Automated Machine Learning Pipeline

• AMLP is an integrated system that automates supervised learning pipeline configuration by jointly optimizing algorithm selection and hyperparameter tuning as a mixed continuous–integer optimization problem.
• It uses ADMM-based operator splitting to decompose the joint optimization into tractable sub-problems, reducing the search space and computational cost.
• The framework incorporates black-box constraints and practical requirements, achieving efficiency gains and superior performance compared to conventional AutoML approaches.

An Automated Machine Learning Pipeline (AMLP) is an integrated, end-to-end system designed to automate the configuration, tuning, and validation of machine learning workflows. In the context of (Liu et al., 2019), AMLP specifically addresses the complex challenge of jointly selecting algorithms and their hyperparameters across all steps of a supervised learning pipeline—formulated as a mixed integer and continuous black-box optimization problem. The framework proposed in this work leverages the Alternating Direction Method of Multipliers (ADMM) to decompose the high-dimensional and tightly coupled optimization tasks into more tractable sub-problems and introduces a principled mechanism for incorporating black-box constraints. Empirical results demonstrate that such an approach provides significant efficiency and effectiveness gains compared to contemporary AutoML frameworks such as Auto-sklearn and TPOT.

1. ADMM-Based Architecture for Automated Pipeline Configuration

The AMLP framework introduced in (Liu et al., 2019) formalizes pipeline configuration as the Combined Algorithm Selection and Hyperparameter Optimization (CASH) problem, encapsulating both discrete algorithmic choices and continuous parameter tuning over a multi-step supervised learning workflow. The key innovation is the splitting of the overall black-box objective into distinct components by means of ADMM operator splitting:

• Continuous variable sub-problem: Hyperparameters for only the currently selected algorithms (“active” set) are optimized, often via Bayesian optimization. This reduces the dimension of the search space at each iteration, as only relevant variables are considered.
• Closed-form projection step: Discrete hyperparameters are resolved by projecting the relaxed solutions back onto their feasible, discrete sets.
• Combinatorial (discrete) sub-problem: Algorithm selection across pipeline modules is tackled as a multi-armed bandit problem, employing, for example, tailored Thompson sampling strategies.

This decomposition allows the complex joint configuration space to be partitioned into lower-dimensional, more manageable segments, with ADMM alternately optimizing each set while synchronizing them through augmented Lagrangian consensus constraints.

2. Optimization Dynamics and Black-Box Handling

The optimization process is specifically designed to accommodate black-box characteristics—where neither gradients nor explicit structure of the loss function or constraints are accessible:

• Surrogate loss function: The objective is modeled over a continuous relaxation of parameters, allowing for surrogate-driven search (such as by Gaussian Process regression).
• Variable block alternation: Each ADMM iteration alternates between optimizing the continuous (hyperparameters) and discrete (algorithm selection) blocks.
• Consensus enforcement: The augmented Lagrangian introduces a quadratic penalty term, with parameter ρ, encouraging equality (consensus) between the relaxed and projected solutions.

This approach dramatically reduces the sample complexity of the exploration space for each sub-problem and enables practical optimization even when pipeline evaluations are expensive and non-differentiable.

3. Integration of Black-Box Constraints

A salient feature of this AMLP is its capacity to directly incorporate black-box constraints—key in real-world deployments where pipelines must meet not only accuracy but also auxiliary requirements (e.g., latency, memory, fairness):

• Constraint functions $g_i$: Arbitrary black-box constraints are supported, without analytic gradients.
• Slack variable reformulation: Each inequality $g_i(...) \leq \epsilon_i$ is re-expressed as an equality with auxiliary variables, bounded by box constraints, making them amenable to inclusion in the augmented Lagrangian.
• Unified operator splitting: All constraints, objective, and variables are handled simultaneously by the same alternating direction scheme, eliminating the need for ad hoc penalties or post hoc adjustments.

This mechanism supports AMLP deployment in contexts demanding robust regulatory or engineering guarantees.

4. Mathematical Formulation

The optimization underpinning AMLP can be formally expressed as follows:

$$\min_{z, \theta} f(z, \theta; \mathcal{A}) \quad \text{s.t.} \quad z_i \in \{0,1\}^{K_i}, \ \mathbf{1}^\top z_i = 1, \ \theta_{ij} \in \mathcal{C}_{ij}, \ \theta_{ij} \in \mathcal{D}_{ij} \ \forall i, j$$

where:

• $z$ encodes discrete algorithm selection (each module chooses a single candidate),
• $\theta$ aggregates all (continuous or discrete) hyperparameters.

The ADMM-based surrogate utilizes an augmented Lagrangian of the form:

$$\mathcal{L}(z, \theta, \delta, \lambda) = \tilde{f}(z, \theta; \mathcal{A}) + I_{\mathcal{Z}}(z) + I_{\mathcal{C}}(\theta) + I_{\mathcal{D}}(\delta) + \lambda^\top (\theta - \delta) + \frac{\rho}{2}\|\theta - \delta\|_2^2$$

where indicator functions enforce feasibility, $\lambda$ denotes the Lagrange multipliers, and $\rho$ is the penalty parameter. For continuous hyperparameter optimization via Bayesian approaches, the expected improvement acquisition function is applied:

$$\text{EI}(\theta) = (y^+ - \mu(\theta)) \Phi\left( \frac{y^+ - \mu(\theta)}{\sigma(\theta)} \right) + \sigma(\theta) \phi\left( \frac{y^+ - \mu(\theta)}{\sigma(\theta)} \right)$$

with $\mu(\theta)$ and $\sigma(\theta)$ representing posterior mean and variance from, e.g., a Gaussian Process surrogate.

5. Empirical Performance and Comparative Analysis

Benchmarking across datasets from UCI, OpenML, and Kaggle demonstrates:

• Superior win rates: The ADMM(BO,Ba) variant attains best results on approximately 50% of datasets, whereas Auto-sklearn and TPOT lead on 27% and 20%, respectively.
• Efficiency: The operator splitting mechanism delivers significant speedups, often exceeding 10× fewer black-box evaluations and reducing overall convergence time.
• Performance gains: In many instances, improvements greater than 10% in the final objective were observed—particularly notable in large-scale, high-dimensional search spaces.

These results suggest that the decomposition strategy not only scales but also delivers practical, measurable gains over contemporary AutoML toolkits.

6. Applications, Robustness, and Limitations

Application scope includes standard supervised learning pipeline configuration—auto-selection and tuning of sequence modules such as imputation, scaling, feature engineering, and model learning. The ability to incorporate practical constraints positions AMLP as especially applicable to domains with operational, regulatory, or resource requirements.

Limitations are primarily tied to the underlying problem's non-convexity and black-box nature. Theoretical convergence guarantees from convex ADMM theory do not apply, so empirical performance validation is essential. Additionally, global solution quality depends on the efficacy of solvers for individual sub-blocks (e.g., surrogate model accuracy for Bayesian optimization). For extremely large or expensive search spaces, total computational burden can remain substantial, despite decomposition-driven gains.

7. Synthesis and Implications

Formulating AutoML pipeline construction as a mixed continuous–integer, black-box optimization problem and applying ADMM-based operator splitting yields a flexible, efficient, and extensible AMLP framework. This decomposition facilitates tractable, sample-efficient joint algorithm and hyperparameter optimization, seamlessly accommodates black-box constraints, and demonstrates strong empirical improvements over leading toolkits. The methodology's practical impact is substantiated across a variety of canonical and challenging datasets, though its full theoretical characterization in non-convex, black-box regimes remains an open issue. The approach provides a robust template for future work on scalable, constraint-aware automated machine learning pipelines.