Joint Accuracy-Cost Optimization

• Joint optimization of accuracy and cost is a framework that balances precise performance with minimized resource expenses using approaches like weighted-sum scalarization and Pareto optimization.
• Researchers employ methods such as feature configuration search, cascaded inference, and gradient-based optimization to achieve optimal trade-offs in various applications.
• Empirical studies show that these techniques can significantly reduce costs in fields like machine learning, radar, and robotics while maintaining high accuracy.

Joint optimization of accuracy and cost refers to methodologies that simultaneously address the competing requirements of achieving high prediction, estimation, or decision-making accuracy while minimizing some notion of cost—typically test cost, evaluation time, hardware/energy expense, or acquisition budget. This paradigm spans fields such as machine learning, optimization, network modeling, resource allocation, and signal processing. The major research thrust is to design principled frameworks, algorithms, and systems that operate at an optimal or Pareto-efficient trade-off along the accuracy-cost spectrum.

1. Foundational Metrics and Problem Definitions

In joint optimization, "accuracy" is context-specific: it may refer to prediction fidelity (classification accuracy or misclassification cost), detection probability (e.g., in radar waveform design), estimation precision (as measured by the Cramér–Rao Bound), or task-specific loss functions. "Cost" is likewise domain-dependent, encompassing:

• Test/feature acquisition cost (e.g. monetary, time, or energy cost for collecting features)
• Inference or evaluation cost (latency, number of MAC operations, query time)
• Resource usage in hardware (memory footprint, energy consumption, accelerator utilization)
• Measurement, acquisition, or deployment cost in physical systems (radar, transportation, facility location)

A unifying element is the formalization of a composite objective or joint cost. This is frequently expressed as a convex combination or via Pareto-dominance, e.g.,

$$\text{JC}_i = \alpha \cdot \text{MC}_i + (1 - \alpha) \cdot \text{TC}_i$$

where $MC_i$ and $TC_i$ are misclassification and test costs for configuration $i$ (Maguedong-Djoumessi et al., 2013), or through joint constraints and multi-objective formulations in optimization.

2. Methodological Approaches

2.1 Scalarization and Pareto Optimization

Scalarization combines multiple objectives into a single function, parameterizing the accuracy-cost trade-off—often as a weighted sum (with, e.g., $\beta$ or $\alpha$ as a tunable trade-off factor) (Fan et al., 21 Apr 2025, Guinet et al., 2020, Maguedong-Djoumessi et al., 2013). Pareto optimization instead seeks a set of non-dominated solutions (Pareto front), where no solution is strictly better in all objectives.

Methods include:

• Weighted sum or convex combination scalarization
• Pareto front enumeration via acquisition strategies (Bayesian optimization, multi-objective exploration)
• Contextual adaptations (e.g., context-aware EI in cost-efficient Bayesian optimization (Guinet et al., 2020))

2.2 Algorithmic Design Patterns

Several algorithmic innovations are utilized:

• Feature Configuration Search: Efficiently searching configuration subspaces (e.g., backward stepwise elimination as quadratic approximations for exponential spaces) (Maguedong-Djoumessi et al., 2013)
• Ensemble Pruning with Feature Sharing: Integer programming and LP-relaxations for joint accuracy-cost pruning in tree ensembles, leveraging feature sharing for cost efficiency (Nan et al., 2016)
• Cascaded Inference: Multi-stage cascaded architectures in classification, passing queries to more complex stages only if confidence is low, with thresholding based on confidence metrics (Latotzke et al., 2021)
• Model Portfolio Optimization: Integer programming to optimally assign classifiers to queries under a cost budget, using white-box accuracy estimators (Ding et al., 6 Jun 2024)
• Channel-wise Mixed-Precision and Pruning: Gradient-based, hardware-aware search over quantization and pruning jointly, providing Pareto-optimal DNNs with low deployment costs (Motetti et al., 1 Jul 2024)
• Multi-Fidelity and Trust-Aware Optimization: Bayesian frameworks integrating fidelity-aware cost models to control the trade-off between expensive, high-accuracy evaluations and cheap, approximate information (Irshad et al., 2021)

3. Optimization Techniques and Theoretical Underpinnings

• Integer Programming and LP Relaxation: Formulations where the cost-accuracy joint objective admits tractable or even exact LP relaxations due to problem structure (e.g., total unimodularity in tree pruning) (Nan et al., 2016)
• Tensor-Based and Block-Coordinate Methods: In non-convex settings (e.g., radar code design) (Fan et al., 21 Apr 2025), tensor relaxations and block coordinate methods (Maximum Block Improvement) are leveraged to find stationary points with closed-form updates.
• Gradient-Based Search with Soft Sampling: For DNN quantization/pruning, learnable "probability" vectors select bit-width or prune channels, and are optimized alongside network weights (Motetti et al., 1 Jul 2024).
• Bilevel and KKT Formulations: In transportation or facility planning, bilevel optimization (e.g., coupling demand and cost function estimation) is reduced to single-level problems via KKT conditions and constraint relaxation, enabling scalable first-order algorithms (Wollenstein-Betech et al., 2019, Duong et al., 2022).

4. Performance, Scalability, and Practical Implications

Empirical results consistently show that integrated, joint optimization frameworks offer substantial cost reduction at minimal (or no) accuracy loss:

• Model pruning and cascade methods: Achieve energy/latency reductions by only using expensive classifiers for "hard" cases, and reducing overall computation (Latotzke et al., 2021, Maguedong-Djoumessi et al., 2013, Ding et al., 6 Jun 2024).
• Gradient-based joint pruning/quantization: Enable up to 69.54% size reduction at iso-accuracy compared to fixed-precision DNNs, with significantly lower search times than black-box methods (Motetti et al., 1 Jul 2024).
• Cost-aware Bayesian optimization: Pareto-efficient acquisition functions provide up to 50% speed-up in hyperparameter tuning, keeping accuracy drop below 1% (Guinet et al., 2020).
• Neural/hardware co-design: In DNN accelerator design, fast Bayesian Pareto optimization achieves a 100× speed-up over genetic algorithms while approximating the best accuracy/cost trade-offs (Parsa et al., 2019).
• Resource-constrained federated learning: Joint optimization at the orchestration and resource allocation level yields improved accuracy, faster convergence, and 75.9% lower operational cost in networked learning (Wu et al., 2023).

5. Domain-Specific Extensions

Joint accuracy-cost optimization occurs in a breadth of domains:

• Radar and Signal Processing: Simultaneous optimization of SINR (detection) and estimation accuracy (e.g., CRB) via waveform design subject to energy and similarity constraints; tensor and block-coordinate relaxation finds trade-off codes robust to interference and Doppler mismatch (Fan et al., 21 Apr 2025).
• Facility Planning: Combining location (discrete) and investment (continuous) decisions under random utility models allows tractable convex or conic optimization of market capture and cost (Duong et al., 2022).
• Quantum Computing: Slice-wise optimization for VQE ansätze reduces function evaluations and improves ground-state fidelity, balancing quantum resource cost and solution accuracy (Gaberle et al., 16 Sep 2025).
• Robotics: Diffusion-based cost models on SE(3) provide differentiable, multimodal measures for joint grasp and motion planning, enabling smooth trade-offs between grasp quality and trajectory constraints (Urain et al., 2022).

6. Visualization, Analysis, and Interpretability

Visualization tools such as JROC plots and Pareto fronts facilitate transparent assessment of the accuracy-cost trade-off (Maguedong-Djoumessi et al., 2013, Guinet et al., 2020). These tools allow practitioners to identify the set of dominant configurations or decision rules as operating parameters (e.g., trade-off weights) are varied.

7. Open Challenges and Future Directions

• Scalability to Large-Scale and Online Settings: Efficient search and optimization strategies that scale with model, feature, or data size, and that adapt online to changing cost contexts or query distributions.
• Generalizability across Domains: Extensions from classification/regression to sequential decision-making, reinforcement learning, and complex system optimization.
• Improved Estimators and Surrogates: Designing statistically-efficient, low-variance accuracy and cost estimators, especially in heterogeneous inference or hardware settings (Ding et al., 6 Jun 2024).
• Integrated Hardware-Software Co-design: Expanding joint optimization frameworks to more tightly couple computational platforms with algorithmic or model selection, incorporating real deployment measurements into the design loop (Motetti et al., 1 Jul 2024, Parsa et al., 2019).
• Trust, Fidelity, and Robustness: Multifold optimization of "quality" beyond accuracy alone (e.g., trust, fidelity, robustness to distribution shift) while adhering to cost constraints remains an active area, particularly in high-stakes or real-time systems (Irshad et al., 2021).

Joint optimization of accuracy and cost remains a foundational pursuit for constructing deployable, efficient, and robust data-driven systems across disciplines, underpinning advances in edge computing, automated decision-making, resource-constrained AI, and physical system design.