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Semantic-Aware Update Admission and Adaptive Byzantine Redundancy for Secure Computation Offloading in COIN-Enabled Metaverse Systems

Ibrahim Aliyu, Jaehyung Park, Jinsul Kim

arXiv:2610.29592v1cs.DC

TL;DR

The paper addresses how to balance persistent shared-state commitment, Byzantine redundancy, and application offloading when resources are shared. It combines a feasibility-filtered redundancy-aware PBFT controller with a game-based offloading method. At z = 3, its average secure timely-update ratio is 62.3% higher than Minimum Secure.

  • Problem

    The paper asks how shared-state persistence and semantic significance should jointly guide update commitment, security-feasible redundancy, and XR offloading under shared-resource constraints.

    Source: §I · p. 1

  • Method

    A hierarchical R-PBFT approach uses an identical-interest game for slot-wise offloading and feasibility-filtered DDQN for sequential update admission and redundancy control.

    Source: §I · p. 1

  • Results

    The average secure timely-update ratio changes by +62.3% for z = 3 compared to Minimum Secure.

    Source: 2) Secure timely-update performance · p. 10

  • Takeaways & Limitations

    Ablations show that w/o-FF and w/o-VD perform worse, supporting the benefits of feasible-action filtering and adaptive deferral.

    Source: F. Ablation and Sensitivity Analysis · p. 11

    The paper identifies Byzantine-state-aware adaptation in non-stationary adversarial settings as future work.

    Source: §VII · p. 12

Abstract

from arXiv · show

Computing in the network (COIN) supports latency-sensitive Metaverse services, but blockchain commitment of persistent shared-state updates competes with application execution for limited resources. We consider the joint problem of deciding which updates to commit, how much Byzantine redundancy to provision, and where to execute Metaverse application tasks. We formulate this problem under resource, latency, and practical Byzantine fault tolerance (PBFT) constraints, accounting for update persistence and semantic significance. We develop a hierarchical redundancy-aware PBFT (R-PBFT) approach that decomposes the decision process into slot-wise computation offloading and sequential update-admission and redundancy control. We formulate the former as an identical-interest game and address the latter using a feasibility-filtered double deep Q-network (DDQN). Analytical downlink allocation accounts for the energy and delivery-feasibility effects of consensus latency. For fixed slot state and redundancy, we establish the game's exact-potential property and finite termination of strict sequential improvements. Feasible-action filtering enforces configured Byzantine redundancy and blockchain-budget constraints independently of learning. Numerical results show relative improvements of up to $46.7\%$ in reward averaged across tested user loads and seeds over Minimum Secure, the strongest baseline on average. At the highest tested Byzantine bound, the secure timely-update ratio improves by $62.3\%$ over the same baseline. Ablations assess the contributions of feasibility filtering and adaptive deferral.

I. INTRODUCTION

The introduction frames a joint resource-allocation problem: protect persistent shared state while balancing update freshness, consensus overhead, and application latency. It presents a hierarchical approach combining computation offloading with update admission and Byzantine redundancy control.

I. INTRODUCTION

  • The open question is how persistence and semantic significance should jointly determine update commitment, Byzantine redundancy, and XR offloading under shared resource constraints.The design must balance state freshness, consensus overhead, and application latency.Source: §I · p. 1
  • The proposed hierarchy pairs an identical-interest offloading game with feasibility-filtered DDQN for sequential update admission and redundancy control.Feasible-action selection enforces configured Byzantine and blockchain-budget constraints independently of learning.Source: §I · p. 1

B. Task Model

  • XR tasks are DAGs of dependent functions, and only persistent authoritative updates—not transient outputs—are eligible for blockchain commitment.The function-level model distinguishes user-specific, shared-intermediate, and persistent authoritative state.Source: §I · p. 1, B. Task Model · p. 2

I. INTRODUCTION

  • For fixed slot state and redundancy, the offloading game has an exact-potential property and strict sequential improvements terminate finitely.The game admits a minimizer on the finite strategy set, which is a pure Nash equilibrium.Source: §I · p. 2

A. Network Architecture

  • The COIN architecture includes users, fog and edge computing nodes, permissioned validators, and a logically centralized controller.The redundancy profile is selected each slot and remains fixed during offloading and channel selection.Source: A. Network Architecture · p. 2

C. Blockchain Model

  • The controller selects a redundancy profile using update age and magnitude, configured fault bounds, and available resources; a positive action admits a commitment attempt, while zero defers.The slot-level transition model assumes successful commitment for admitted security-feasible updates, while timely delivery is evaluated separately.Source: A. Network Architecture · p. 2, C. Blockchain Model · p. 2

D. Communication Model

The communication model accounts for the uplink costs of remote execution and models communication and latency across PBFT stages. Its blockchain estimates represent nominal consensus operation, excluding view-change and committee-reconfiguration overhead.

1) Uplink Transmission:

  • Users choose local execution or an uplink channel; remote execution incurs uplink latency and transmit energy, while both are zero for local execution.The uplink model also accounts for channel rate and background interference.Source: 1) Uplink Transmission · pp. 2–3

2) Blockchain Communication:

  • The blockchain communication model covers dissemination, pre-prepare, prepare, commit, and reply stages, and models consensus latency, communication volume, and replicated storage.Prepare traffic uses an all-validator approximation rather than a certificate threshold.Source: 2) Blockchain Communication · p. 3
  • The consensus estimates cover nominal operation and exclude view-change and committee-reconfiguration overhead.This bounds what the modeled blockchain communication and latency costs include.Source: 2) Blockchain Communication · p. 3

3) Downlink Transmission:

This section describes downlink allocation and service-cost components, then states the validation and threat assumptions under which updates are processed.

3) Downlink Transmission:

  • Downlink power is recomputed for each candidate offloading profile using the remaining service time.The downlink model also identifies the assigned bandwidth, delivery latency, and transmitter-side energy.Source: 3) Downlink Transmission · p. 3

1) Local Computing:

  • Local computing is characterized by execution latency and energy for the selected processor frequency.Source: 1) Local Computing · p. 3

3) Service latency and user energy:

  • Remote execution latency excludes blockchain validation, while physical service latency includes only applicable delivery and validation components.Local execution does not remove dependencies on shared state; receiving downlink data consumes user-device energy, with inactive components set to zero.Source: 2) Remote Computing · p. 3, 3) Service latency and user energy · p. 4

1) Threat Model and Validation:

  • Validators check signatures, permissions, version and replay consistency, and deterministic application rules; false inputs that pass validation remain outside the guarantee.Compromised users and computing nodes may submit false inputs, while Byzantine validators may equivocate or disrupt consensus.Source: 1) Threat Model and Validation · p. 4

2) Consensus Configuration:

The section sets out consensus configuration and cost components, including conditions for agreement and limits on what agreement guarantees.

2) Consensus Configuration:

  • Preparation requires a primary pre-prepare and matching backup prepares, while commitment requires preparation and q distinct matching commits.View changes preserve the highest-view prepared value, and reconfiguration requires a certified outgoing state and successor attestations.Source: 2) Consensus Configuration · p. 4
  • Adaptive BRF preserves agreement within and across certified configurations under Assumption 1 and the stated consensus conditions.The proof relies on intersecting view-change reporters and certified handoffs to preserve committed history.Source: 2) Consensus Configuration · p. 4
  • Agreement guarantees neither input truth nor timely, fresh delivery, and deferral neither starts a new attempt nor cancels ongoing consensus.Source: 2) Consensus Configuration · p. 4

1) User-Oriented Cost:

  • The user-oriented cost model includes required-state age, successful delivery of required updates, effective-latency penalties, and user energy.An update counts as a feasible fresh delivery only when it meets the configured Byzantine requirement, downlink feasibility, and freshness deadline.Source: 1) User-Oriented Cost · p. 4

2) Commitment Cost:

  • Commitment cost accounts for validation latency and energy for communication, processing, and newly stored bits; its redundancy-margin penalty is not a failure probability.Source: 2) Commitment Cost · pp. 4–5

3) Update-Deferral Cost:

This section models update-deferral and system operating costs, then formulates joint optimization and establishes hardness for a static admission subproblem.

3) Update-Deferral Cost:

  • Deferral cost uses an increasing, saturating exposure score based on update age, magnitude, sharing, and criticality; the score is a modeling assumption, not a calibrated failure probability.The total deferral cost also includes age-dependent and obsolescence terms.Source: 3) Update-Deferral Cost · p. 5

4) System Operating Cost:

  • Per-slot system operating cost combines user costs, operator cost, and aggregate redundancy-margin penalties.The weights balance user cost, operator cost, and redundancy-margin penalties.Source: 4) System Operating Cost: ( · p. 5

C. Problem Formulation

  • The formulation jointly optimizes offloading and BRF decisions over causal policies because commitment competes with application execution for resources and deferral affects later shared-state age and service cost.Constraints cover security-feasible admission, committee size, blockchain budget, task dependencies, and downlink transmit power.Source: C. Problem Formulation · p. 5
  • The static additive update-admission problem is NP-hard when positive integer resource weights and nonnegative integer commitment savings are independently specified inputs.The proof reduces 0–1 knapsack to the admission problem.Source: C. Problem Formulation · pp. 5–6

IV. PROPOSED SOLUTION

The proposed solution separates sequential update admission and redundancy control from conditional slot-wise offloading. For fixed slot state and BRF, offloading has an exact-potential structure.

IV. PROPOSED SOLUTION

  • The solution decomposes decisions into an upper DDQN layer for admission and redundancy and a lower layer that computes offloading through sequential updates in an identical-interest game.The upper layer learns from a discounted reward balancing service performance, resource expenditure, and update freshness.Source: §IV · p. 6

A. Multiuser Offloading Game

  • The controller recomputes interference, downlink power, and costs for each candidate offloading profile while holding BRF and exogenous slot state fixed.A user's decision affects others through interference and shared resources, so unilateral changes are evaluated using system operating cost.Source: A. Multiuser Offloading Game · p. 6
  • Sequential best responses seek a coordinatewise minimum without guaranteeing global optimality.Source: A. Multiuser Offloading Game · p. 6
  • For fixed exogenous slot state and BRF, the identical-interest game admits an exact potential and a pure Nash equilibrium.A minimizer of the finite system-cost function has no improving unilateral deviation.Source: A. Multiuser Offloading Game · p. 6

1) Sequential Best Response and Convergence:

The lower layer uses sequential strict-improvement updates, while the upper layer selects admission and redundancy from an aggregate observation. The procedure has a finite termination and equilibrium certificate under the stated conditions, but does not guarantee global optimality or convergence of the full hierarchy.

1) Sequential Best Response and Convergence:

  • At each cyclic user visit, a candidate action replaces the current action only when it improves the objective by at least the tolerance ϵ_BR; otherwise, the current action is retained.The sequential updates seek a coordinatewise minimum, not guaranteed global optimality.Source: 1) Sequential Best Response and… · p. 7
  • At most |S_t|−1 changes are accepted, and an unchanged complete sweep certifies an ϵ_BR-Nash equilibrium (a pure Nash equilibrium when ϵ_BR = 0).The certificate applies under Proposition 2.Source: 1) Sequential Best Response and… · p. 7
  • Finite termination of the lower-layer updates does not guarantee global optimality or convergence of the overarching hierarchical procedure.An iteration cap ensures termination but does not yield an equilibrium certificate.Source: 1) Sequential Best Response and… · p. 7

B. DDQN-Based Adaptive BRF Optimization

  • The upper layer observes an aggregate approximation of system state, then selects update-admission and redundancy actions whose lower-layer offloading outcomes determine reward and the next observation.Exact Markov sufficiency is not assumed.Source: B. DDQN-Based Adaptive BRF Optimization · p. 7

1) Observation:

  • The observation summarizes demand, update urgency, configured security requirements, and operating conditions, including request mix, affected-user fraction, update age, fault bound, active-user fraction, uplink quality, and episode progress.The listed features are normalized where specified.Source: 1) Observation · p. 7

2) Action:

  • Zero denotes deferral, while positive actions represent security-feasible commitment attempts.Source: 2) Action · p. 7

3) Reward:

The reward combines service incentives with resource and update-management penalties, while branch-wise DDQN and constrained action selection address the large admission-and-redundancy action space. Feasible selection enforces security and blockchain-budget constraints, though conservative discretization can omit some feasible actions.

3) Reward:

  • The clipped reward uses weighted scalarization to group service incentives, resource penalties, and update-management penalties.Auxiliary incentives, discounting, and clipping make the objective a surrogate rather than an equivalent reformulation of (P1).Source: 3) Reward · p. 7

4) Branch-Wise DDQN and Feasible Selection:

  • Per-update action branches use an additive approximation and output |P|(r_max + 1) scores rather than enumerating the joint action space or assuming the true action-value function is separable.Source: 4) Branch-Wise DDQN and Feasible… · p. 8
  • Insecure positive actions are masked, and dynamic programming selects actions under a discretized blockchain budget; conservative discretization can exclude feasible actions but cannot cause a budget violation.Source: 4) Branch-Wise DDQN and Feasible… · p. 8
  • Every action returned by the feasible BRF selector satisfies configured redundancy requirements and the blockchain-resource budget.Source: 4) Branch-Wise DDQN and Feasible… · p. 8

5) BRF-Aware Downlink Power Allocation:

The downlink allocation minimizes transmit energy subject to a reserved delivery-time target, linking consensus latency to delivery feasibility and service cost. The implementation bounds per-slot inference through knapsack selection and capped offloading sweeps, with a pseudopolynomial budget-discretization cost.

5) BRF-Aware Downlink Power Allocation:

  • Longer validation leaves less transmission time and increases required power, coupling BRF selection to service cost.For each candidate offloading profile and selected BRF, the allocation minimizes downlink transmit energy subject to a reserved delivery-time target.Source: 5) BRF-Aware Downlink Power Allocation · p. 8

6) Computational Complexity:

  • Per-slot inference includes network evaluation, knapsack selection at cost O(PA(b_B + 1)), and at most I_max K(M + 1) candidate evaluations across capped offloading sweeps.Budget discretization gives a pseudopolynomial DP bound; finer resolution increases cost, and a sweep cap bounds runtime without certifying equilibrium.Source: 6) Computational Complexity · p. 8

V. NUMERICAL SIMULATION

Across tested Byzantine severities, DDQN-RPBFT improves average reward over Minimum Secure and shows larger secure timely-update gains at higher severity. The simulations also report stable training behavior and compare controlled baselines, architectural ablations, and learning variants.

V. NUMERICAL SIMULATION

  • The evaluation varies Byzantine severity, user load, shared-state validity, arrival intensity, and computing capacity, with default system, learning, and reward parameters summarized in Table II.Experiment-specific variations are stated with the corresponding results.Source: §V · p. 9, Table II · p. 9

1) Controlled BRF Baselines:

2) Architectural Ablations:

B. Convergence Analysis

  • For K = 20 and H_f = 3, episodic return improves rapidly and stabilizes near −50; the lower-layer game achieves higher instantaneous reward than Minimum Secure and Excess Redundancy, particularly after initial best-response iterations.The passage attributes the advantage to state-dependent BRF adaptation balancing redundancy overhead against offloading performance.Source: B. Convergence Analysis · p. 9, Figure 2 · p. 10

1) Byzantine Robustness and System Reward:

  • 46.7%, 33.2%, and 32.4% average-reward improvements over Minimum Secure are reported for z = 1, 2, and 3, respectively.Reward decreases as Byzantine severity and user load increase, but the advantage is maintained and becomes more pronounced at higher loads.Source: 1) Byzantine Robustness and System… · p. 10

2) Secure timely-update performance:

  • At z = 1, 2, and 3, the average secure timely-update ratio changes by −3.1%, +26.3%, and +62.3%, respectively, versus Minimum Secure.At z = 1, Minimum Secure performs slightly better; DDQN-RPBFT outperforms at higher user counts K = 25–35.Source: 2) Secure timely-update performance · p. 10

D. User-Oriented Evaluation

The evaluations report user-facing reward and secure-update outcomes, infrastructure adaptation, and ablation findings, followed by related-work positioning and the paper’s conclusion.

D. User-Oriented Evaluation

  • DDQN-RPBFT gains 20.3%, 20.7%, and 21.2% in average reward over Random Feasible for Hf = 1, 3, and 6, respectively.Reward declines as user count increases, but the advantage persists across the tested shared-state validity horizons.Source: D. User-Oriented Evaluation · p. 10, Figure 3 · p. 11

E. Infrastructure-Oriented Evaluation

F. Ablation and Sensitivity Analysis

  • Ablations show worse performance without feasible-action filtering or adaptive deferral; explicit Byzantine-state inputs offer limited benefit under tested stationary conditions.Adaptation to time-varying Byzantine conditions remains future work.Source: F. Ablation and Sensitivity Analysis · p. 11, Figure 5 · p. 12

VI. RELATED WORK

  • Prior work addresses XR offloading, shared-state protection, BFT adaptation, and blockchain-edge coordination, while this work couples persistent-update admission and security-feasible redundancy with XR execution under shared resource constraints.The scope excludes transient intermediate outputs and assumes certified configuration transitions.Source: §VI · p. 12

VII. CONCLUSION

  • The conclusion reports improved system performance, secure timely-update delivery, and infrastructure adaptation, with future work targeting Byzantine-state-aware adaptation in non-stationary adversarial settings.The authors also identify feasible-action filtering and resource-aware deferral as valuable in ablations.Source: §VII · p. 12

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