Defense Success Rate (DSR) Overview

• Defense Success Rate (DSR) is a multidimensional metric that quantifies the proportion of successful defense outcomes against adversarial or fault events.
• It integrates methods such as packet delivery metrics, adaptive randomization, and reinforcement learning to assess and enhance defense robustness.
• Evaluations of DSR incorporate factors like protocol overhead, resource management, and multi-criteria aggregation, providing actionable insights for optimizing cyber-physical defenses.

Defense Success Rate (DSR) is a multidimensional performance metric that quantifies the effectiveness, resilience, and efficiency of defense strategies in adversarial, mission-critical, and cyber-physical systems. DSR measures the proportion or probability of successful defense outcomes—such as thwarted attacks, sustained service continuity, maintained network connectivity, or privileged route integrity—relative to the total number of adversarial or fault events. Across AI-empowered defense methodologies, DSR is central for evaluating protocol robustness, system survivability, and strategic adaptability in dynamically hostile environments.

1. Foundations and Definitions

DSR is not defined by a universal formula, but rather by implementation-specific metrics reflecting the successful prevention or mitigation of disruptive events. In networking contexts (e.g., MANET protocols such as PDSR and TORA (Ramesh et al., 2010)), DSR aligns with packet delivery fraction and throughput: $$\text{Packet Delivery Fraction (PDF)} = \frac{\sum_{f} R_f}{\sum_{f} N_f}$$ where $R_f$ and $N_f$ are packets received and transmitted per flow, respectively. In adversarial ML (e.g., output randomization for DNNs (Park et al., 2021)), DSR is effectively $1$ minus the attack success rate (ASR) on adversarial samples. Decision support for mission success (Mattioli et al., 2021) applies composite, multi-criteria aggregation: $\text{DSR} = \sum_{i=1}^n w_i \cdot I_i$ and, in complex scenarios, $$C_\mu(x) = \sum_{j=1}^n \left( x_{(j)} - x_{(j-1)} \right) \mu\left(\{(j),..., n\}\right)$$ using a Choquet integral over sorted indicators $x_{(j)}$ weighed by fuzzy capacities $\mu$. In dynamic adversarial settings (e.g., RL-driven cyber defense (Zhang et al., 2022)), DSR is tracked by the defender’s cumulative reward and as the inverse of the attacker’s ASR.

2. Key Mechanisms Elevating DSR

Protocol Overhead and Resource Management

PDSR minimizes control packet overhead, maximizing the bandwidth and energy available for data payload, thereby improving both throughput and reliability relative to TORA (Ramesh et al., 2010). Control packet suppression is critical: excessive broadcasts (as with TORA’s UPD/CLEAR) inflate congestion, undermining DSR especially in dense, high-mobility networks.

Adaptive Randomization

Output randomization (test-time and training-phase) disrupts adversarial optimization processes by introducing unpredictable noise to model outputs (Park et al., 2021).

• Test-time: $d(p) = p + \epsilon$, $\epsilon \sim \mathcal{N}(\mu, \sigma^2 I)$, impedes finite-difference based attacks.
• Training: $$\min_{\theta} \mathbb{E}_{(x,y)\sim\mathcal{P}} \mathbb{E}_{\epsilon}[\mathcal{L}(f_\theta(x) + \epsilon, y)]$$ flattening the Hessian and forcing adversaries to require larger perturbations, raising the DSR against strong white-box attacks.

Frequency Domain Filtering in 3D Perception

LPF-Defense applies spherical harmonic low-pass filtering, removing mid- and high-frequency perturbations from point clouds (Naderi et al., 2022). $$f(\theta, \phi) = \sum_{l=0}^{\infty} \sum_{m=-l}^{l} c_l^m Y_l^m(\theta, \phi); \quad \hat{c}_l^m = c_l^m \times w_l$$ By regularizing models on low-frequency features, DSR is universally improved across attack modalities.

Game-Theoretic and Reinforcement Learning Strategies

Reward randomization in multi-domain cyberspace security, and FMADRL-driven MTD mechanisms (leader switching, route mutation, frequency hopping) in UAV swarms, elevate DSR by promoting policy exploration, distributed learning, and proactive uncertainty injection (Zhang et al., 2022, Zhou et al., 9 Jun 2025). Key RL update step in FMADRL: $$\theta^{Q'} \leftarrow \tau \theta^Q + (1-\tau)\theta^{Q'}$$ Coordinated multi-agent adaptation is essential for sustaining high mitigation rates, minimal recovery times, and optimal resource consumption.

3. Contextual Factors Affecting DSR Performance

Network Density and Mobility

PDSR’s effectiveness is maximal in slow, sparsely connected MANETs, with high throughput ($383$–$425$ kBps, delivery $>93\%$), while TORA adapts faster in high-mobility dense networks despite its control overhead (Ramesh et al., 2010).

Data and Model Characteristics

In federated learning, DataDefense leverages small external datasets and client importance scoring to reduce ASR (thus improving DSR) by $40$–$80+$ percentage points—sometimes requiring as few as $5$ defense samples for maximal effectiveness (Purohit et al., 2023):

$$C(\phi_j; \theta) = \frac{\mathrm{ReLU}(\theta^T s(\phi_j))}{\sum_{j=1}^M \mathrm{ReLU}(\theta^T s(\phi_j))}$$

Adversary Adaptability & System Uncertainty

FMADRL-driven strategies maintain high DSR ($0.9975$ for fixed node attacks, $0.9367$ for greedy link attacks), but adaptive adversaries, scaling, and computational constraints present ongoing challenges (Zhou et al., 9 Jun 2025).

4. Analytical, Experimental, and Composite Measurement

Empirical studies systematically benchmark DSR across protocols, models, and game frameworks: | Domain | Defense Approach | DSR Improvement | |:-------------:|:--------------------------|:--------------------:| | MANET | PDSR vs. TORA (Ramesh et al., 2010) | +93–99% packet delivery| | ML Robustness | Output Rand. (Park et al., 2021) | ASR $\downarrow$ to $0-12\%$| | 3D Vision | LPF-Defense (Naderi et al., 2022) | +3.8–4.26% acc. on hard attacks| | Cyber RL | Reward Rand. (Zhang et al., 2022) | DR $\uparrow$, ASR $\downarrow$| | Federated | DataDefense (Purohit et al., 2023) | ASR $\downarrow$ by $40$–$80+$%|

Composite metrics—e.g., the Choquet integral—are frequently used in mission support (Mattioli et al., 2021) to account for indicator interdependencies (RAMT, OEE, cost).

5. Strategic Recommendations and Future Research

Optimal DSR correlates with protocol and framework adaptivity:

• Incorporate multi-agent, federated, or hybrid learning to counteract attacker learning.
• Enhance route cache invalidation in high-mobility environments.
• Modulate randomization/noise dynamically based on input characteristics or observed attack sophistication.
• Expand frequency-domain defenses to broader modality classes (meshes, volumetric data).
• Refine multi-criteria aggregation (e.g., fuzzy measures, hierarchical evaluation trees) for holistic assessment (Mattioli et al., 2021).
• Deploy blended control strategies (e.g., ADM combining PP and DM with observation reliability weighting (Sung et al., 2022)) for real-time systems.

Challenges persisting in DSR optimization include handling adaptive adversaries (including RL-driven attackers), scaling distributed defenses in large swarms, balancing false positives in LLM defense, and robust aggregation under evolving threat landscapes.

6. Notable Controversies and Open Problems

A central controversy remains whether aggressive randomization or hybrid filtering introduces collateral degradation in system utility, such as reduced accuracy for legitimate use cases or elevated operational cost. The tradeoff between control overhead and rapid adaptation presents a persistent optimization problem in mobile networking (Ramesh et al., 2010, Zhou et al., 9 Jun 2025). Additionally, in federated and adversarial ML systems, distinctions between model accuracy and DSR raise questions about the prioritization of defense strictness versus productive capability.

7. Synthesis and Significance

DSR functions as a primary criterion for the rigor and practicality of defense mechanisms across a broad spectrum of systems: from mobile ad hoc networks and 3D perception architectures to federated and multi-agent reinforcement learners, and decision support in cyber-physical missions. Empirical findings across cited work confirm that adaptive, resource-efficient, and context-aware strategies consistently achieve superior DSR, particularly when defense actions balance system robustness, performance, and scalability. Future trajectories in DSR research will likely center on multi-domain, federated defense strategies, refined randomization, and multi-modal aggregation—integrating advances across networking, ML, optimization, and autonomous systems.