Constrained Hyperparameter Optimization for Streaming Data

Optimization of hyperparameters is a critical factor to obtain optimal model performance. While existing research has predominantly concentrated on batch-learning scenarios, addressing the complexities inherent in data streams presents a challenge. The deployment of sophisticated methodologies to manage data streams becomes highly important. Consequently, the capacity for self-adjusting hyperparameters during on-line learning phases emerges as a goal. Many hyperparameters exhibit constraints and are confined within bounded search spaces, rendering specific solutions unacceptable upon applying optimization operators. To solve this issue, employing boundary constraint- handling techniques becomes imperative to rectify invalid solutions. This paper presents strategies for effectively managing boundary constraints within constrained numerical optimization problems. Recent methodologies, including heuristic and evolutionary-based optimization, employ a "boundary" strategy, wherein values that surpass boundary thresholds for a given hyperparameter are realigned to the respective limits. Our study introduces four strategies to navigate boundary constraints in online optimization algorithms. Through empirical investigations conducted on established datasets, we demonstrate that adopting boundary strategies outperforms the "boundary" strategy.

Distributional Extrapolation for Interactions

Predicting combinatorial effects from limited-range observations is a fundamental challenge in many scientific domains, including drug discovery and hyperparameter optimization. We study combinatorial extrapolation, where training data consists of axis-aligned samples with only one active covariate, while test-time inputs involve multiple simultaneously active covariates. We introduce DExtrI, a method for extrapolating interaction effects beyond the support of the training data. We provide theoretical guarantees characterizing when such extrapolation is possible. Empirical results on synthetic and real-world datasets demonstrate that DExtrI successfully generalizes to unseen combinations of covariates. Our approach enables applications such as predicting previously untested drug combinations and improving the efficiency of hyperparameter optimization.

Many Optimizers But Only One Training Path: Repeated Resampling for Adaptive Optimizer Selection

An optimizer is usually chosen before training a deep neural network and then kept fixed. Treating optimizer choice as a hyperparameter could boost performance, but it requires several complete training runs and discards all but the winner. Repeated Optimizer Resampling (ROR) instead searches during one evolving run. Every $b$ epochs, each candidate optimizer scouts from the current model weights for $s$ epochs. The best scout continues for the remaining $b-s$ epochs, and that completed segment becomes the new incumbent if it improves the validation objective. This design allows the preferred optimizer to change as training progresses. We compare two variants of ROR on MNIST, Fashion-MNIST, and two motor insurance claim-count models. Nine fixed optimizers and both ROR variants are evaluated with the same ten seeds. One-epoch ROR uses 24\% to 35\% of the aggregate training needed to identify the best fixed optimizer exhaustively and remains close to that optimizer on all four tasks. These results support short scouting as a practical way to search over optimizers without completing every candidate run.

TRACE-CASH: Trial-History-Conditioned Reinforcement Learning for Adaptive Configuration Exploration in Time-Series CASH

Combined algorithm selection and hyperparameter optimization (CASH) searches a conditional space in which the selected model determines which hyperparameters are active. In time-series forecasting, temporal choices, chronological validation, and costly evaluations further complicate this search. Controlled comparisons of heterogeneous search methods under a shared time-series CASH (TS-CASH) evaluation protocol remain limited. Within this setting, we study TRACECASH, a task-local hybrid sequential optimizer combining grouped actor-critic candidate generation with fixed rules for model coverage, validation-guided exploitation, and exploration after stalled progress. A model actor proposes an initial forecasting model; three model-conditioned actors generate temporal, architectural, and training actions; and a modelspecific decoder constructs the configuration ultimately evaluated. We compare TRACE-CASH with six alternatives spanning random, Bayesian, evolutionary, multi-objective, and language-model-assisted search across 41 dataset-frequency task variants. TRACE-CASH has the lowest mean rank on both MASE and WQL. Descriptively, it also has the lowest window-averaged test-MASE rank in the predefined full and late windows. These results support the complete TRACECASH procedure as competitive among the evaluated methods.

On the Brittleness of Maximum Likelihood Estimation for Gaussian Process Hyperparameter Optimization

Machine learning (ML) has become an indispensable part of modern engineering design workflows. A crucial step in training an ML model is the selection of the loss function which can be systematically formulated via various techniques such as maximum likelihood estimation (MLE) and cross-validation . While MLE is one of the most popular, effective, and intuitive mechanisms for training ML models, it is brittle: if the assumptions underpinning it are not met, the trained ML model may generalize poorly. This brittleness affects even Gaussian processes (GPs) which are widely used in engineering design and are often (incorrectly) presumed to be very robust to overfitting. In this paper, we fundamentally evaluate the brittleness of MLE in the context of training GPs for probabilistic regression or classification tasks. We compare theoretically grounded metrics against MLE and propose practical solutions. Our extensive studies demonstrate the effectiveness of our solutions in downstream design tasks such as Bayesian optimization and provide a blueprint for practitioners to build accurate and robust GPs that can even outperform tabular foundation models in terms of prediction accuracy, uncertainty quantification, and inference cost. Our contributions are publicly available via GitHub at https://github.com/Bostanabad-Research-Group/GP-vs-TabPFN-vs-GPyTorch.

Out-Of-The-Loop Multi-Fidelity Bayesian Optimization

Black-box optimization is a ubiquitous problem in science and engineering, often dealing with expensive objective functions with cheaper lower-fidelity proxies available. Multi-fidelity Bayesian optimization (MF-BO) is a principled approach to this problem, leveraging correlations across different fidelities when querying the objective. However, for many important MF-BO tasks, the true highest-fidelity function is prohibitively expensive to be part of the optimization loop. Nevertheless, practitioners often have gold standard data (observations of the highest-fidelity function) obtained from previous experiments that might provide information for the current task. For instance, in molecular optimization, chemists often pick the top-$k$ candidate molecules using various computer simulations, and later reveal their true objective function values. In this work, we demonstrate the suboptimality of standard MF-BO algorithms in the real-world scenarios above, even under ideal assumptions. Next, we mitigate this problem by incorporating historical high-fidelity data accompanied by task descriptors---which can be explicitly given or extracted from unstructured metadata. We demonstrate the effectiveness of our methods on synthetic functions, as well as real-world problems in chemistry and hyperparameter optimization.

Frequency-Based Reservoir computing

Reservoir computing has emerged as an efficient machine learning framework for predicting time series generated by dynamical systems. In contrast to other machine and deep learning approaches, a reservoir computing trains only the output layer via linear regression, leaving the reservoir (recurrent layer) untrained. This simplification makes reservoir computers easier to train and more amenable to experimentation. However, because current reservoirs consist of networks of randomly connected nodes and require the optimization of numerous hyperparameters, a framework that precisely explains how reservoir computing operates and how it can be optimized remains missing. Here, we propose a frequency-based reservoir inspired by the brain's oscillatory dynamics and its hierarchy of timescales. The frequency-based reservoir can be interpreted as an ensemble of independent oscillatory units, each processing a portion of the input's frequency content. This allows us to understand the reservoir's internal behavior by modeling it as a single unit driven by an external input. Borrowing from the theory of a nonlinear oscillator forced by complex periodic inputs, we found that units of the frequency-based reservoir selectively amplify and store specific input frequencies, which are then used for prediction. The frequency-based reservoir performs as well as or better than equivalent random reservoirs. Furthermore, the frequency-based approach can be optimized to improve short-term prediction, a property that random reservoirs lack. Finally, we show that the frequency-based reservoir can also predict complex spatiotemporal dynamics. Our results show that reservoir computing can be designed using brain properties and theoretical insights borrowed from the physics of forced nonlinear oscillators.

Systematic Evaluation of Learning Rate Scheduling Strategies Across Heterogeneous Architectures

Choosing a learning rate scheduling strategy is critical to neural network training, but manual selection is costly and rarely exhaustive. While classical AutoML approaches often treat the scheduler as a secondary hyperparameter, we systematically investigate its impact on classification accuracy across a diverse pool of architectures. We evaluated 30 representative architectures from convolutional and transformer families within the LEMUR neural network dataset. Through automated source-code injection, we applied 25 scheduler configurations across nine PyTorch families, evaluating a total of 3,938 model variants on CIFAR-10. Our best configuration achieved a top-1 accuracy of 86.45%, with 237 variants exceeding 80%. The results show that the choice of scheduler depends heavily on the architecture: CosineAnnealingWarmRestarts and CyclicLR consistently outperform basic decay strategies. The resulting accuracy landscape, contributed to the LEMUR nn-dataset, provides a practical reference for principled scheduler selection.

TabPack: Efficient Hyperparameter Ensembles for Tabular Deep Learning

In deep learning for tabular data, efficient ensembles of multilayer perceptrons (MLPs) have recently emerged as effective and practical architectures. Existing methods of this kind use the same hyperparameters for all underlying MLPs, which requires hyperparameter tuning for achieving the best performance. In this work, we introduce TabPack, an efficient MLP ensemble with strong out-of-the-box performance and reduced reliance on traditional tuning. In a single run, TabPack samples and trains many MLPs with different hyperparameters efficiently in parallel and selects ensemble members on the fly during training. Thus, TabPack only requires specifying ranges from which to sample MLP hyperparameter rather than exact hyperparameter values, which naturally demands less precision for good performance. In experiments on medium-to-large public datasets, TabPack with default settings performs on par with extensively tuned prior methods, thus substantially reducing effort and compute resources needed to achieve competitive results on tabular tasks. Notably, running the default TabPack configuration on a modern MacBook took less time than tuning some baselines on an industry-grade GPU.

MMAO-Cls: Metabolic Multi-Agent Optimization for Joint Feature Selection and Classifier Tuning

This paper studies whether the Metabolic Multi-Agent Optimizer (MMAO) can act as a credible outer-loop optimizer for classification model selection. We propose MMAO-Cls, a mixed-space realization in which each agent jointly encodes a binary feature mask and classifier hyperparameters, while private energy, communal budget, role drift, and lifecycle turnover are mapped to the accuracy-complexity tradeoff of wrapper learning. The implementation is strengthened by deriving feature-budget adaptation from feature-information priors and by regularizing validation reward with both subset compactness and train-validation overfitting gap. We evaluate MMAO-Cls on seven standard tabular benchmarks with three seeds each and compare it against RandomSearch, GA-lite, PSO-lite, and an endogenous no-sharing ablation. On the aggregate validation objective, MMAO-Cls ranks second ($0.9433$) behind GA-lite ($0.9446$). On held-out test performance, it reaches mean score $0.8882$, improving over RandomSearch ($0.8808$) and GA-lite ($0.8857$), remaining close to PSO-lite ($0.8874$) and the no-sharing ablation ($0.8900$), while using the most compact mean held-out feature subset among all compared methods (feature ratio $0.4881$). Pairwise tests show that these margins are not yet statistically significant. The resulting claim is therefore conservative: MMAO-Cls supports classification applicability and compact mixed-space search more clearly than it isolates communal sharing as a decisive standalone advantage.

Gradient-Descent Steps to Success over Mean Accuracy: A Paradigm Shift for ML

Traditional evaluation of machine learning (ML) models typically focuses on achieving the maximum possible accuracy irrespective of the computational cost. In this article, we propose a paradigm shift towards evaluating performance based on computational effort-explicitly defined here as the total number of gradient descent steps required to reach an acceptable level of accuracy with high probability. Building upon the concept of computational effort originally introduced by Koza for Genetic Programming, we extend this metric to any ML model trained via gradient descent. Furthermore, we demonstrate that minimising this effort acts as a novel form of Automatic Machine Learning (AutoML). By evaluating it across 11 diverse ML models and five standard classification datasets, we uncover significant insights into the dynamics of gradient-based learning. Our findings reveal that optimal hyper-parameters consistently favour unusually large learning rates. Crucially, we demonstrate that the rapid, aggressive landscape traversal enabled by these large rates not only promotes generalisation-as seen in phenomena like superconvergence-but also statistically minimises the expected computational effort for training. Furthermore, we identify distinct phase transitions in the optimal search strategy: while a single training run suffices for lower accuracy targets, reaching a model's performance limit requires a dramatic shift towards conducting numerous independent, short restarts. Finally, we illustrate how this effort-based paradigm provides a robust framework for model selection, allowing practitioners to choose optimal algorithms based on the difficulty of a problem as perceived by different models for a given target accuracy, or to maximise the achievable accuracy for a fixed budget of gradient descent steps.

When Is an LLM Worth It for Hyperparameter Optimization? A Budget-Matched Study on Tabular Data Finds the Warm-Start Is a Default Configuration, Not the Model

Large language models (LLMs) have been proposed as hyperparameter-optimization (HPO) advisors that "warm-start" search from prior knowledge, proposing strong configurations in very few evaluations. We test that claim under a budget-matched, multi-seed protocol on eight PMLB tabular benchmarks, comparing an LLM advisor (LLM-OptFlow) against four classical baselines (random search, Optuna-TPE, Gaussian-process Bayesian optimization, and successive halving) over one shared search space, with paired tests and bootstrap 95% CIs across 8 x 5 = 40 (task, seed) units. The finding is cautionary. The advisor's strong first point is not an LLM output at all: like prior LLM-HPO systems the loop is seeded with a fixed default configuration, evaluated before any model call, which alone reaches 88.7% mean best-CV, identical to within 0.01 pp across all seven advisor models tested. The LLM's own proposals add only +0.40 pp of cross-validation accuracy over that seed and nothing on held-out test (LLM-Default = -0.01 pp, p = 0.92). When the same seed is granted to classical search, the apparent lead collapses: against seeded random search it leads by +0.20 pp at 2 evaluations, is tied by 5, and is behind by 12 (-0.37 pp). Without the seed, classical search ties the advisor by 12 evaluations and beats it by 40 (+0.6 to +0.8 pp, p <= 1e-4). Two LLM-specific behaviors survive: a single-task exploration failure (vehicle), and a rule-based confidence filter that removes ~33% of wasted compute without changing accuracy. The recommendation is deflationary: on tabular HPO, seed classical search with a sensible default; an LLM advisor adds no measurable generalization benefit and is overtaken within a handful of evaluations. We release the harness and a script that reproduces every statistic.

A Systematic Approach for Selecting Trajectories for Data Augmentation

Trajectory data augmentation is a promising approach to mitigate data scarcity in machine learning applications, but its utility has been limited by the complexity of preserving spatio-temporal coherence. Although prior work demonstrated the viability of geometric perturbation, it relied on naive random selection, leaving a critical gap in understanding which trajectories should be augmented for maximal benefit. This thesis addresses this gap by developing a systematic and scalable framework to evaluate five systematic selection strategies: Outlierness, Diversity, Representativeness, Uncertainty, and Random selection. These strategies were rigorously tested across four datasets covering animal behavior (Foxes and Starkey), maritime traffic (AIS), and urban traffic (Car) using a suite of linear and non-linear machine learning models. As part of this evaluation, an Optuna-based hyperparameter optimization loop was integrated to empirically identify the best-performing augmentation parameters for each dataset within the explored search space. The results indicate that, while systematic selection is not a universal solution, it offers distinct advantages over the random baseline. Systematic strategies, particularly Outlierness and Uncertainty, demonstrated higher stability and were less prone to performance degradation observed with random sampling in dense datasets. However, the findings also reveal that the value of augmentation is strictly conditional. Visual analysis via UMAP demonstrates that while systematic augmentation successfully repairs topological fragmentation in sparse datasets, it can act as a corrupting noise signal in high-quality, dense datasets. Furthermore, the study identified physical limitations in high-velocity domains, where standard perturbation techniques lead to divergence in feature space...

Importance-Aware Scheduling for High-Dimensional Hyperparameter Optimization

Hyperparameter Optimization (HPO) is essential for building high-performing ML/DL models, yet conventional optimizers often struggle in high-dimensional spaces where evaluations are costly and progress is diluted across many low-impact variables. We propose Greedy Importance First (GIF), an importance-aware scheduling strategy that uses a small-sample warm start to estimate hyperparameter importance, forms importance-based groups, allocates trials proportionally, and retains a full-space fallback. We evaluate GIF under fixed evaluation budgets on five anisotropic analytic functions, Bayesmark, and NAS-Bench-301. On the higher-dimensional benchmarks, GIF reaches better incumbents with faster convergence than TPE, BOHB, Random Search, and Sequential Grouping. On Bayesmark, where the effective dimensionality is smaller, GIF remains competitive but the margins are smaller. Ablation studies show that importance estimation, proportional allocation, and the fallback step all contribute to the gains. We also verify that the HIA component recovers the intended anisotropy on the analytic benchmarks. These results suggest that GIF is a simple and plug-compatible way to improve sample efficiency in high-dimensional HPO.

Provably Reduced Sample Cost in Prior-Guided Hyperparameter Optimization

Large-scale hyperparameter optimization (HPO) in automated machine learning (AutoML) consumes substantial computational resources, raising growing concerns about scalability and energy efficiency. Existing methods use prior information heuristically to accelerate both black-box and multi-fidelity settings, but they lack a characterization of how prior informativeness quantitatively reduces sample complexity. In this work, we provide the first distribution-dependent sample complexity bounds for multi-fidelity HPO with priors through the formal lens of fixed-budget best-arm identification. By modeling priors directly over arm means as configuration performance, we derive explicit, distribution-dependent error bounds that quantify the relationship between priors and evaluation budget. Our analysis shows that informative priors, which concentrate probability mass on near-optimal arms, yield reductions in the number of required evaluations, whereas baseline performance is recovered with uninformative or misleading priors. We conduct proof-of-concept experiments on a synthetic benchmark and on LCBench, a common multi-fidelity HPO benchmark for deep learning, to confirm our theoretical results, achieving up to 90% budget reduction while retaining solution quality. Together, our results provide a principled foundation for prior-guided and compute-efficient green AutoML.

Optuna Constrained Tree-Structured Parzen Estimator Is a Joint Density Generalization of c-TPE

Constrained hyperparameter optimization (HPO) is common in practice, yet Optuna's widely used constrained TPE lacks algorithmic analysis. While c-TPE proposes an expected constrained improvement (ECI) approach assuming independence between the objective and constraints, Optuna uses a single joint density over both. We show that Optuna's constrained TPE is joint c-TPE -- the same ECI acquisition function using a joint likelihood. We demonstrate joint c-TPE is invariant to constraint duplication whereas independent c-TPE degrades as the product accumulates duplicated factors. We outline practical tradeoffs between the formulations and directions for future study.

Hyperparameter Learning for Latent Factorization of Tensors for Representation Learning to Large-scale Dynamic Weighted Directed Network

Large-scale dynamic weighted directed networks (DWDNs) are widely used to model time-varying interactions among nodes. Latent factorization of tensors (LFT) extracts target knowledge from DWDNs via low-rank embedding. However, similar to many machine learning models, the performance of LFT heavily depends on the selection of hyperparameters. In practice, these parameters are often tuned manually or through grid search, which requires significant computational resources and human effort. Motivated by this challenge, this paper proposes an automated hyperparameter optimization framework based on Differential Evolution (DE) for LFT (DE-LFT). The proposed method integrates DE into the training process of the LFT model to automatically learn optimal regularization parameters $λ_1$, $λ_2$ and $λ_3$. As a result, the model can adaptively search the hyperparameter space and improve prediction accuracy. Experimental results on four real-world datasets demonstrate that the proposed approach achieves lower MAE and RMSE compared with manually tuned baselines while reducing the need for extensive parameter tuning.

How Many Trees in a Random Forest? A Revisited Approach with Plateau Search and Optuna Integration

Hyperparameter optimization (HPO) for Random Forest faces a specific difficulty in tuning the number of trees: the predictive score typically improves monotonically with ensemble size, so standard methods such as Tree-structured Parzen Estimator (TPE) and Hyperband require a predefined search range and often drive the estimate toward its right boundary. Early-stopping strategies avoid fixing such a range, but can be sensitive to score noise and prone to premature stopping. To address this, we propose an integrated triplet-based plateau-search algorithm that removes the number of trees from the direct TPE search space and still exploits information accumulated across HPO trials. The method adaptively tracks a near-minimal sufficient ensemble size by monitoring relative changes in the out-of-bag (OOB) score across a triplet of forest sizes and shifting this triplet accordingly. This yields an automated and user-interpretable procedure based on a tolerance parameter. We also provide a theoretical analysis: we relate the proposed relative OOB-score criterion to the gap between the current and limiting scores, and derive an asymptotic variance estimate for the corresponding OOB-based absolute relative difference. Experiments show that the selected number of trees can differ substantially from the common heuristic: for most classical benchmark datasets it is smaller, whereas for some high-dimensional bioinformatics datasets, such as Arcene and Dorothea, it is larger. The source code and reproducible experiments are available at https://github.com/lange-am/rf_plateau_hpo.