Entropy-Gated Belief Coordination for Decentralized Multi-Agent Search Under Intermittent Communication

Mohamed Abdelnaby; Kevin Leahy

cs.ROOct 5, 2026

Entropy-Gated Belief Coordination for Decentralized Multi-Agent Search Under Intermittent Communication

Authors: Mohamed Abdelnaby, Kevin Leahy

Organizations: Department of Robotics Engineering, Worcester Polytechnic Institute

Abstract

We study decentralized multi-agent target search where homogeneous agents communicate intermittently at Poisson-distributed times. Standard unconditional belief fusion wastes communication opportunities by synchronizing agents during high-entropy exploration, when diverse independent beliefs provide better coverage than a premature consensus. We introduce \emph{entropy-gated belief coordination}, in which agents skip fusion while their collective entropy ratio exceeds a threshold~ $θ$ and merge only during exploitation, consistent with the bifurcation structure of nonlinear opinion dynamics and the submodular structure of the per-step information gain objective. We further derive $\Istep(α,β)$ , the expected mutual information per observation step between two agents' binary sensors, as an interpretable, communication-free measure of sensor informativeness that motivates the gating design and guides system-level analysis. Experiments across 103{,}680 trials (nine grid sizes up to $100{\times}100$ , Poisson communication timing, four target movement patterns) show that the Entropy-Gated Trust-Decay Planner (\textsc{EG-TDP}), which adds a detection-probability planner switch in exploitation mode, achieves mean belief quality $\bar{Q}=0.300$ (mean belief mass at the true target cell, averaged across all trials and steps), a $58.9\%$ gain over arithmetic mean and a $37.4\%$ gain over visit-weighted fusion. On representative configurations, EG-TDP also outperforms a joint-Bayesian reference that uses all agents'~observations at every step, despite operating under random intermittent contact only.

Figures & tables

Fig. 1: Decision overview for the three proposed coordination policies. At each communication event the team computes

H_{\mathrm{ratio}}

, the entropy gate determines whether to merge and, for EG-TDP and EG-Istep, which planner objective to use.

Fig. 2:

I_{\mathrm{step}}(\alpha,\beta)

over the binary sensor parameter space. Higher values indicate faster belief divergence during blackouts, making coordination more valuable. The star marks our sensor profile (

\alpha{=}0.1,\beta{=}0.2

I_{\mathrm{step}}{=}0.114

bits).

Fig. 3: Trust-decay factor

\gamma

as a function of blackout length

k

for (

N{=}2

) agents. The complement

1{-}\gamma

goes to entropy-reduction.

Fig. 4: Overall

\bar{Q}

per method (95% CI, 12,960 trials per method). VW-KL-R is shown for completeness, results are nearly identical to EG-KL and it is omitted from Table I .

Ablations: TD-KL $\bar{Q}{=}0.021$ , TD-KL-A $\bar{Q}{=}0.033$ (Sec. VI-H ).
Method	$\bar{Q}\;\pm\;\sigma$	Succ.	Steps
Arith	$0.189\pm 0.278$	$83.0\%$	$431$
Geom	$0.256\pm 0.405$	$79.2\%$	$389$
VW-KL	$0.218\pm 0.296$	$86.2\%$	$430$
EG-KL	$0.225\pm 0.298$	$86.8\%$	$434$
EG-TDP	$\mathbf{0.300}\pm 0.401$	$\mathbf{88.2\%}$	$\mathbf{317}$

TABLE I: Overall

\bar{Q}

and discovery statistics (

\alpha{=}0.1

\beta{=}0.2

, Poisson comm., 12,960 trials per method). Steps on successful trials only.

Fig. 5:

\bar{Q}

vs grid size. EG-KL (red solid line) leads at

10{\times}10

but falls to

\bar{Q}{\approx}0.003

100{\times}100

. EG-TDP (purple solid line) maintains

\bar{Q}{=}0.218

at the largest scale, validating the planner switch. Geom degrades gracefully but at the cost of the lowest success rate.

Fig. 6: Success rate (left) and steps to discovery on successful trials (right). EG-TDP achieves the highest success rate and fastest discovery simultaneously. Geom finds the target quickly when it succeeds (389 steps) but fails most often (20.8% failure rate). All pairwise success-rate differences are statistically significant at

p{<}0.001

(two-proportion

z

-test, Bonferroni-corrected) except VW-KL vs EG-KL (

p{=}0.158

)

Fig. 7: Coordination dynamics (

\theta{=}0.6

, aggregated over patterns and

\bar{k}

). (a) Expected merges per trial (baselines always merge, EG-TDP fires only

\sim

3.6 of 156 events at

100{\times}100

, a 97% bandwidth reduction). (b) First exploitation step, annotations: % of trials never crossing

H_{\mathrm{ratio}}<\theta

. (c) Fraction of steps in exploitation (for ungated methods, we show percentages of when entropy

<\theta

Method	Stationary	Patrol	Evasive	Random
EG-TDP	0.954 (100%)	0.226 (81%)	0.016 (80%)	0.003 (93%)
EG-KL	0.579 (96%)	0.224 (82%)	0.095 (80%)	0.003 (89%)
Geom	0.926 (76%)	0.077 (74%)	0.018 (75%)	0.003 (91%)
VW-KL	0.563 (96%)	0.213 (80%)	0.094 (79%)	0.003 (90%)

TABLE II:

\bar{Q}

and success rate by target movement pattern.

$\theta$	$\bar{k}{=}5$	$\bar{k}{=}25$	$\bar{k}{=}100$
0.4	0.460	0.477	0.469
0.5	0.518	0.529	0.530
0.6	0.594	0.599	0.586
0.7	0.602	0.602	0.596
0.8	0.602	0.602	0.596

TABLE III: EG-TDP mean

\bar{Q}

by entropy threshold

\theta

and expected communication interval

\bar{k}

Method	$\bar{Q}\;\pm\;\sigma$	Succ.	Steps
Arith	$0.313\pm 0.284$	$89.7\%$	$517$
VW-KL	$0.396\pm 0.299$	$91.1\%$	$421$
EG-KL	$0.412\pm 0.294$	$92.6\%$	$434$
EG-Istep	$0.543\pm 0.379$	$92.9\%$	$319$
Full-Comm (reference)	$0.552\pm 0.318$	$95.4\%$	$323$
EG-TDP	$\mathbf{0.593}\pm 0.395$	$\mathbf{93.8\%}$	$\mathbf{296}$

TABLE IV: Proposed method comparison on representative configurations (stationary + patrol, three grid sizes, 20 trials,

\theta{=}0.6

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