arXiv subjects

Stefan Falkner

Publications and source records attributed to Stefan Falkner.

14 recordsLinked to original sources

arXiv2024

MALIBO: Meta-learning for Likelihood-free Bayesian Optimization

Bayesian optimization (BO) is a popular method to optimize costly black-box functions. While traditional BO optimizes each new target task from scratch, meta-learning has emerged as a way to leverage knowledge from related tasks to optimize new tasks faster. However, existing meta-learning BO methods rely on surrogate models that suffer from scalability issues and are sensitive to observations with different scales and noise types across tasks. Moreover, they often overlook the uncertainty associated with task similarity. This leads to unreliable task adaptation when only limited observations are obtained or when the new tasks differ significantly from the related tasks. To address these limitations, we propose a novel meta-learning BO approach that bypasses the surrogate model and directly learns the utility of queries across tasks. Our method explicitly models task uncertainty and includes an auxiliary model to enable robust adaptation to new tasks. Extensive experiments show that our method demonstrates strong anytime performance and outperforms state-of-the-art meta-learning BO methods in various benchmarks.

cs.LG↗

arXiv2023

Scalable Meta-Learning with Gaussian Processes

Meta-learning is a powerful approach that exploits historical data to quickly solve new tasks from the same distribution. In the low-data regime, methods based on the closed-form posterior of Gaussian processes (GP) together with Bayesian optimization have achieved high performance. However, these methods are either computationally expensive or introduce assumptions that hinder a principled propagation of uncertainty between task models. This may disrupt the balance between exploration and exploitation during optimization. In this paper, we develop ScaML-GP, a modular GP model for meta-learning that is scalable in the number of tasks. Our core contribution is a carefully designed multi-task kernel that enables hierarchical training and task scalability. Conditioning ScaML-GP on the meta-data exposes its modular nature yielding a test-task prior that combines the posteriors of meta-task GPs. In synthetic and real-world meta-learning experiments, we demonstrate that ScaML-GP can learn efficiently both with few and many meta-tasks.

stat.ML↗

arXiv2022

Auto-Sklearn 2.0: Hands-free AutoML via Meta-Learning

Automated Machine Learning (AutoML) supports practitioners and researchers with the tedious task of designing machine learning pipelines and has recently achieved substantial success. In this paper, we introduce new AutoML approaches motivated by our winning submission to the second ChaLearn AutoML challenge. We develop PoSH Auto-sklearn, which enables AutoML systems to work well on large datasets under rigid time limits by using a new, simple and meta-feature-free meta-learning technique and by employing a successful bandit strategy for budget allocation. However, PoSH Auto-sklearn introduces even more ways of running AutoML and might make it harder for users to set it up correctly. Therefore, we also go one step further and study the design space of AutoML itself, proposing a solution towards truly hands-free AutoML. Together, these changes give rise to the next generation of our AutoML system, Auto-sklearn 2.0. We verify the improvements by these additions in an extensive experimental study on 39 AutoML benchmark datasets. We conclude the paper by comparing to other popular AutoML frameworks and Auto-sklearn 1.0, reducing the relative error by up to a factor of 4.5, and yielding a performance in 10 minutes that is substantially better than what Auto-sklearn 1.0 achieves within an hour.

cs.LG↗

arXiv2020

Meta-Learning Acquisition Functions for Transfer Learning in Bayesian Optimization

Transferring knowledge across tasks to improve data-efficiency is one of the open key challenges in the field of global black-box optimization. Readily available algorithms are typically designed to be universal optimizers and, therefore, often suboptimal for specific tasks. We propose a novel transfer learning method to obtain customized optimizers within the well-established framework of Bayesian optimization, allowing our algorithm to utilize the proven generalization capabilities of Gaussian processes. Using reinforcement learning to meta-train an acquisition function (AF) on a set of related tasks, the proposed method learns to extract implicit structural information and to exploit it for improved data-efficiency. We present experiments on a simulation-to-real transfer task as well as on several synthetic functions and on two hyperparameter search problems. The results show that our algorithm (1) automatically identifies structural properties of objective functions from available source tasks or simulations, (2) performs favourably in settings with both scarse and abundant source data, and (3) falls back to the performance level of general AFs if no particular structure is present.

stat.ML↗

arXiv2019

Probabilistic Rollouts for Learning Curve Extrapolation Across Hyperparameter Settings

We propose probabilistic models that can extrapolate learning curves of iterative machine learning algorithms, such as stochastic gradient descent for training deep networks, based on training data with variable-length learning curves. We study instantiations of this framework based on random forests and Bayesian recurrent neural networks. Our experiments show that these models yield better predictions than state-of-the-art models from the hyperparameter optimization literature when extrapolating the performance of neural networks trained with different hyperparameter settings.

cs.LG↗

arXiv2019

Learning to Design RNA

Designing RNA molecules has garnered recent interest in medicine, synthetic biology, biotechnology and bioinformatics since many functional RNA molecules were shown to be involved in regulatory processes for transcription, epigenetics and translation. Since an RNA's function depends on its structural properties, the RNA Design problem is to find an RNA sequence which satisfies given structural constraints. Here, we propose a new algorithm for the RNA Design problem, dubbed LEARNA. LEARNA uses deep reinforcement learning to train a policy network to sequentially design an entire RNA sequence given a specified target structure. By meta-learning across 65000 different RNA Design tasks for one hour on 20 CPU cores, our extension Meta-LEARNA constructs an RNA Design policy that can be applied out of the box to solve novel RNA Design tasks. Methodologically, for what we believe to be the first time, we jointly optimize over a rich space of architectures for the policy network, the hyperparameters of the training procedure and the formulation of the decision process. Comprehensive empirical results on two widely-used RNA Design benchmarks, as well as a third one that we introduce, show that our approach achieves new state-of-the-art performance on the former while also being orders of magnitudes faster in reaching the previous state-of-the-art performance. In an ablation study, we analyze the importance of our method's different components.

cs.LG↗

arXiv2018

Towards Automated Deep Learning: Efficient Joint Neural Architecture and Hyperparameter Search

While existing work on neural architecture search (NAS) tunes hyperparameters in a separate post-processing step, we demonstrate that architectural choices and other hyperparameter settings interact in a way that can render this separation suboptimal. Likewise, we demonstrate that the common practice of using very few epochs during the main NAS and much larger numbers of epochs during a post-processing step is inefficient due to little correlation in the relative rankings for these two training regimes. To combat both of these problems, we propose to use a recent combination of Bayesian optimization and Hyperband for efficient joint neural architecture and hyperparameter search.

cs.LG↗

arXiv2018

BOHB: Robust and Efficient Hyperparameter Optimization at Scale

Modern deep learning methods are very sensitive to many hyperparameters, and, due to the long training times of state-of-the-art models, vanilla Bayesian hyperparameter optimization is typically computationally infeasible. On the other hand, bandit-based configuration evaluation approaches based on random search lack guidance and do not converge to the best configurations as quickly. Here, we propose to combine the benefits of both Bayesian optimization and bandit-based methods, in order to achieve the best of both worlds: strong anytime performance and fast convergence to optimal configurations. We propose a new practical state-of-the-art hyperparameter optimization method, which consistently outperforms both Bayesian optimization and Hyperband on a wide range of problem types, including high-dimensional toy functions, support vector machines, feed-forward neural networks, Bayesian neural networks, deep reinforcement learning, and convolutional neural networks. Our method is robust and versatile, while at the same time being conceptually simple and easy to implement.

cs.LG↗

arXiv2017

Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasets

Bayesian optimization has become a successful tool for hyperparameter optimization of machine learning algorithms, such as support vector machines or deep neural networks. Despite its success, for large datasets, training and validating a single configuration often takes hours, days, or even weeks, which limits the achievable performance. To accelerate hyperparameter optimization, we propose a generative model for the validation error as a function of training set size, which is learned during the optimization process and allows exploration of preliminary configurations on small subsets, by extrapolating to the full dataset. We construct a Bayesian optimization procedure, dubbed Fabolas, which models loss and training time as a function of dataset size and automatically trades off high information gain about the global optimum against computational cost. Experiments optimizing support vector machines and deep neural networks show that Fabolas often finds high-quality solutions 10 to 100 times faster than other state-of-the-art Bayesian optimization methods or the recently proposed bandit strategy Hyperband.

cs.LG↗

arXiv2016

Asynchronous Stochastic Gradient MCMC with Elastic Coupling

We consider parallel asynchronous Markov Chain Monte Carlo (MCMC) sampling for problems where we can leverage (stochastic) gradients to define continuous dynamics which explore the target distribution. We outline a solution strategy for this setting based on stochastic gradient Hamiltonian Monte Carlo sampling (SGHMC) which we alter to include an elastic coupling term that ties together multiple MCMC instances. The proposed strategy turns inherently sequential HMC algorithms into asynchronous parallel versions. First experiments empirically show that the resulting parallel sampler significantly speeds up exploration of the target distribution, when compared to standard SGHMC, and is less prone to the harmful effects of stale gradients than a naive parallelization approach.

stat.ML↗

arXiv2015

Relation between Random Walks and Quantum Walks

Based on studies on four specific networks, we conjecture a general relation between the walk dimensions $d_{w}$ of discrete-time random walks and quantum walks with the (self-inverse) Grover coin. In each case, we find that $d_{w}$ of the quantum walk takes on exactly half the value found for the classical random walk on the same geometry. Since walks on homogeneous lattices satisfy this relation trivially, our results for heterogeneous networks suggests that such a relation holds irrespective of whether translational invariance is maintained or not. To develop our results, we extend the renormalization group analysis (RG) of the stochastic master equation to one with a unitary propagator. As in the classical case, the solution $ρ(x,t)$ in space and time of this quantum walk equation exhibits a scaling collapse for a variable $x^{d_{w}}/t$ in the weak limit, which defines $d_{w}$ and illuminates fundamental aspects of the walk dynamics, e.g., its mean-square displacement. We confirm the collapse for $ρ(x,t)$ in each case with extensive numerical simulation. The exact values for $d_{w}$ in themselves demonstrate that RG is a powerful complementary approach to study the asymptotics of quantum walks that weak-limit theorems have not been able to access, such as for systems lacking translational symmetries beyond simple trees.

cond-mat.stat-mech↗

arXiv2014

One-Dimensional Coinless Quantum Walks

A coinless, discrete-time quantum walk possesses a Hilbert space whose dimension is smaller compared to the widely-studied coined walk. Coined walks require the direct product of the site basis with the coin space, coinless walks operate purely in the site basis, which is clearly minimal. These coinless quantum walks have received considerable attention recently because they have evolution operators that can be obtained by a graphical method based on lattice tessellations and they have been shown to be as efficient as the best known coined walks when used as a quantum search algorithm. We argue that both formulations in their most general form are equivalent. In particular, we demonstrate how to transform the one-dimensional version of the coinless quantum walk into an equivalent extended coined version for a specific family of evolution operators. We present some of its basic, asymptotic features for the one-dimensional lattice with some examples of tessellations, and analyze the mixing time and limiting probability distributions on cycles.

quant-ph↗

arXiv2014

Weak Limit of the 3-State Quantum Walk on the Line

We revisit the one dimensional discrete time quantum walk with 3 states and the Grover coin. We derive analytic expressions for observed the localization, an long time approximation for the probability density function (PDF). We also connect the time averaged approximation to the PDF found by Inui et. al. to a spatial average of the walk. We show that this smooth approximation constitutes a proper PDF that predicts moments of the real PDF accurately.

quant-ph↗

arXiv2012

Finite-Size Corrections for Ground States of Edwards-Anderson Spin Glasses

Extensive computations of ground state energies of the Edwards-Anderson spin glass on bond-diluted, hypercubic lattices are conducted in dimensions d=3,..,7. Results are presented for bond-densities exactly at the percolation threshold, p=p_c, and deep within the glassy regime, p>p_c, where finding ground-states becomes a hard combinatorial problem. Finite-size corrections of the form 1/N^w are shown to be consistent throughout with the prediction w=1-y/d, where y refers to the "stiffness" exponent that controls the formation of domain wall excitations at low temperatures. At p=p_c, an extrapolation for $d\to\infty$ appears to match our mean-field results for these corrections. In the glassy phase, w does not approach the value of 2/3 for large d predicted from simulations of the Sherrington-Kirkpatrick spin glass. However, the value of w reached at the upper critical dimension does match certain mean-field spin glass models on sparse random networks of regular degree called Bethe lattices.

cond-mat.dis-nn↗