$α$-PFN: Fast Entropy Search via In-Context Learning

Information-theoretic acquisition functions such as Entropy Search (ES) offer a principled exploration-exploitation framework for Bayesian optimization (BO). However, their practical implementation relies on complicated and slow approximations, i.e., a Monte Carlo estimation of the information gain. This complexity can introduce numerical errors and requires specialized, hand-crafted implementations. We propose a two-stage amortization strategy that learns to approximate entropy search-based acquisition functions using Prior-data Fitted Networks (PFNs) in a single forward pass. A first PFN is trained to be conditioned on information about the optima; second, the $α$-PFN is trained to predict the expected information gain by training on information gains measured with the first PFN. The $α$-PFN offers a flexible learned approximation, which replaces the complex heuristic approximations with a single forward pass per candidate, enabling rapid and extensible acquisition evaluation. Empirically, our approach is competitive with state-of-the-art entropy search implementations on synthetic and real-world benchmarks, while accelerating the different entropy search variants across all our experiments, with speed ups over 50x. Source code: https://github.com/automl/AlphaPFN.

An Open-Source Training Dataset for Foundation Models for Black-box Optimization

Most black-box optimization methods require extensive hyperparameter tuning, often limiting their ability to generalize across different optimization domains. Foundation models for black-box optimization that learn optimization principles from a large collection of optimization trajectories offer a promising alternative, with the potential to outperform manually designed methods across diverse problem classes. However, prior work has either relied on non-public datasets or on purely synthetic data, limiting reproducibility and generalization to real-world problems. As a result, progress in this area has been constrained by the lack of large-scale, real-world, publicly available pre-training data. We introduce BBO-Pile, the first open-source dataset comprising over 500K optimization trajectories evaluated across 3095 different black-boxes for different optimizers, which represents by far the largest public dataset for this task. Using this dataset, we train a family of foundation models at multiple scales, ranging from 2M to 80M parameters and from 200M to 2B training tokens, and study their scaling behavior with respect to compute. Our results demonstrate that large-scale pre-training is a viable and effective approach to imitate black-box optimization methods, paving the way for future research in this direction.

When is Warmstarting Effective for Scaling Language Models?

Model growth from a given checkpoint aims to accelerate training of a larger model, offering potential resource savings. Despite recent interest, warmstarting has seen limited practical adoption in large-scale training. We attribute this to two underexplored factors: (1) an overemphasis on preserving the smaller model's performance at initialization, which constrains operator design for new architectures, and (2) insufficient analysis of how growth interacts with hyperparameters and scaling behavior, compounded by inconsistent growth factors across the literature. We show that preserving the base model's initial post-growth performance is not necessary for strong final performance, and that simple, architecture-agnostic growth strategies can outperform more complex warmstarting operators. Crucially, we empirically identify an upper bound on the growth factor $g$ beyond which training from scratch is more efficient. We observe this across multiple ablation setups. Notably, this limit is also present, but unreported, in prior published results. Across our experiments on dense MLPs and dense language models, we find that a $2\times$ growth factor is the most reliable in yielding convergence speedups, with gains most pronounced under 20 tokens/parameter budgets and diminishing as budget increases. We fit scaling laws over these observations to provide predictive guidance for practitioners deciding when and how much to grow. Together, our analysis provides practical guidelines and empirical limits for model growth.

Warmstarting for Scaling Language Models

Scaling model sizes to scale performance has worked remarkably well for the current large language models paradigm. The research and empirical findings of various scaling studies led to novel scaling results and laws that guides subsequent research. High training costs for contemporary scales of data and models result in a lack of thorough understanding of how to tune and arrive at such training setups. One direction to ameliorate the cost of pretraining large models is to warmstart the large-scale training from smaller models that are cheaper to tune. In this work, we attempt to understand if the behavior of optimal hyperparameters can be retained under warmstarting for scaling. We explore simple operations that allow the application of theoretically motivated methods of zero-shot transfer of optimal hyperparameters using {\mu}Transfer. We investigate the aspects that contribute to the speedup in convergence and the preservation of stable training dynamics under warmstarting with {\mu}Transfer. We find that shrinking smaller model weights, zero-padding, and perturbing the resulting larger model with scaled initialization from {\mu}P enables effective warmstarting of $\mut{}$.

In-Context Freeze-Thaw Bayesian Optimization for Hyperparameter Optimization

With the increasing computational costs associated with deep learning, automated hyperparameter optimization methods, strongly relying on black-box Bayesian optimization (BO), face limitations. Freeze-thaw BO offers a promising grey-box alternative, strategically allocating scarce resources incrementally to different configurations. However, the frequent surrogate model updates inherent to this approach pose challenges for existing methods, requiring retraining or fine-tuning their neural network surrogates online, introducing overhead, instability, and hyper-hyperparameters. In this work, we propose FT-PFN, a novel surrogate for Freeze-thaw style BO. FT-PFN is a prior-data fitted network (PFN) that leverages the transformers' in-context learning ability to efficiently and reliably do Bayesian learning curve extrapolation in a single forward pass. Our empirical analysis across three benchmark suites shows that the predictions made by FT-PFN are more accurate and 10-100 times faster than those of the deep Gaussian process and deep ensemble surrogates used in previous work. Furthermore, we show that, when combined with our novel acquisition mechanism (MFPI-random), the resulting in-context freeze-thaw BO method (ifBO), yields new state-of-the-art performance in the same three families of deep learning HPO benchmarks considered in prior work.

Efficient Bayesian Learning Curve Extrapolation using Prior-Data Fitted Networks

Learning curve extrapolation aims to predict model performance in later epochs of training, based on the performance in earlier epochs. In this work, we argue that, while the inherent uncertainty in the extrapolation of learning curves warrants a Bayesian approach, existing methods are (i) overly restrictive, and/or (ii) computationally expensive. We describe the first application of prior-data fitted neural networks (PFNs) in this context. A PFN is a transformer, pre-trained on data generated from a prior, to perform approximate Bayesian inference in a single forward pass. We propose LC-PFN, a PFN trained to extrapolate 10 million artificial right-censored learning curves generated from a parametric prior proposed in prior art using MCMC. We demonstrate that LC-PFN can approximate the posterior predictive distribution more accurately than MCMC, while being over 10 000 times faster. We also show that the same LC-PFN achieves competitive performance extrapolating a total of 20 000 real learning curves from four learning curve benchmarks (LCBench, NAS-Bench-201, Taskset, and PD1) that stem from training a wide range of model architectures (MLPs, CNNs, RNNs, and Transformers) on 53 different datasets with varying input modalities (tabular, image, text, and protein data). Finally, we investigate its potential in the context of model selection and find that a simple LC-PFN based predictive early stopping criterion obtains 2 - 6x speed-ups on 45 of these datasets, at virtually no overhead.

Black-Box Optimization Revisited: Improving Algorithm Selection Wizards through Massive Benchmarking

Existing studies in black-box optimization suffer from low generalizability, caused by a typically selective choice of problem instances used for training and testing different optimization algorithms. Among other issues, this practice promotes overfitting and poor-performing user guide-lines. To address this shortcoming, we propose in this work a benchmark suite which covers a broad range of black-box optimization problems, ranging from academic benchmarks to real-world optimization problems, from discrete over numerical to mixed-integer problems, from small to very large-scale problems, from noisy over dynamic to static problems, etc. We demonstrate the advantages of such a broad collection by deriving from it NGOpt8, a general-purpose algorithm selection wizard. Using three different types of algorithm selection techniques, NGOpt8 achieves competitive performance on all benchmark suites. It significantly outperforms previous state of the art on some of them, including the MuJoCo collection,YABBOB, and LSGO. A single algorithm therefore performed best on these three important benchmarks, without any task-specific parametrization. The benchmark collection, the wizard, its low-level solvers, as well as all experimental data are fully reproducible and open source. They are made available as a fork of Nevergrad, termed OptimSuite.

Distribution-Based Invariant Deep Networks for Learning Meta-Features

Recent advances in deep learning from probability distributions enable to achieve classification or regression from distribution samples, invariant under permutation of the samples. This paper extends the distribution-based deep neural architectures to achieve classification or regression from distribution samples, invariant under permutation of the descriptive features, too. The motivation for this extension is the Auto-ML problem, aimed to identify a priori the ML configuration best suited to a dataset. Formally, a distribution-based invariant deep learning architecture is presented, and leveraged to extract the meta-features characterizing a dataset. The contribution of the paper is twofold. On the theoretical side, the proposed architecture inherits the NN properties of universal approximation, and the robustness of the approach w.r.t. moderate perturbations is established. On the empirical side, a proof of concept of the approach is proposed, to identify the SVM hyper-parameters best suited to a large benchmark of diversified small size datasets.

Automated Machine Learning with Monte-Carlo Tree Search (Extended Version)

The AutoML task consists of selecting the proper algorithm in a machine learning portfolio, and its hyperparameter values, in order to deliver the best performance on the dataset at hand. Mosaic, a Monte-Carlo tree search (MCTS) based approach, is presented to handle the AutoML hybrid structural and parametric expensive black-box optimization problem. Extensive empirical studies are conducted to independently assess and compare: i) the optimization processes based on Bayesian optimization or MCTS; ii) its warm-start initialization; iii) the ensembling of the solutions gathered along the search. Mosaic is assessed on the OpenML 100 benchmark and the Scikit-learn portfolio, with statistically significant gains over Auto-Sklearn, winner of former international AutoML challenges.