Adaptive Share Delay Provision (ASDP)

• Adaptive Share Delay Provision (ASDP) is a timing-aware mechanism that strategically delays resource sharing to enable malicious model poisoning in DPML or optimize performance in control systems.
• It is applied in diverse contexts—from exploiting delayed commitments in DPML attacks to enhancing autoscaling, URLLC scheduling, and network QoS control.
• Adaptive control in ASDP leverages real-time delay measurements to tune provisioning policies, aligning with reliability, service-level, and security constraints in distributed settings.

Searching arXiv for the cited papers and ASDP-related entries to ground the article in current sources. Adaptive Share Delay Provision (ASDP) denotes a delay-aware adaptive mechanism whose meaning depends on context. In the supplied literature, the term is used explicitly in distributed privacy-preserving machine learning (DPML) as a malicious timing strategy that delays share provision until other participants’ information is observable, enabling customized model poisoning while preserving verifiability constraints (Li et al., 16 Sep 2025). In several other works, ASDP is not a formal term but is used as a conceptual lens for mechanisms that adapt provisioning, blocklength, scheduling, or learning dynamics to measured or predicted delays, especially in container orchestration, URLLC access, asynchronous stochastic approximation, and shared-network QoS control (Baghel, 15 May 2026, Zhang et al., 2024, Fabbro et al., 2024, Nguyen et al., 1 Sep 2025). The common substrate is adaptive control of a delayed resource or contribution—shares, replicas, packets, or updates—under system constraints such as reliability, liveness, or service-level guarantees.

1. Terminological scope and explicit definition

In the current corpus, ASDP is explicitly defined only in "EByFTVeS: Efficient Byzantine Fault Tolerant-based Verifiable Secret-sharing in Distributed Privacy-preserving Machine Learning" (Li et al., 16 Sep 2025). There, ASDP is introduced as a strategy used by a malicious dealer in a Byzantine Fault Tolerant (BFT)-based Verifiable Secret Sharing (VSS) system. Its defining properties are threefold: it passes commitment-based VSS validity checks, respects the “on-chain once” constraint of BFT, and still enables customized model poisoning targeted at specific participants (Li et al., 16 Sep 2025).

Formally in that DPML setting, the malicious dealer delays provision of shares until enough honest participants’ shares or gradients have already been committed through the BFT system. After observing these on-chain gradients, the dealer reconstructs or aggregates them, designs a malicious gradient $w'^i$ with controlled geometric properties such as cosine similarity, and then broadcasts shares and commitments at the last moment of the round. Because VSS checks only that each share matches its commitment, the shares remain verifiable even though their timing has been strategically manipulated (Li et al., 16 Sep 2025).

Outside that paper, several works explicitly state that ASDP is not their formal term, but the supplied discussions interpret their mechanisms as conceptually aligned with ASDP. In "ADAPT: A Self-Calibrating Proactive Autoscaler for Container Orchestration" (Baghel, 15 May 2026), ASDP is mapped to continual learning of provisioning delay and adaptation of autoscaling horizons. In "Adaptive Finite Blocklength for Low Access Delay in 6G Wireless Networks" (Zhang et al., 2024), ASDP is interpreted as adaptive distribution of total access delay between queuing and transmission via blocklength selection. In "DASA: Delay-Adaptive Multi-Agent Stochastic Approximation" (Fabbro et al., 2024), it is treated as a delay-aware server-side mechanism that selects which delayed updates to use. This suggests that ASDP is best understood as a family resemblance term rather than a single standardized construct.

A consequential distinction follows. In DPML, ASDP is an attack strategy. In the other supplied works, it is an interpretive label for adaptive, delay-aware control policies. Conflating these usages obscures the fact that one line of work studies exploitability of delayed share release, whereas the others study constructive delay adaptation.

2. ASDP as a timing attack in BFT-based verifiable secret sharing

The explicit ASDP construction arises in a DPML system with participants $P_1,\dots,P_n$, threshold $th$, model parameters $w_t^i$, Shamir VSS shares $s_j^i$, and polynomial commitments $c_0^i,\dots,c_{th-1}^i$ (Li et al., 16 Sep 2025). The communication model is partially synchronous with unknown GST and post-GST delay bound $\Delta$, and a PBFT-like layer is used as the broadcast and ordering substrate. The threat model permits up to $f \le \frac{n-1}{3}$ Byzantine participants, a bounded cryptographic adversary, and a network adversary that can eavesdrop, control message arrival time, drop messages, and collude with compromised participants (Li et al., 16 Sep 2025).

The underlying VSS machinery is standard. A dealer with secret $s\in\mathbb{Z}_q$ samples coefficients $a_1,\dots,a_{th-1}$, defines

$P_1,\dots,P_n$0

sends shares $P_1,\dots,P_n$1, and publishes commitments

$P_1,\dots,P_n$2

Verification checks

$P_1,\dots,P_n$3

and reconstruction uses standard Lagrange interpolation (Li et al., 16 Sep 2025).

ASDP exploits a gap between verifiability and timing. The BFT layer guarantees agreement on what becomes committed, but existing schemes do not force participants to aggregate only those gradients whose commitments were posted within a fixed time window. Consequently, a malicious user can aggregate the gradients at the start and provide the commitment with the share at the very last moment (Li et al., 16 Sep 2025). This timing asymmetry gives the attacker informational advantage without violating commitment consistency.

The ASDP algorithm takes as input a correct gradient $P_1,\dots,P_n$4, a cosine-similarity threshold $P_1,\dots,P_n$5, and a step parameter $P_1,\dots,P_n$6, and outputs a malicious gradient $P_1,\dots,P_n$7 (Li et al., 16 Sep 2025). It sets

$P_1,\dots,P_n$8

orders coordinates by $P_1,\dots,P_n$9, initializes $th$0 as a sparse sign vector, and iteratively updates the dot product and norm so that

$th$1

reaches the desired threshold. After the stopping criterion is met, the vector is rescaled to $th$2 (Li et al., 16 Sep 2025). The attack is adaptive because the malicious vector is chosen after observing honest gradients and can be tailored to defense thresholds such as $th$3 or $th$4.

The paper embeds this mechanism in the ASDP-based Customized Model Poisoning Attack (ACuMPA), where malicious participants reconstruct and aggregate honest model parameters, generate $th$5 using the ASDP procedure, and then inject those poisoned updates through the VSS and BFT pipeline (Li et al., 16 Sep 2025). Honest participants still accept the shares because Vrfy validates commitment consistency, not semantic benignity or timing independence. The central lesson is structural: cryptographic consistency and consensus ordering do not by themselves prevent adaptive, timing-driven manipulation of model updates.

3. Formal properties, attack rationale, and defenses

The formal rationale for ASDP in the DPML setting is that consistency of commitments does not imply consistency of intent (Li et al., 16 Sep 2025). A dealer may choose its committed gradient in response to already visible honest gradients and still satisfy all local verifiability checks. This breaks what the paper characterizes as global semantic consistency: the protocol ensures that all honest replicas agree on the committed sequence, but it does not ensure that a gradient was chosen independently of others’ committed values (Li et al., 16 Sep 2025).

The paper also states a theorem on the existence of a common substitute vector. Let

$th$6

If $th$7 for a constant $th$8, then there exists a vector $th$9 with support $w_t^i$0 such that

$w_t^i$1

for at least $w_t^i$2 clients (Li et al., 16 Sep 2025). This establishes that sparse sign vectors can remain sufficiently similar to many client gradients while still being adversarially useful. A plausible implication is that defenses based only on cosine similarity or norm filtering are structurally vulnerable when an attacker can delay and adapt after observing committed information.

The defensive answer proposed in the same paper is EByFTVeS, which forces participants to aggregate only those shares whose commitments are provided in the BFT system at a special time period (Li et al., 16 Sep 2025). The scheme replaces naive broadcast and direct receive operations with consensus-mediated procedures such as broadcast_update and receiving_update, and inserts consensus not only for share dissemination but also for verification results and aggregated shares (Li et al., 16 Sep 2025). It also uses time-windowed batching in which only requests appearing in more than $w_t^i$3 proposals are included in the final batch.

Theoretical properties claimed for EByFTVeS include validity, liveness, consistency, and privacy (Li et al., 16 Sep 2025). Validity is expressed as agreement on committed batches and sequence numbers; liveness ensures commitment after GST; consistency states that computed results across honest participants remain identical; and privacy is reduced to privacy of the underlying VSS. The consistency claim is specifically framed as security against ACuMPA because all honest participants see identical sets of shares and verification results (Li et al., 16 Sep 2025).

The empirical results in that paper quantify the impact of ASDP-based poisoning and the recovery under EByFTVeS. On CNN/MNIST, FedAvg attains accuracy $w_t^i$4 with inference time 30, ACuMPA keeps accuracy at $w_t^i$5 but increases inference time to 36, and ACuMPA + EByFTVeS gives accuracy $w_t^i$6 with inference time 30 (Li et al., 16 Sep 2025). On ResNet/CIFAR-10, FedAvg achieves $w_t^i$7 with inference time 24, ACuMPA reduces accuracy to $w_t^i$8 and increases inference time to 43, and ACuMPA + EByFTVeS restores $w_t^i$9 with inference time 27 (Li et al., 16 Sep 2025). These results indicate that ASDP is principally a timing-enabled integrity attack rather than a failure of commitment verification per se.

4. Constructive reinterpretations: provisioning delay in orchestration and networks

A distinct body of supplied material uses ASDP as a conceptual label for constructive adaptive control. In "ADAPT: A Self-Calibrating Proactive Autoscaler for Container Orchestration" (Baghel, 15 May 2026), the relevant object is provisioning delay

$s_j^i$0

where $s_j^i$1 is the scale-out decision time and $s_j^i$2 is when the new replica becomes ready (Baghel, 15 May 2026). The paper treats this delay as non-trivial and highly variable, tracks it online via EWMA,

$s_j^i$3

and feeds the estimate into a dynamic planning horizon for a Model Predictive Controller (Baghel, 15 May 2026). The supplied discussion interprets this as ASDP because capacity shares become usable only after a learned, environment-specific delay. The closed loop adapts its planning horizon through

$s_j^i$4

so that scale-out decisions are advanced by approximately the amount of estimated cold-start delay (Baghel, 15 May 2026).

This constructive ASDP interpretation is supported by performance results. Across three policies, six workload archetypes, and five random seeds, MPC+LSTM achieves below $s_j^i$5 SLA violation on all workloads, compared with $s_j^i$6–$s_j^i$7 for reactive HPA and up to $s_j^i$8 for MPC+Prophet on bimodal traffic (Baghel, 15 May 2026). The article-level significance is not that ASDP is named there, but that adaptive delay estimation and delay-aware control materially alter the timing of capacity provision.

In 6G URLLC, ASDP is interpreted as adaptive redistribution of access delay components through finite blocklength. "Adaptive Finite Blocklength for Low Access Delay in 6G Wireless Networks" (Zhang et al., 2024) models grant-free access, collision probability, packet error, queuing delay, and transmission delay jointly. The successful access probability is

$s_j^i$9

and the average access delay is minimized over adaptive blocklengths $c_0^i,\dots,c_{th-1}^i$0 via problem P1 (Zhang et al., 2024). The supplied discussion explicitly frames this as ASDP because larger blocklength increases transmission delay but may reduce retransmissions and queue growth, whereas smaller blocklength has the opposite effect. The adaptation therefore provisions total delay between competing components rather than simply minimizing one latency term.

Related URLLC material in "Delay Tradeoff and Adaptive Finite Blocklength Framework for URLLC" (Zhang et al., 2024) describes the same tradeoff at the over-the-air level: $c_0^i,\dots,c_{th-1}^i$1 The discussion supplied for that paper interprets ASDP as adaptive partition of the delay budget $c_0^i,\dots,c_{th-1}^i$2 across these components using blocklength, TTI, bandwidth, and grant-free random access configuration (Zhang et al., 2024). This suggests a broader constructive meaning of ASDP as budgeted delay allocation under reliability constraints.

In shared-network QoS control, "A QoS Framework for Service Provision in Multi-Infrastructure-Sharing Networks" (Nguyen et al., 1 Sep 2025) proposes probabilistic service guarantees with queue stability. QoS is stated as

$c_0^i,\dots,c_{th-1}^i$3

and the paper derives an average delay bound

$c_0^i,\dots,c_{th-1}^i$4

under feasibility conditions (Nguyen et al., 1 Sep 2025). The supplied interpretation presents this as ASDP because the controller adaptively shares service probabilities across infrastructures so that under-service tail probability and average delay remain bounded.

5. Delay-adaptive learning and scheduling interpretations

Several supplied works connect ASDP-like reasoning to adaptive treatment of delayed updates or packets, even though the term is not explicit in the original papers. In "DASA: Delay-Adaptive Multi-Agent Stochastic Approximation" (Fabbro et al., 2024), the server aggregates delayed operators from multiple agents and accepts only the less stale half of the workers when the median staleness remains within a threshold. The update is

$c_0^i,\dots,c_{th-1}^i$5

with

$c_0^i,\dots,c_{th-1}^i$6

Its convergence rate depends on average delay

$c_0^i,\dots,c_{th-1}^i$7

and mixing time $c_0^i,\dots,c_{th-1}^i$8, not worst-case delay (Fabbro et al., 2024). The supplied interpretation identifies this as an ASDP mechanism because the server adaptively decides which delayed contributions to accept and when to skip updates.

A related asynchronous-learning perspective appears in "Delay-adaptive step-sizes for asynchronous learning" (Wu et al., 2022). There the learning rate is chosen using actual time-varying delays rather than a worst-case bound: $c_0^i,\dots,c_{th-1}^i$9 Two concrete policies, Adaptive 1 and Adaptive 2, instantiate this budget principle (Wu et al., 2022). The supplied discussion presents this as ASDP because the algorithm allocates a per-iteration “step-size mass” budget over the delay window, shrinking or zeroing updates when stale information would otherwise destabilize learning.

At the communication-scheduling level, "Delay-Optimal Buffer-Aware Scheduling with Adaptive Transmission" (Chen et al., 2016) studies a Constrained Markov Decision Process in which queue-aware transmission decisions minimize average delay under an average power constraint. The queue evolves as

$\Delta$0

and the optimal policies of the Lagrangian relaxation and the CMDP are threshold-based (Chen et al., 2016). The supplied interpretation uses ASDP to describe the resulting state-dependent sharing of transmission effort: more packets are sent as the queue grows, thereby provisioning delay through adaptive use of the shared transmitter. This is again a constructive use of the term, distinct from the DPML attack semantics.

Across these learning and scheduling examples, the recurring pattern is that ASDP-like mechanisms monitor a delayed state, infer or measure the operational effect of that delay, and adapt admissible actions—update acceptance, step size, transmission rate, or packet coding—to remain within stability or QoS envelopes.

6. Comparative synthesis and recurring mechanisms

Although the supplied sources do not define a unified ASDP theory, they do expose recurrent structural motifs. First is online delay measurement or estimation. In autoscaling, ADAPT estimates cold-start delay with EWMA (Baghel, 15 May 2026). In asynchronous learning, delays are measured as write-event counts and directly fed into the step-size rule (Wu et al., 2022). In DASA, delay enters through stale-iterate selection and average-delay analysis (Fabbro et al., 2024). In URLLC blocklength adaptation, delay is inferred indirectly through queue evolution, collision probability, and error probability (Zhang et al., 2024, Zhang et al., 2024).

Second is adaptive control using the measured delay. In the constructive line, the controller expands or contracts its planning horizon, accepted update set, service probabilities, or transmission blocklength as delay changes. In the adversarial line, the malicious dealer uses delayed share provision to maximize informational asymmetry before committing its own shares (Li et al., 16 Sep 2025). The difference is normative rather than structural: both rely on delayed commitment of a resource contribution after observing system state.

Third is the importance of timing constraints beyond validity. The DPML attack literature shows that commitment verification without timing constraints is insufficient (Li et al., 16 Sep 2025). The autoscaling and QoS literature show, conversely, that explicit modeling of timing yields performance gains through better synchronization of action and effect (Baghel, 15 May 2026, Nguyen et al., 1 Sep 2025). This suggests that timing is not a secondary implementation detail but a first-class protocol variable.

The table summarizes the supplied usages.

Context	ASDP status	Core delayed object
DPML with VSS+BFT (Li et al., 16 Sep 2025)	Explicit term	Secret shares / poisoned gradients
Container autoscaling (Baghel, 15 May 2026)	Conceptual mapping	Provisioned replicas becoming Ready
6G mURLLC adaptive blocklength (Zhang et al., 2024)	Conceptual mapping	Access service via blocklength-controlled packets
Delay-adaptive SA (Fabbro et al., 2024)	Conceptual mapping	Agent updates arriving at server
Shared-network QoS (Nguyen et al., 1 Sep 2025)	Conceptual mapping	Per-frame service opportunities
Asynchronous learning (Wu et al., 2022)	Conceptual mapping	Stale gradients / coordinate updates
Buffer-aware transmission (Chen et al., 2016)	Conceptual mapping	Packets served from a queue

A plausible implication is that ASDP can serve as an umbrella descriptor for systems in which delayed availability of a shared contribution is itself adaptively controlled or exploited. However, the supplied corpus also shows that this umbrella meaning is not standardized; only one paper uses ASDP as the formal name of a mechanism.

7. Limitations, misconceptions, and open interpretive issues

A common misconception would be to treat ASDP as an established general-purpose technical term across distributed systems, networking, and machine learning. The supplied literature does not support that conclusion. Rather, ASDP is explicitly named in one DPML security paper, while other appearances in the supplied material are interpretive mappings supplied alongside papers whose original titles and abstracts do not use the term (Li et al., 16 Sep 2025, Baghel, 15 May 2026, Zhang et al., 2024, Fabbro et al., 2024). Any encyclopedic treatment must therefore distinguish explicit terminology from conceptual analogy.

Another misconception would be to assume that ASDP is inherently beneficial. In the explicit DPML usage, ASDP is malicious by construction: it is a strategy for adaptive share delay provision that facilitates model poisoning while passing VSS checks (Li et al., 16 Sep 2025). In autoscaling, wireless scheduling, or QoS control, the analogous mechanisms are beneficial because the controller, not the adversary, uses delay adaptation to improve SLA satisfaction, access delay, or queue stability (Baghel, 15 May 2026, Zhang et al., 2024, Nguyen et al., 1 Sep 2025). The same timing lever can therefore either improve system performance or undermine integrity, depending on who controls it and what temporal constraints the protocol enforces.

The supplied works also reveal a broader methodological issue. Many classical systems model validity, stability, or utility without making timing itself part of the formal constraint set. The DPML attack exploits precisely that omission (Li et al., 16 Sep 2025). By contrast, ADAPT models provisioning delay directly, DASA makes average delay a convergence determinant, and the QoS framework translates probabilistic service guarantees into linearized constraints (Baghel, 15 May 2026, Fabbro et al., 2024, Nguyen et al., 1 Sep 2025). This suggests that future formalizations of ASDP, if standardized, would likely treat timing not as exogenous noise but as a controlled state variable.

Taken together, the supplied literature supports a precise but two-level description. At the narrow level, Adaptive Share Delay Provision is a timing-based malicious strategy in BFT-backed VSS for DPML (Li et al., 16 Sep 2025). At the broader interpretive level, it names a class of delay-aware adaptive mechanisms that learn, budget, or exploit the lag between decision and effective resource availability across orchestration, wireless access, asynchronous learning, and communication scheduling (Baghel, 15 May 2026, Zhang et al., 2024, Fabbro et al., 2024, Wu et al., 2022, Chen et al., 2016, Nguyen et al., 1 Sep 2025).