Machine-Learning-Aided Joint Optimization

• Machine-learning-aided joint optimization is a paradigm that uses neural networks to map input features to optimal system parameters in complex engineering systems.
• Techniques include supervised learning, loss-based unsupervised training, deep unfolding, and optimization-inspired layers to tackle nonconvex, high-dimensional problems.
• Its application in wireless communications, resource allocation, and network operations yields near-optimal performance with drastically reduced online computation.

Machine-learning-aided joint optimization is a paradigm in which statistical learning models—typically neural networks—are used to perform simultaneous optimization of multiple system parameters in complex engineering systems. Distinguished by its ability to overcome computational bottlenecks and nonconvexity, these models either substitute for or augment traditional numerical optimizers by learning mappings from input features (e.g., channel statistics, resource demands, or physical parameters) to optimal or near-optimal decision variables. This approach has seen rapid adoption in fields such as wireless communications, resource allocation, physical layer design, and network operations, especially as systems scale in dimensionality and complexity.

1. Mathematical Formulation of Joint Optimization Problems

Joint optimization problems commonly arise in settings where several coupled decision variables must be optimized together under resource, physical, or performance constraints. Examples include joint power sharing and allocation $[\alpha, \beta]$ to minimize bit-error probability in NOMA-CRS systems (Kara et al., 2021), or simultaneous design of pilot signals, antenna positions, and precoders in multiuser MIMO setups (Zhang et al., 30 Aug 2025).

Typical structural forms are:

• Objective: $$\min_{\mathbf{x}, \mathbf{y}} F(\mathbf{x}, \mathbf{y}; \mathbf{a})$$,
• Constraints: $g_i(\mathbf{x}, \mathbf{y}; \mathbf{a}) \le 0$, $h_j(\mathbf{x}, \mathbf{y}; \mathbf{a}) = 0$.

Closed-form solutions are usually intractable for nonconvex, high-dimensional, or combinatorial cases, especially when real-time adaptation is needed.

2. Learning-Based Model Architectures for Joint Optimization

Machine-learning-aided joint optimization relies on either supervised or unsupervised neural networks to learn the mapping from system features or statistical channel information to optimal decision variables:

• Supervised regression: A feedforward network is trained on labeled data, e.g., optimal $(\alpha^*, \beta^*)$ for given CSI in NOMA-CRS (Kara et al., 2021).
• Unsupervised loss-based training: Deep networks are trained with model-based objective functions as loss criteria, e.g., maximizing sum-rate by jointly learning pilot generators, quantizers, antenna positions, and precoders (Zhang et al., 30 Aug 2025).

Networks may be structured as multi-task DNNs, conditional routers for heterogeneous resource allocation (Mitsiou et al., 14 Feb 2025), deep-unfolded optimizers with interpretable layers mimicking algorithmic iterations (Ma et al., 2024), or with optimization-inspired layers that embed convex subproblems (Chen et al., 2024).

Key components typically encompass:

• Input: statistical or instantaneous CSI, network topology, or resource demands.
• Output: optimal or near-optimal system parameters (power coefficients, beamformers, phase shifts, subcarrier allocations, etc.).
• Postprocessing: projection operators (constant modulus, quantization), resource normalization, constraint enforcement.

3. Training and Inference Workflow

Training is often conducted offline to generate optimal or suboptimal solutions via exhaustive search, convex optimization, or advanced numerical methods. This dataset is then used for regression (Kara et al., 2021, Amiriara et al., 2022), or the network is trained end-to-end using differentiable simulators and loss functions derived from system performance metrics (Dong et al., 2020, Zhang et al., 30 Aug 2025).

Inference is performed online with extremely low complexity: a single forward network pass yields the joint optimal variables, eliminating the need for iterative solvers (e.g., grid search, alternating optimization, numerical projection). In many cases, inference complexity is $O(\text{layer\ ops})$ compared to $O(N^2)$ or higher for brute-force optimization.

Specific methods include:

• Straight-through estimators for discrete decisions and quantization (Zhang et al., 30 Aug 2025),
• Routing DNN masks for conditional computation in multi-task regimes (Mitsiou et al., 14 Feb 2025),
• Transformer encoders for statistical CSI aggregation (Zhang et al., 30 Aug 2025),
• Deep meta-learning for adaptation and robustness (Zhou et al., 14 Jun 2025).

4. Performance, Complexity, and Comparative Evaluation

Empirical evaluations demonstrate that machine-learning-aided joint optimization achieves near-optimal performance relative to exhaustive or alternating numerical methods in a wide range of scenarios:

• In NOMA-CRS, ML-selected $(\alpha, \beta)$ matches full-search BER but at orders of magnitude lower online complexity (Kara et al., 2021).
• In MIMO and MA-enabled systems, joint learning of pilots, quantization, and precoding retains almost the full-CSI benchmark performance under limited feedback (Zhang et al., 30 Aug 2025).
• In IRS-user association, regression via FNN is 30–300x faster than convex optimization, with negligible loss (Amiriara et al., 2022).
• Deep-unfolded AO networks for JCAS beamforming generalize across user numbers, outperforming hand-tuned iterative algorithms and yielding Pareto improvements (Ma et al., 2024).
• Hybrid mmWave MIMO deep-learning frameworks achieve performance within a few dB of fully-digital upper bounds while requiring only phase-only analog hardware (Dong et al., 2020).
• Optimization-embedded learning with convex layers (e.g., OpenRANet) maintains mathematical feasibility, drastically reduces online iterations, and yields resource-optimal allocations (Chen et al., 2024).

Performance gains typically arise from eliminating suboptimal fixed parameterization, mitigating error propagation, and exploiting joint learning of interdependent system variables.

5. Specialized Methodologies and Techniques

A variety of ML methodologies have been adapted specifically for joint optimization in complex systems:

• Meta-learning: Networks learn update rules robust to initialization, rapidly adapting to new sub-tasks such as channel realizations (Zhou et al., 14 Jun 2025).
• Multi-agent RL: FL-MARL achieves distributed, scalable joint design of beamforming and RIS phase-shifts under local CSI, reducing backhaul and computation (Zhu et al., 2024).
• Data-model hybrid loss functions: Model-informed surrogate loss functions allow for unsupervised learning in complex joint optimization tasks (Zhang et al., 30 Aug 2025, Lu et al., 2024).
• End-to-end differentiability: Custom simulator layers propagate gradients through nontrivial RF and digital layers, enabling holistic optimization (Dong et al., 2020).
• Sensitivity analysis for interpretability: SHAP values assist in resolving conflicts between coupled parameters for multiple KPIs (e.g., in joint handover parameter optimization) (Farooq et al., 2022).

6. Application Domains and Representative Problems

Machine-learning-aided joint optimization is deployed in:

• Wireless communications: power control, beamforming, user association, phase-shifter design (Kara et al., 2021, Amiriara et al., 2022, Yang et al., 2021, Wang et al., 21 Jul 2025).
• Resource allocation: multi-task wireless scheduling, multi-cell subcarrier assignment (Mitsiou et al., 14 Feb 2025, Chen et al., 2024).
• Photonic systems: Raman amplifier pump configuration, including joint optimization of forward and backward stages (Yankov et al., 2022).
• Mobility management: multi-band handover parameter tuning for cellular networks (Farooq et al., 2022).
• Hybrid MIMO/JCAS: holistic transceiver design, analog/digital hybrid architecture, sensing/communications tradeoff (Dong et al., 2020, Ma et al., 2024).
• mmWave communications: joint probe beam codebook and beam predictor design under physical constraints (Lu et al., 2024).

7. Limitations, Extensions, and Future Directions

While machine-learning-aided joint optimization is highly effective, its limitations include dependence on the training data (statistical law, system model), potential need for retraining when models change (e.g., modulation, fading, topology), and scalability for extremely large joint parameter spaces. For extension to multiuser/multirelay scenarios, the input/output dimension and network complexity must scale appropriately (Kara et al., 2021).

Promising future avenues involve:

• Online adaptive fine-tuning for nonstationary or previously unseen environments,
• Integration of estimation and optimization into unified frameworks,
• Low-precision or quantized models for embedded/edge deployment,
• Reinforcement learning adaptation for dynamic, sequential decision problems,
• Automated architecture search for multi-task resource allocation.

Table: Representative Models and Their Domains

Study (arXiv ID)	Jointly Optimized Variables	ML Model Type
(Kara et al., 2021)	Power sharing/allocation $(\alpha,\beta)$	Feedforward NN
(Zhang et al., 30 Aug 2025)	Pilots, quantizer, antenna positions, BF	End-to-end DNN
(Mitsiou et al., 14 Feb 2025)	Multi-task resource variables	Base+Router DNN
(Amiriara et al., 2022)	IRS-user association, beamforming, phase	FNN regressor
(Dong et al., 2020)	Analog/digital beamformers, demodulator	Modular FC-NN
(Zhou et al., 14 Jun 2025)	Beamforming and antenna position	Meta-learning gradient NN
(Chen et al., 2024)	Subcarrier+power allocation	DNN with convex opt. layer

Machine-learning-aided joint optimization is now foundational for large-scale network control and resource allocation, offering orders-of-magnitude improvements in speed and adaptivity compared to legacy numerical optimization. Its adoption in communications and networking continues to accelerate, driven by expanding system complexity and real-time operational requirements.