receiver-private information.Source: §VI · p. 6
  • On MRIR, receiver-specific selection outperformed shared and random alternatives, while exhaustive subset selection exceeded full-payload transmission at full affordability.Source: §VI · p. 6
  • Useful payload decisions can still arise from imperfect atom values when selection-relevant signs and rankings are preserved.Source: §VI · pp. 6–7
  • Adaptive policies and multi-round communication require utility models beyond the fixed, myopic setting studied here.Source: §VI · p. 7
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