Joint End-to-End Optimization Techniques

Updated 8 December 2025

Joint end-to-end optimization is a holistic approach that integrates architectural, algorithmic, and task-specific objectives into a single differentiable learning loop.
It employs differentiable proxies, compressed search spaces, and dynamic scheduling to align sub-module performance with an overall unified objective.
Empirical studies across fields like AutoML, computational imaging, and communications have demonstrated improved robustness, efficiency, and performance compared to traditional modular approaches.

Joint end-to-end optimization refers to the simultaneous, often differentiable, optimization of multiple interacting system components, typically encompassing architectural parameters, algorithmic modules, transformation layers, and task-specific objectives within a single integrated learning loop. Instead of optimizing sub-modules sequentially or in isolation, the joint strategy seeks a global optimum with respect to an overall objective—often incorporating task, resource, and information-theoretic losses—by propagating gradients through the entire computational graph. This paradigm underlies state-of-the-art advances in AutoML, computational imaging, communications, resource allocation, machine task pipelines, and beyond, enabling direct optimization of end-task performance, robustness, and resource efficiency.

1. Fundamental Concepts and Rationale

Joint end-to-end optimization replaces traditional siloed or multi-stage training regimes with a holistic approach in which all or multiple system parameters are adjusted together with respect to a unified loss. In classic "two-stage" workflows, upstream modules (e.g., predictors, encoders, architectures) are trained using surrogate losses, then downstream solvers or decoders are trained or applied separately, often resulting in a mismatch between local module performance and holistic system objectives. This can manifest as degraded task quality, increased regret (in predict-then-optimize), or pronounced inefficiency in downstream resource-constrained settings (Kotary et al., 7 Sep 2024, Zhou et al., 2021).

By coupling all components through end-to-end differentiability and shared objectives, joint optimization mitigates issues such as error amplification, local suboptimality, and poor transfer between nominal and actual operating conditions (e.g., gap between architectural search and retraining in NAS (Zhou et al., 2021) or coding distortion and downstream analytic accuracy in neural codecs (Chamain et al., 2020, Ballé et al., 2016)). It enables direct sensitivity to the final objective, ensuring that upstream components adapt to maximize utility as measured at the system output.

2. Key Methodologies

Several architectural and algorithmic strategies have been developed to realize joint end-to-end optimization, spanning classical learning (sparse coding, augmented Lagrangians), deep learning (differentiable surrogates, attention blocks), and modern probabilistic (EM, stochastic approximation) or combinatorial (differentiable solvers) frameworks.

Unified loss formulation: All relevant variables—network weights ( $\theta$ ), architecture codes ( $\alpha$ or latent codes $b$ ), hyper-parameters ( $\eta$ ), data augmentation policies ( $\tau$ ), task losses ( $\mathcal{L}$ ), structural or resource constraints ( $c_i(\alpha)\leq C_i$ )—are optimized according to a global, possibly multi-term scalar objective (Zhou et al., 2021, Chamain et al., 2020).
Differentiable proxies and surrogates: Non-differentiable subproblems (e.g., quantization, combinatorial optimization, permutation constraints) are replaced or approximated with relaxations (e.g., uniform noise injection for quantizers (Ballé et al., 2016), Gumbel-Softmax for discrete DA policy (Zhou et al., 2021), finite-difference gradients for LP/assignment layers (Dinh et al., 22 Oct 2024), Moreau envelope for OWA (Dinh et al., 22 Oct 2024)).
Compressed search spaces: High-dimensional search (e.g., for architectures $\alpha$ in NAS) is mapped into compressed codes $b$ via measurement matrices or ISTA, enabling practical gradient flow in large spaces while preserving end-to-end transitivity (Zhou et al., 2021).
Coupled scheduling and unrolling: Joint schemes represent auxiliary parameters (DA probabilities, learning rates) as "dynamic schedulers" that co-adapt with main model weights, ensuring simultaneous optimization (Zhou et al., 2021).
Alternating minimization & block coordinate descent: For complex, coupled objectives (e.g., joint embedding and optimal transport (Yu et al., 26 Feb 2025)), block-alternating schemes allow tractable convergence, updating variables such as couplings, thresholds, and model weights in turn.
Integration of neural and physical models: Physics-based system elements (e.g., rate-equation surrogates for lasers (F. et al., 16 May 2024), wave-optics simulators for compound lenses (Ho et al., 13 Dec 2024), metasurface phase distributions (Zhang et al., 2022)) are embedded as differentiable layers, permitting backpropagation through hardware constraints and non-idealities.
End-to-end resource allocation & scheduling: Full pipeline differentiation enables learning of resource allocations (CPU, bandwidth, compression, channel cutoffs) that minimize global criteria (E2E latency (Ye et al., 2023, Chi et al., 29 Mar 2024), fairness (Dinh et al., 22 Oct 2024), or regret), often in hybrid optimization frameworks (Lyapunov + RL + convex programming (Ye et al., 2023)).

3. Representative Application Domains

Neural Architecture Search and AutoML

DHA jointly optimizes data-augmentation policy, learnable hyperparameters, and neural architecture parameters in a single loop using compressed representations and dynamic schedulers; this avoids expensive retraining and achieves superior correlation between search and final deployment accuracy (Zhou et al., 2021).

Computational Imaging and Optical Design

End-to-end joint optimization of front-end hardware and back-end algorithms enables realization of computational imaging systems with maximal information throughput and robustness. Metasurface-based snapshot imaging jointly optimizes the phase distribution (via learned polynomials $\{a_i\}$ ) and a neural recovery network, leading to higher fidelity reconstruction than any partial optimization (Zhang et al., 2022). In compound imaging optics, joint training of lens shapes and neural reconstruction nets using a differentiable wave optics simulator enforces physical realism and robustness to aberration/diffraction (Ho et al., 13 Dec 2024).

Communications and Signal Processing

In waveform design, the joint shaping of transmitter pulse and constellation, together with learning-based receivers, enables trade-offs among information rate, spectral leakage (ACLR), and power envelope (PAPR), outperforming separated filter design plus conventional modulation (Aoudia et al., 2021). End-to-end optimization of transmitter bias, modulation current, pulse-shaping, equalization, and demapper parameters in DML optical links achieves significant SNR and mutual information gains relative to partial or iterative approaches (F. et al., 16 May 2024). Joint source-channel coding for multi-device systems allows adaptive allocation of compression, transmission slots, and edge resources to minimize E2E latency subject to task-distortion constraints (Chi et al., 29 Mar 2024).

Machine Learning for Combinatorial and Fairness-Critical Problems

Learning-to-Optimize (LtO) frameworks bypass inner-loop hand-crafted solvers entirely, learning surrogate mappings from features to near-optimal solutions, often employing augmented Lagrangian or primal-dual self-supervised corrections to enforce feasibility and minimize regret (Kotary et al., 7 Sep 2024). In scheduling, joint optimization of a matching network and fair aggregation metrics (e.g., OWA) enables interpretable, tractable, and fair assignment strategies that optimize group or individual fairness directly, with efficient differentiation through assignment layers (Dinh et al., 22 Oct 2024).

Joint loss frameworks integrating information- and perceptual-based terms permit end-to-end learning of models that are optimal with respect to multiple (potentially conflicting) metrics. In speech denoising, joint losses for signal-to-distortion ratio (SDR), perceptual speech quality (PESQ), and short-time objective intelligibility (STOI) achieve simultaneous improvement over MSE-only or single-metric schemes (Kim et al., 2019, Kim et al., 2019).

JOENA demonstrates the hybridization of optimal transport and node/edge embedding in network alignment, using differentiable Gromov–Wasserstein distances and learnable cost matrices. Alternating joint minimization achieves up to 16% MRR improvement and 20× speedup over prior methods (Yu et al., 26 Feb 2025).

4. Optimization Landscape and Convergence Properties

Simultaneous joint end-to-end optimization induces a non-separable, highly coupled landscape. Empirical findings indicate that joint schemes converge to flatter, wider minima with better generalization (Zhou et al., 2021). Subgradient or block coordinate methods are often employed to handle piecewise-linear aggregators (e.g., OWA in fairness objectives (Dinh et al., 22 Oct 2024)), non-differentiable resource constraints, or discrete layers (assignment, quantization). For alternating minimization frameworks, monotonic non-increasing objectives and boundedness yield convergence to stationary points, though global optimality is rarely guaranteed for non-convex set-ups (Yu et al., 26 Feb 2025).

Joint end-to-end methods routinely employ differentiable relaxations or surrogates (e.g., Gumbel-Softmax, uniform noise injection) to propagate gradients and maintain tractability. Hybrid or multi-level optimization—including Lyapunov-drift regularization, reinforcement learning for discrete partitioning, and convex subproblems for continuous resources—is used in resource allocation (Ye et al., 2023, Chi et al., 29 Mar 2024).

5. Empirical Results and Impact

Across domains, joint end-to-end optimization has consistently yielded superior task performance, resource efficiency, and system robustness relative to both sequential and modularly optimized baselines. Notable empirical findings include:

Setting	Joint vs. Sequential Gain	Reference
AutoML (DHA)	+1.4% Top-1 (ImageNet), +0.9% CIFAR10	(Zhou et al., 2021)
E2E Speaker Verif	8.0% EER (multi-enroll), −21.4% rel.	(Zeng et al., 2022)
Machine-Task Codec	+7.1% COCO mAP, superior low-rate perf.	(Chamain et al., 2020)
Compressive Sensing	+0.8 dB PSNR, +0.02 SSIM	(Zhang et al., 2022)
Compound Optics	+16% RMSE, +23% top-1 (ImageNet10)	(Ho et al., 13 Dec 2024)
OT-based Network Align.	Up to +16% MRR, 20× speedup	(Yu et al., 26 Feb 2025)
SDR/PESQ Speech	+1.15 dB SDR, +0.17 PESQ (QUT)	(Kim et al., 2019)

These gains stem from direct sensitivity of upstream configurations to downstream loss, adaptive adjustment to hard constraints, and ability to learn non-trivial system-internal trade-offs.

6. Challenges, Limitations, and Extensions

Despite their demonstrated merit, joint end-to-end optimization poses significant challenges:

Computational cost and differentiability: Full-graph backpropagation is memory-intensive, often requiring custom surrogates or relaxations for non-differentiable or combinatorial blocks (Ballé et al., 2016, Dinh et al., 22 Oct 2024).
Scalability: Large search spaces (NAS, resource scheduling) require compression, sparse parameterizations, or sampling (Zhou et al., 2021, Ye et al., 2023).
Convergence/stationarity only: Most frameworks guarantee convergence to stationary points but not global optima due to complex, non-convex couplings (Yu et al., 26 Feb 2025).
Domain knowledge integration: Accurate physical modeling (e.g., of diffraction or nonlinearities) is indispensable for robustness but can increase computational complexity (Ho et al., 13 Dec 2024).
Extension to broader input types: LtO-style models enable broader generality but may sacrifice performance on particular structured domains (Kotary et al., 7 Sep 2024).

Ongoing research is directed toward increased sample- and compute-efficiency, adaptive architecture search with lifelong learning, more powerful differentiable combinatorial solvers, and broader applicability to stochastic, dynamic, and real-time settings.

7. Significance and Outlook

Joint end-to-end optimization constitutes a paradigm shift for integrated system design in AI, communications, signal processing, and decision-making systems. By dissolving artificial boundaries between components, it enables emergence of globally optimal, robust, and interpretable solutions that would be inaccessible by modular optimization. Major impacts are found in AutoML, integrated sensing and communication, task-aware codec design, computational optics, multi-resource allocation, and fair algorithmic decision-making. Its proliferation is driven by advances in differentiable programming, deep surrogates for physical processes, and algorithmic flexibility in constraint enforcement, suggesting broadening adoption in future intelligent and autonomous systems.