Attention-based Hierarchical Variational Information Bottleneck for Robust Multi-Agent Communication under Variable Bandwidth

I. INTRODUCTION

• The motivating task requires agents to share compact information to avoid redundant coverage despite partial observability and changing communication budgets.Useful messages should give a coarse description even when only a portion is received.Source: §I · p. 1
• Variable-bandwidth communication is modeled as prefix truncation, a controlled abstraction in which only the first k message dimensions are received.Packet loss, delay, asymmetry, and retransmission are outside the stated scope.Source: §I · pp. 1–2
• AH-VIB generates message dimensions autoregressively with attention and applies a hierarchical robustness loss to encourage useful message prefixes.The loss penalizes reductions in the centralized critic’s estimated team return when messages are truncated during training.Source: §I · pp. 1–2
• The study evaluates fixed and variable bandwidth on a cooperative object-inspection and occupancy-mapping task against MADDPG, CommNet, flat VIB, and an autoregressive MLP ablation.Agents with limited fields of view coordinate to scan inspection objects.Source: §I · pp. 1–2
• AH-VIB provides more reliable behavior than VIB and MADDPG baselines when only short message prefixes are available.The reported advantage is strongest at the most constrained bandwidths.Source: §I · p. 2

II. RELATED WORK

• Prior MARL communication work emphasizes what to communicate and to whom, whereas this work studies how to order information when only a message prefix may arrive.Source: §II · p. 2

A. Learned Communication in MARL

• CommNet uses fixed mean pooling over communication rounds, while TarMAC learns message targeting; AH-VIB instead addresses what survives bandwidth limitation.MADDPG is cited as popularizing centralized training with decentralized execution.Source: A. Learned Communication in MARL · p. 2

B. Information-Theoretic Communication

• IMAC applies VIB to multi-agent message encoding, but its flat encoder does not order message dimensions; AH-VIB adds autoregressive prefixes and a robustness loss for task utility.Source: B. Information-Theoretic Communication · p. 2

C. Bandwidth-Constrained Multi-Robot Communication

• Real multi-robot systems can face intermittent connectivity and queued data awaiting a connectivity window, unlike the full-delivery assumption common in learned communication.ACHORD is the cited example of such deployments.Source: C. Bandwidth-Constrained Multi-Robot… · p. 2

D. Hierarchical and Progressive Message Encoding

• Progressive coding and nested representations place useful coarse information in early portions and refinement later, a principle adapted here to task-utility-preserving message prefixes.The cited examples include embedded zerotree wavelet coding, nested dropout, and Matryoshka Representation Learning.Source: D. Hierarchical and Progressive… · p. 2

III. SYSTEM MODEL

• The system model considers cooperative MARL in which agents pursue a shared objective under partial observability using local observations and explicit communication.Source: §III · p. 2

• The formulation models each agent’s composite action as a physical action paired with a shared-space message in a communication-augmented Dec-POMDP.Source: A. Dec-POMDP Formulation · p. 2
• Before delivery, each message is truncated to its first k dimensions and broadcast to the other agents for use at the next timestep.Source: A. Dec-POMDP Formulation · p. 3
• Joint physical actions determine state transitions, messages do not directly affect the world state, and all agents receive the same scalar team reward.Source: A. Dec-POMDP Formulation · p. 3
• At each timestep, agents use local observations and messages from other agents sent at the previous timestep; messages start at zero and reception has a one-step delay.Source: A. Dec-POMDP Formulation · p. 3, Figure 2 · p. 3
• The joint policy objective is to maximize expected discounted return.Source: A. Dec-POMDP Formulation · p. 3

B. Centralized Training with Decentralized Execution (CTDE)

• During training, a centralized critic receives pooled observations and contexts plus all agents’ actions and messages; agents execute using only local observations and contexts.The critic is not used during execution.Source: B. Centralized Training with… · p. 3

C. Communication Model

• Only the first k dimensions of each learned message are delivered, with later dimensions unavailable to receiving agents.The received message is formed by prefix truncation, with d denoting the message-vector index.Source: C. Communication Model · p. 3
• The same prefix length applies to all agents, and the bandwidth fraction ρ = k/dm is sampled per episode; early dimensions therefore need to carry task-relevant information.The episode-level sampler enforces k ≥ 1, while evaluation schedules may reach k = 0.Source: C. Communication Model · p. 3

IV. ATTENTION-BASED HIERARCHICAL VARIATIONAL INFORMATION BOTTLENECK

• AH-VIB combines an autoregressive attention-based encoder with a hierarchical robustness loss that penalizes team-value drops under message truncation.The encoder conditions each dimension on the preceding prefix; the loss encourages task utility at reduced bandwidth.Source: §IV · p. 3

A. Variational Information Bottleneck

• VIB uses a stochastic encoder to learn compressed representations retaining task-relevant information, and AH-VIB adopts it as the probabilistic basis for communication.IMAC applies VIB to compact, informative multi-agent messages; VIB is described as a framework for compressed representations [8].Source: A. Variational Information Bottleneck · p. 4
• A flat encoder generates all dimensions simultaneously from a shared hidden state, so early dimensions are not necessarily self-contained when later dimensions are truncated.This leaves the information ordering across dimensions to be learned.Source: A. Variational Information Bottleneck · p. 4

B. Autoregressive Message Encoding

• Each message dimension is conditioned on the previously generated prefix, so no dimension depends on later dimensions and truncated prefixes remain self-consistent by construction.The attention encoder uses the agent hidden state and a position embedding for its query, while prior sampled dimensions join the growing key-value context.Source: B. Autoregressive Message Encoding · p. 4
• At each autoregressive step, attention output is combined with the hidden state to produce a mean and variance, and the sampled dimension is bounded by tanh and fed into the next step.The attention mechanism can focus on previously generated dimensions; its projection Wz is shared across steps.Source: B. Autoregressive Message Encoding · p. 4

C. Hierarchical Robustness Loss

• The truncation sampler is independent of environment-interaction bandwidth dynamics, encouraging progressive message structure that generalizes across varying bandwidth conditions.The complete actor objective combines full-bandwidth task performance, VIB compression, and graceful-degradation terms.Source: C. Hierarchical Robustness Loss · p. 5
• The hierarchical robustness loss penalizes the gap between full and truncated team value, encouraging the truncated value toward the full-bandwidth reference.The full-value reference is stop-gradient, so the loss does not reduce it to satisfy the objective.Source: C. Hierarchical Robustness Loss · p. 5

A. Environment

• The task places three agents in a 50 × 50 occupancy grid with three randomly placed 6 × 4 inspection objects and 60° field-of-view sensors reaching eight cells.Agents move continuously with a maximum displacement of two cells per step; each sensor uses 16 rays.Source: A. Environment · p. 5
• A team-shared reward uses newly revealed object-surface cells, newly revealed free cells, and a proximity penalty between agents.Object cells occlude scans, so only their surface cells can be revealed.Source: A. Environment · p. 5
• Object scanning dominates the deliberately small free-space exploration bonus, with weights wobj = 1.0 and wfree = 0.01.The object term counts newly revealed inspection-object surface cells; the exploration term incentivizes discovery of unoccupied geometry.Source: A. Environment · p. 5
• Each agent receives a 17 × 17 local occupancy patch and its normalized pose, and episodes last 200 timesteps.Communication passes through an external channel module rather than being included in the observation.Source: A. Environment · pp. 5–6
• Messages have 32 dimensions and episode-level bandwidth is sampled from Beta(3.0, 7.0), with prefix truncation applied uniformly across agents.The robustness loss uses a separate sampler with the same Beta parameters and pfull = 0.10.Source: A. Environment · p. 6

B. Baselines

• HVIB retains stochastic compression and hierarchical robustness but replaces AH-VIB’s attention mechanism with an MLP, while flat VIB generates all dimensions simultaneously.The comparison of HVIB and AH-VIB tests attention beyond autoregressive ordering and truncation-aware training; flat VIB tests stochastic compression without ordered generation.Source: B. Baselines · p. 6
• MADDPG uses deterministic continuous messages, while CommNet pools messages over three rounds; neither has explicit dimensional ordering.The baselines also differ in bottleneck and robustness design: MADDPG lacks a stochastic bottleneck and robustness loss, and CommNet lacks an explicit bottleneck.Source: B. Baselines · p. 6

C. Evaluation Metrics

• Evaluation measures mean undiscounted episode return, fixed-bandwidth reward across truncation cutoffs, and episode reward under bandwidth schedules that decrease or increase within an episode.Higher, or less negative, episode return indicates better performance.Source: C. Evaluation Metrics · p. 6

D. Training Configuration

• All methods share a 500,000-step training setup; VIB variants use β = 0.001, and hierarchical variants use λ = 0.05 with one sampled prefix per update.Hierarchical variants use a stop-gradient target on Qfull.Source: D. Training Configuration · pp. 6–7

E. Training Dynamics

• AH-VIB, HVIB, VIB, and MADDPG converge to similar final returns, while CommNet converges more slowly and remains more variable.Because asymptotic mean return weakly separates the stronger methods, the evaluation focuses on reliability under restricted bandwidth.Source: E. Training Dynamics · p. 7
• Across ρ = 0.10, 0.25, 0.75, and 1.00, AH-VIB’s return standard deviation is 19.7–23.8 lower than VIB’s, with a 100% bootstrap probability of lower variation at each bandwidth.Against MADDPG, that probability is at least 86.8% at all bandwidths; against CommNet, it is at least 99.3% at ρ = 0.10 and 0.25, while CommNet is most consistent at ρ ≥ 0.75.Source: E. Training Dynamics · p. 7

F. Performance Under Variable Bandwidth

• AH-VIB has the best mean return and lowest return variation at ρ = 0.10 and ρ = 0.25, while CommNet performs best at ρ = 0.75 and ρ = 1.00.AH-VIB also has compact return distributions with shorter low-return tails at the two tightest bandwidths; VIB and MADDPG show broader distributions and more severe low-return episodes there.Source: F. Performance Under Variable Bandwidth · p. 7

G. Per-Dimension KL Divergence

• On MPE Simple Spread at full bandwidth, AH-VIB has lower mean per-dimension KL divergence than HVIB and VIB, with tighter SEM bands across evaluation episodes.The analysis is complementary to the main object-inspection and occupancy-mapping evaluation and reflects native dimension usage rather than masking.Source: G. Per-Dimension KL Divergence · pp. 7–8, Figure 6 · p. 8

H. Discussion and Future Work

• The communication setup omits scheduling and resource allocation, and the channel model excludes packet loss, delay, and asymmetric links.The simulated inspection environment also uses rectangular objects, idealized ray-casting sensors, simplified motion, and perfect localization, limiting conclusions about transfer to physical multi-robot inspection.Source: H. Discussion and Future Work · p. 8
• Future work proposes combining task-oriented message ordering with communication-slot scheduling and resource allocation, and testing more challenging tasks with realistic channel models.Source: H. Discussion and Future Work · p. 8

VI. CONCLUSION

• On the cooperative object-inspection task, AH-VIB achieves competitive mean return while improving performance consistency under bandwidth restriction.The paper presents progressive message encoding as a useful design principle for bandwidth-constrained multi-robot communication.Source: §VI · p. 8