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Multi-Objective Hyperparameter Optimization in Machine Learning -- An Overview

Florian Karl, Tobias Pielok, Julia Moosbauer, Florian Pfisterer, Stefan Coors, Martin Binder, Lennart Schneider, Janek Thomas, Jakob Richter, Michel Lang, Eduardo C. Garrido-Merchán, Juergen Branke, Bernd Bischl

arXiv:2206.07438v3cs.LGstat.ML

TL;DR

Hyperparameter optimization often requires choosing among configurations when predictive accuracy is not the only relevant objective. This paper reviews MOHPO methods and applications; its conclusion is that multi-objective formulations can offer Pareto trade-offs for selecting suitable models.

  • Problem

    The paper addresses the need to tune ML hyperparameters while accounting for goals beyond predictive performance, which may involve trade-offs among model requirements.

    Source: §1 · p. 1, §6 · p. 35

  • Method

    The paper reviews MOHPO concepts, optimization strategies, challenges and applications, including evolutionary algorithms and Bayesian optimization.

    Source: §1 · p. 2

  • Results

    Application examples support the merit of multi-objective ML problem formulations, which can provide Pareto-optimal trade-offs for choosing a suitable model.

    Source: §6 · p. 35

  • Takeaways & Limitations

    Practitioners can use MOHPO to choose among models that balance predictive performance with secondary goals.

    Source: §6 · p. 35

    Industrial application is difficult to gauge, and use is limited where notions such as fairness, robustness or interpretability lack established metrics.

    Source: §5.7 · p. 34

Abstract

from arXiv · show

Hyperparameter optimization constitutes a large part of typical modern machine learning workflows. This arises from the fact that machine learning methods and corresponding preprocessing steps often only yield optimal performance when hyperparameters are properly tuned. But in many applications, we are not only interested in optimizing ML pipelines solely for predictive accuracy; additional metrics or constraints must be considered when determining an optimal configuration, resulting in a multi-objective optimization problem. This is often neglected in practice, due to a lack of knowledge and readily available software implementations for multi-objective hyperparameter optimization. In this work, we introduce the reader to the basics of multi-objective hyperparameter optimization and motivate its usefulness in applied ML. Furthermore, we provide an extensive survey of existing optimization strategies, both from the domain of evolutionary algorithms and Bayesian optimization. We illustrate the utility of MOO in several specific ML applications, considering objectives such as operating conditions, prediction time, sparseness, fairness, interpretability and robustness.

1 INTRODUCTION

The introduction argues that ML configuration often involves competing objectives that cannot be assigned a clear trade-off in advance. It presents a review of MOHPO methods and applications, where Pareto-optimal alternatives can be examined after optimization.

1 INTRODUCTION

  • MOHPO addresses black-box, often noisy and expensive optimization where a single obvious performance metric is rarely available.The paper notes that stakeholders also value reliability, robustness, accountability and deployment efficiency, sometimes in trade-off with predictive performance.Source: §1 · p. 2
  • When trade-offs cannot be set a priori, Pareto-optimal configurations preserve alternatives for domain experts to assess post hoc.The paper argues that aggregating objectives into one metric can require defining a trade-off before alternative solutions are known.Source: §1 · p. 2
  • The paper reviews MOHPO methods, challenges and applications, restricting its scope to supervised machine learning.It explains popular algorithms and surveys applications for practitioners interested in multi-objective optimization for HPO.Source: §1 · p. 2
  • The application survey groups objectives into predictive-performance metrics, deployment costs or restrictions, and reliability or interpretability.Examples of relevant deployment considerations include power consumption, memory and inference latency.Source: §1 · pp. 2–3

2 HYPERPARAMETER OPTIMIZATION

This section defines the learning and HPO problems, then extends HPO to multiple criteria and characterizes the resulting black-box search. It distinguishes this focus on tuning hyperparameters from multi-objective learning of model parameters.

2.1 The machine learning problem

  • HPO selects hyperparameters to minimize estimated generalization error, with nested resampling used to keep test data out of tuning and final assessment.A single train-test split can yield a high-variance estimate, so outer resampling such as cross-validation is usually used.Source: §2.1 · p. 4

2.2 Multi-objective hyperparemter optimization as a black box optimization problem

  • MOHPO assigns each hyperparameter configuration a vector of evaluation criteria and searches a potentially expensive, mixed, hierarchical, noisy, and high- or low-dimensional space.Bayesian optimization can use surrogate models and batches; evolutionary algorithms naturally handle mixed and hierarchical spaces but usually need more proposals, while multi-fidelity methods can improve resource allocation.Source: §2.2 · pp. 5–6

2.3 Multi-objective machine learning

  • MOHPO tunes second-level hyperparameters, whereas multi-objective machine learning focuses on first-level model parameters, sometimes alongside hyperparameters.Feature selection borders the two areas and is often treated in a multi-objective manner.Source: §2.3 · p. 6

3 FOUNDATIONS OF MULTI-OBJECTIVE OPTIMIZATION

The foundations section defines objectives and constraints, Pareto-optimal solutions, and ways to evaluate solution sets. It also discusses indicator choice, objective normalization, and multimodal optimization challenges.

3.1 Objectives and constraints

  • A practitioner must decide whether a requirement, such as a memory limit, is an objective to optimize or a constraint to satisfy.The review excludes constrained optimization from its main scope, noting its challenges are orthogonal to the multi-objective aspect.Source: §3.1 · pp. 6–7

3.2 Pareto optimality

  • Because Pareto dominance is only a partial order, optimization seeks a set of non-dominated configurations rather than one universally best solution.The estimated Pareto set maps to an estimated Pareto front in objective space.Source: Figure 2 · p. 7, §3.2 · p. 8

3.3 Evaluation

  • Comparing estimated Pareto fronts requires defining what makes one front better, commonly through quantitative quality indicators.The section also describes weak dominance and four qualities for assessing a solution set: convergence, spread, uniformity and cardinality.Source: §3.3 · p. 8, §3.3.1 · p. 8

3.3.1 Comparing solution sets.

  • Solution-set quality comprises convergence, spread, uniformity and cardinality; spread and uniformity together are called diversity.Visualization and decision-making become more challenging as the number of objectives increases.Source: §3.3.1 · p. 8

3.3.2 Quality indicators.

  • The hypervolume indicator measures the dominated area relative to a reference point and does not require prior knowledge of the Pareto front.Distance-based indicators instead require the true front or a suitable approximation; hypervolume is strictly Pareto compliant.Source: §3.3.2 · pp. 8–9, Figure 3 · p. 9

3.3.3 A note on normalizing objectives.

  • Objective scales can bias indicators such as hypervolume, so normalization to [0, 1] is generally recommended for reliable algorithm analysis and comparison.Ideal and nadir points can scale objectives when known; estimates from evaluated points can be updated during optimization, though effects depend on the MOO method.Source: §3.3.3 · pp. 9–10

3.3.4 A note on multimodal multi-objective optimization.

  • Multimodal MOO may seek diverse decision-space alternatives with similar trade-offs, but identifying all global optima remains an open quality-measurement problem.The review notes that proposed indicators for this purpose lack a theoretical foundation.Source: §3.3.4 · p. 10

4 MULTI-OBJECTIVE OPTIMIZATION METHODS

The section surveys multi-objective optimization methods applied to MOHPO, focusing mainly on methods that approximate the Pareto set while also briefly covering preference-based methods that return one configuration. It reviews scalarization, search baselines, evolutionary algorithms, and Bayesian optimization approaches.

4.1 Scalarization approaches

  • Scalarization reduces multiple criteria to one, but depends on sensible weights or constraints and cannot recover Pareto-optimal solutions on non-convex frontier regions with weighted sums.The section covers weighted sum, Tchebycheff, and ε-constraint approaches.Source: §4.1 · pp. 10–11

4.2 Random and grid search

  • Random and grid search return all non-dominated evaluated configurations, providing simple baselines for more sophisticated MOHPO methods.Random search is often preferred as an anytime method that scales better with low effective dimensionality and low-impact parameters.Source: §4.2 · p. 11

4.3 Evolutionary algorithms

  • Evolutionary algorithms evolve a population through parent selection, crossover and mutation, and survival selection; their populations suit simultaneous approximation of a Pareto front.They are flexible for complex search spaces and straightforward to parallelize, but often need many evaluations and converge relatively slowly.Source: §4.3.1 · p. 12, §4.3.3 · p. 14

4.3.2 Multi-objective evolutionary algorithms (MOEAs).

  • MOEAs use dominance ranking plus diversity, scalarized subproblems, or an indicator such as hypervolume to guide selection.NSGA-II uses nondominated sorting and crowding distance; MOEA/D coordinates scalarized subproblems; SMS-EMOA uses marginal hypervolume contribution.Source: §4.3.2 · p. 13, §4.3.3 · pp. 13–14

4.3.4 Relevant software and implementations.

  • PlatEMO and pymoo offer broad EMOA collections, while mle-hyperopt provides MOHPO through NSGA-II and nevergrad.Many EAs can make expensive ML optimization costly; surrogate modeling or gradient-based local search are proposed combinations to alleviate this.Source: §4.3.4 · p. 14, §4.3.3 · p. 14

4.4 Model-based optimization

  • Bayesian optimization fits a surrogate to evaluated configurations, balances predicted performance against uncertainty through an acquisition function, and evaluates proposed candidates iteratively.It is sample-efficient for expensive black-box problems, while Gaussian processes can struggle with mixed or hierarchical search spaces.Source: §4.4.1 · pp. 14–15

4.4.2 Multi-objective Bayesian Optimization.

  • MO-BO either scalarizes objectives or models them separately; ParEGO repeatedly scalarizes normalized objectives and optimizes expected improvement on the fitted surrogate.Uniformly sampled weights may not yield the best distribution of nondominated points, though ParEGO can focus search on one objective by limiting other weights.Source: §4.4.2 · p. 15
  • Other MO-BO methods use entropy reduction, expected hypervolume improvement, hypervolume-based lower confidence bounds, or jointly optimized acquisition functions to propose candidates.Hypervolume-based BO can require non-trivial multidimensional integration; Multi-EGO generates multiple proposals per iteration, supporting parallelization.Source: §4.4.2 · pp. 15–16

4.5 Multi-fidelity optimization

The review covers multi-fidelity methods, preference-guided optimization, noisy evaluations, realistic assessment, and current MOHPO benchmarks. Existing comparisons suggest optimizer performance depends on the task, while broad recommendations remain limited by benchmark coverage.

4.5 Multi-fidelity optimization

  • Multi-fidelity optimization allocates more resources to promising configurations and discards weaker ones, making evaluation more efficient for costly pipelines such as deep learning.The bracket-run figure depicts faint future-performance lines for HPCs discarded early.Source: §4.5 · p. 17, Figure 5 · p. 18

4.6.1 Focusing optimization through user preferences.

  • Preference information can focus searches on relevant Pareto regions, potentially speed costly optimization, and restore ordering when many objectives make dominance less useful.Preferences may be specified through reference points, constraints, trade-offs, and desirability functions, or learned from rankings; knee solutions can also be targeted.Source: §4.6.1 · pp. 18–19

4.6.2 Noisy environments.

  • Noise can invert inferred dominance, wrongly retaining dominated HPCs or discarding Pareto-optimal ones; repeated evaluations are expensive, so the review surveys statistical, surrogate, and probabilistic approaches.It also describes rolling-tide evolutionary search and noise-aware Bayesian optimization approaches.Source: §4.6.2 · p. 19

4.6.3 Realistic evaluation of multi-objective optimization methods.

  • Nested-resampling evaluation can automatically test each Pareto-set candidate on its outer test set, but selecting one deployable solution across folds remains impractical.The review identifies proper MOHPO evaluation as an understudied open challenge.Source: §4.6.3 · p. 20

4.7 Relevant benchmarks and results

  • Random search is a competitive baseline: it has outperformed some model-based optimizers on fairness tasks, while grid search failed to approximate the SVM error–training-time Pareto front well.Pfisterer et al. [2022] found Multi-EGO, ParEGO, and mixed integer evolution strategy on par with or better than random search, while EHVI or SMS-EGO sometimes did not outperform it.Source: §4.7 · p. 20
  • Optimizer performance depends on the MOHPO task: mixed integer evolution strategy excels on some benchmarks but is average or below par on others.Pfisterer et al. [2022] report strong hypervolume differences across optimizers; Lu et al. [2023] also test evolutionary algorithms on NAS instances.Source: §4.7 · pp. 20–21
  • BO methods, especially PESMO, performed well in fewer iterations on an expensive neural-network task with classification error and prediction time objectives.Hernández-Lobato et al. [2016] studied a feed-forward network on MNIST.Source: §4.7 · p. 21
  • Current benchmarks are only first steps toward broad MOHPO coverage, so the literature does not yet support general recommendations about which optimizer to use when.HPOBench and YAHPO Gym support selected multi-objective use cases, while some published findings are restricted to specific scenarios.Source: §4.7 · pp. 20–21

5 OBJECTIVES AND APPLICATIONS

The section organizes MOHPO applications around prediction performance, computational efficiency, and reliability or interpretability. It discusses why these objectives may need joint consideration and how their relationships can vary.

Prediction performance

  • Prediction-performance metrics may be optimized together when their trade-offs cannot be specified in advance, and the appropriate metric depends on the use case and data.ROC analysis is given as an example involving multiple performance metrics with unquantifiable trade-offs.Source: §5 · p. 22

Computational efficiency

  • Model efficiency concerns training or prediction effort, but measuring qualities such as memory or energy efficiency is not straightforward.The section distinguishes model efficiency from efficiency of the optimization process itself.Source: §5 · p. 22

Fairness, interpretability, robustness and sparseness

  • Fairness, interpretability, robustness, and sparseness are discussed as objectives beyond predictive performance; sparseness may proxy complexity, interpretability, or data-acquisition cost.The review also addresses robustness to domain shift, perturbations, and adversarial attacks.Source: §5 · p. 22
  • Objectives can be positively correlated or conflicting: sparsity may align with efficiency and interpretability, while greater model complexity may improve accuracy but reduce interpretability.The review notes that quantifying such relationships is difficult without comprehensive benchmarks.Source: §5 · p. 23

5.1 Prediction performance

Prediction performance often involves multiple metrics whose trade-offs cannot be fixed in advance. The section illustrates this through ROC analysis and examples from multiclass classification, language generation, and object detection.

5.1 Prediction performance

  • Prediction metrics may penalize errors differently and correlate to varying degrees, so metric choice depends on task, use case, and available data.ROC analysis is presented as one example of a task with multiple prediction-performance metrics.Source: §5.1 · p. 23

5.1.1 ROC analysis.

  • ROC analysis treats threshold selection as a multi-objective problem because improving one of TPR or FPR typically worsens the other.Similar AUC values can conceal different curve shapes; a combined Pareto front preserves the available trade-offs. SVM configurations and false-positive/false-negative rates are also optimized jointly in cited applications.Source: §5.1.1 · pp. 23, 25, Figure 7 · p. 24
  • Multiclass ROC optimization considers g(g−1) misclassification rates, but evaluating many decision-weight vectors makes post-hoc surfaces costly to obtain.Approaches may select one classifier for later cost-sensitive decisions or provide a pool of classifiers; binary AUC does not carry over directly to multiclass classification.Source: §5.1.1 · pp. 24–25

5.1.2 Natural language processing.

  • Across popular natural-language-generation metrics, no single metric correlates with all desirable text qualities.A separate application uses successive halving to optimize perplexity and word error rate for transformer language models.Source: §5.1.2 · p. 25

5.1.3 Object detection.

  • Object detection combines localization and classification, while detection speed adds another relevant evaluation dimension.The cited proposal examines detection rate and false alarm rate alongside the need to account for speed.Source: §5.1.3 · p. 25

5.2 Computational efficiency

The section reviews model efficiency as an optimization objective alongside predictive performance, covering computational complexity, model size, and prediction or training time. It surveys measures and applications while noting practical constraints on interpreting and measuring efficiency.

5.2 Computational efficiency

  • Efficiency refers to computational effort for training or prediction, and resource limits such as available memory can make constrained optimization useful.The review treats efficiency as a property of a configured model, not the efficiency of the optimization process itself.Source: §5.2 · pp. 25–26
  • FLOPs are used as a measure of model complexity in multi-objective NAS, including an image-classification example that finds some CIFAR-10 models more accurate than DenseNet-121 with fewer FLOPs.The cited overview identifies FLOPs as an ideal complexity metric; Aladdin is an example simulator for estimating neural-network energy use.Source: §5.2 · p. 26
  • The review describes efficiency MOHPO as established yet still somewhat novel, with a broader survey scope than prediction-performance work can receive.It also points to hardware-aware NAS studies that jointly consider accuracy, FLOPs, parameters, or prediction time.Source: §5.2 · pp. 26–27
  • Model size, often measured by parameter count, is another efficiency objective; DeepMaker jointly optimizes accuracy and model size for embedded devices.The cited work reports a high correlation between model size and prediction time and evaluates selected architectures after 300 training epochs.Source: §5.2 · pp. 26–27
  • Prediction time is often the deployment concern, but it is difficult to measure reliably across computing environments; some applications also require fast retraining.PESMO optimizes prediction error and the time to predict 10,000 MNIST images and reports superior hypervolume to named alternatives.Source: §5.2 · p. 27

5.3 Fairness

Fairness can be optimized alongside predictive performance, but its measurement depends on the decision context and the fairness criterion chosen. The COMPAS example illustrates differing accuracy–fairness trade-offs across debiasing strategies and strengths.

5.3 Fairness

  • Statistical group-fairness criteria are widely used because they are easy to implement and do not require access to the causal data-generating mechanism.Examples include equalized odds, equality of opportunity, and calibration; equality of opportunity relaxes equalized odds to the advantageous outcome.Source: §5.3 · p. 28
  • Fairness-aware MOHPO approaches jointly optimize fairness and accuracy, constrain fairness while optimizing accuracy, or treat sensitive-group risks as separate objectives.Fairness can also depend on the ML algorithm and its hyperparameters, not only on debiasing-method parameters.Source: §5.3 · p. 28
  • For COMPAS, reweighing, Equalized Odds, and nonlinear-program debiasing at different strengths yield different accuracy–fairness trade-offs.The example measures fairness using the ratio of false-positive rates across advantaged and disadvantaged groups; Figure 8 depicts the strategies on test data.Source: §5.3 · p. 29, Figure 8 · p. 29

5.4 Interpretability

Interpretability is difficult to quantify, and common approaches either restrict model classes or explain models after training. The section presents sparseness as a proxy and reviews measures of main-effect complexity and interaction strength.

5.4 Interpretability

  • Interpretability may mean an inherently understandable model or a post-hoc explanation, but explanation methods can mislead and the concept is difficult to quantify.The review notes that current quantification approaches focus mainly on tabular data and presents sparseness, or number of features, as a commonly used proxy for complexity.Source: §5.4 · pp. 29–30
  • The reviewed measures quantify main-effect complexity through the number of linear segments used to approximate an ALE curve and interaction strength through variance unexplained by main effects.The definitions identify the segment count, feature count, slopes, sample count, prediction function, first-order ALE effects, and mean prediction.Source: §5.4 · p. 30
  • A white-wine study optimized crossvalidated mean absolute error, feature count, main-effect complexity, and interaction strength using ParEGO over 500 iterations.Another cited application optimizes accuracy and introspectability for image classification on ImageNet-16-120, CIFAR-10, and MNIST.Source: §5.4 · p. 30

5.5 Robustness

This section reviews robustness as a model property under shifts in prediction data, covering distribution shifts, adversarial examples, and other perturbations. It also connects robustness with uncertainty quantification and illustrates architecture selection for adversarial robustness and model size.

5.5 Robustness

  • The section focuses on fitted-model susceptibility to prediction-time data shifts, mainly in classification, while noting regression where relevant.It distinguishes this from robustness of the training procedure.Source: §5.5 · p. 30

5.5.1 Robustness metrics and approaches.

  • Effective robustness adjusts post-shift accuracy against the expected drop for models without a robustness intervention at the same pre-shift accuracy.The metric uses pre- and post-shift accuracies and a baseline function β.Source: §5.5.1 · p. 31
  • Adversarial accuracy measures correctly classified samples after an attack, while adversarial frequency and severity concern worst-case accuracy and minimum distance to an adversarial example.The text notes that Bastani et al. [2016] regard frequency as generally more important, while substantial work also studies minimum distance.Source: §5.5.1 · p. 31
  • Common perturbation robustness and adversarial robustness are not necessarily interchangeable: Laugros et al. [2019] argue they are independent model attributes.Gaussian noise is one common perturbation considered in the cited work.Source: §5.5.1 · p. 31

5.5.2 A note on robustness and uncertainty quantification.

  • Better uncertainty calibration tends to accompany less susceptibility to adversarial examples, while aleatoric uncertainty quantification benefits robustness to noise.The section describes uncertainty quantification for MOHPO as under-explored, with few exceptions.Source: §5.5.2 · p. 32

5.5.3 Application and example use case.

  • Guo et al. [2020] search, fine-tune, and evaluate architectures, comparing robustness to adversarial examples and model size to identify suitable models; Figure 9 classifies selected architectures by number of parameters and adversarial accuracy.Source: §5.5.3 · p. 32, Figure 9 · p. 32

5.6 Sparseness via Feature Selection

Feature selection is a multi-objective problem because sparsity and predictive performance can conflict, while feature count also bears on interpretability and cost. The section reviews feature-selection approaches and their integration with MOHPO.

5.6 Sparseness via Feature Selection

  • Sparse models can improve interpretability and reduce fitting, inference, storage, or data-acquisition costs, although fewer features may reduce predictive performance.Feature selection therefore seeks a desirable feature quantity rather than necessarily the maximum number.Source: §5.6 · p. 33
  • Embedded methods select features during fitting, filter methods rank subsets independently of the learner, and wrapper methods search subsets using model performance.Embedded methods are model-specific; wrappers are more computationally expensive but are most amenable to MOO extensions.Source: §5.6 · p. 33

5.6.1 Sparseness Metrics.

  • Feature-count objectives can weight included features differently when their acquisition costs differ, and stability measures compare selected feature sets across resampling iterations.Stability is useful when identifying important features, such as genes for later laboratory examination.Source: §5.6.1 · p. 33
  • Joint feature and hyperparameter search spans a binary feature-selection space whose dimensionality grows exponentially with feature count, with possible feature–hyperparameter interactions.Expensive wrapper evaluations increase the need for efficient search; evolutionary algorithms and more recent BO methods are discussed [29].Source: §5.6.1 · pp. 33–34
  • MOHPO tuning for performance, feature count, and selection stability found configurations with comparable or better performance that used fewer features and selected them more stably than performance-only tuning.Bommert et al. [2017] discarded configurations more than 5% below the best predictive performance identified so far.Source: §5.6.2 · p. 34

5.7 MOHPO applications in industry

The overview finds that industrial deployment of MOHPO is difficult to assess and that commercial AutoML tools have not widely adopted it. It also describes several applications in industrial or proprietary-data settings.

5.7 MOHPO applications in industry

  • Industrial MOHPO deployment is hard to gauge because companies do not necessarily advertise or quantify their success with such tools.Commercial AutoML tools have not widely adopted multi-objective methods, while applicability also depends on the metrics involved.Source: §5.7 · p. 34
  • Industrial examples include speech recognition optimized for performance metrics and memory footprint on an LGE Electronics dataset, and song embeddings evaluated partly on Apple proprietary data.The song-embedding work examines two datasets, including anonymized streaming listening sequences and playlists.Source: §5.7 · p. 35

6 DISCUSSION AND OPEN CHALLENGES

The discussion argues that MOHPO offers practitioners Pareto trade-offs for models with multiple goals, while identifying methodological, evaluation, and application gaps. It highlights priorities including user preferences, broader task coverage, benchmarks, and metric development.

6 DISCUSSION AND OPEN CHALLENGES

  • MOHPO can present Pareto-optimal trade-offs and avoid reducing multiple metrics to one aggregate, with objectives intended to reflect real-world goals closely.The authors advise care with aggregate measures such as AUC or F-score.Source: §6 · p. 35
  • Meaningful integration of user preferences remains a challenge, especially when preferences are noisy or cannot be quantified through the available metrics.The authors identify preference learning as a promising direction [98] [175].Source: §6 · p. 35
  • MOHPO beyond supervised learning remains challenging because evaluating unsupervised tasks and standardizing their performance metrics are difficult.Other objectives, such as efficiency, may still be concretely evaluated and included.Source: §6 · p. 35
  • MOHPO lags behind single-objective HPO in several respects, including methods such as multi-fidelity optimization that were implemented for MOHPO only recently.The discussion also identifies noisy evaluations, early stopping, and mixed or hierarchical search spaces as challenges to address.Source: §6 · p. 36
  • The field lacks extensive benchmarks, and evaluation of MOHPO methods remains an open research topic.The authors also call for more transparent and exhaustive experimental setups and baselines.Source: §6 · p. 36
  • Metrics for interpretability and fairness remain difficult to establish, even as applications of MOHPO to these objectives become increasingly relevant.The discussion distinguishes this metric-development need from an open topic for methodological MOHPO research.Source: §6 · p. 36

A LIST OF APPLICATIONS OF MOHPO WITH AT LEAST ONE OBJECTIVE RELATED TO EFFICIENCY

The surveyed applications pair predictive objectives with efficiency measures across machine-learning tasks. Efficiency dimensions include energy, latency, prediction and training time, model size, memory, and computation.

A LIST OF APPLICATIONS OF MOHPO WITH AT LEAST ONE OBJECTIVE RELATED TO EFFICIENCY

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