arXiv subjects

Chansoo Lee

Publications and source records attributed to Chansoo Lee.

18 recordsLinked to original sources

arXiv2024

Language Model Embeddings Can Be Sufficient for Bayesian Optimization

Bayesian Optimization is ubiquitous in experimental design and black-box optimization for improving search efficiency. However, most existing approaches rely on regression models which are limited to fixed search spaces and structured, tabular input features. This paper explores the use of LLM embeddings over string inputs for in-context regression in Bayesian Optimization. Our results show that representing inputs as strings enables general-purpose regression across diverse domains, including synthetic, combinatorial, and hyperparameter optimization. Furthermore, our approach achieves optimization performance comparable to state-of-the-art Gaussian Process-based methods such as Google Vizier, and demonstrates potential for broader and more flexible applications.

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arXiv2024

The Vizier Gaussian Process Bandit Algorithm

Google Vizier has performed millions of optimizations and accelerated numerous research and production systems at Google, demonstrating the success of Bayesian optimization as a large-scale service. Over multiple years, its algorithm has been improved considerably, through the collective experiences of numerous research efforts and user feedback. In this technical report, we discuss the implementation details and design choices of the current default algorithm provided by Open Source Vizier. Our experiments on standardized benchmarks reveal its robustness and versatility against well-established industry baselines on multiple practical modes.

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arXiv2024

Position: Leverage Foundational Models for Black-Box Optimization

Undeniably, Large Language Models (LLMs) have stirred an extraordinary wave of innovation in the machine learning research domain, resulting in substantial impact across diverse fields such as reinforcement learning, robotics, and computer vision. Their incorporation has been rapid and transformative, marking a significant paradigm shift in the field of machine learning research. However, the field of experimental design, grounded on black-box optimization, has been much less affected by such a paradigm shift, even though integrating LLMs with optimization presents a unique landscape ripe for exploration. In this position paper, we frame the field of black-box optimization around sequence-based foundation models and organize their relationship with previous literature. We discuss the most promising ways foundational language models can revolutionize optimization, which include harnessing the vast wealth of information encapsulated in free-form text to enrich task comprehension, utilizing highly flexible sequence models such as Transformers to engineer superior optimization strategies, and enhancing performance prediction over previously unseen search spaces.

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arXiv2024

OmniPred: Language Models as Universal Regressors

Regression is a powerful tool to accurately predict the outcome metric of a system given a set of parameters, but has traditionally been restricted to methods which are only applicable to a specific task. In this paper, we propose OmniPred, a framework for training language models as universal end-to-end regressors over $(x,y)$ data from arbitrary formats. Using data sourced from Google Vizier, one of the largest proprietary blackbox optimization databases in the world, our extensive experiments demonstrate that language models are capable of very precise numerical regression using only textual representations of mathematical parameters and values, and if given the opportunity to train at scale over multiple tasks, can significantly outperform traditional regression models.

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arXiv2023

Open Source Vizier: Distributed Infrastructure and API for Reliable and Flexible Blackbox Optimization

Vizier is the de-facto blackbox and hyperparameter optimization service across Google, having optimized some of Google's largest products and research efforts. To operate at the scale of tuning thousands of users' critical systems, Google Vizier solved key design challenges in providing multiple different features, while remaining fully fault-tolerant. In this paper, we introduce Open Source (OSS) Vizier, a standalone Python-based interface for blackbox optimization and research, based on the Google-internal Vizier infrastructure and framework. OSS Vizier provides an API capable of defining and solving a wide variety of optimization problems, including multi-metric, early stopping, transfer learning, and conditional search. Furthermore, it is designed to be a distributed system that assures reliability, and allows multiple parallel evaluations of the user's objective function. The flexible RPC-based infrastructure allows users to access OSS Vizier from binaries written in any language. OSS Vizier also provides a back-end ("Pythia") API that gives algorithm authors a way to interface new algorithms with the core OSS Vizier system. OSS Vizier is available at https://github.com/google/vizier.

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arXiv2022

Towards Learning Universal Hyperparameter Optimizers with Transformers

Meta-learning hyperparameter optimization (HPO) algorithms from prior experiments is a promising approach to improve optimization efficiency over objective functions from a similar distribution. However, existing methods are restricted to learning from experiments sharing the same set of hyperparameters. In this paper, we introduce the OptFormer, the first text-based Transformer HPO framework that provides a universal end-to-end interface for jointly learning policy and function prediction when trained on vast tuning data from the wild, such as Google's Vizier database, one of the world's largest HPO datasets. Our extensive experiments demonstrate that the OptFormer can simultaneously imitate at least 7 different HPO algorithms, which can be further improved via its function uncertainty estimates. Compared to a Gaussian Process, the OptFormer also learns a robust prior distribution for hyperparameter response functions, and can thereby provide more accurate and better calibrated predictions. This work paves the path to future extensions for training a Transformer-based model as a general HPO optimizer.

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arXiv2022

Task Selection for AutoML System Evaluation

Our goal is to assess if AutoML system changes - i.e., to the search space or hyperparameter optimization - will improve the final model's performance on production tasks. However, we cannot test the changes on production tasks. Instead, we only have access to limited descriptors about tasks that our AutoML system previously executed, like the number of data points or features. We also have a set of development tasks to test changes, ex., sampled from OpenML with no usage constraints. However, the development and production task distributions are different leading us to pursue changes that only improve development and not production. This paper proposes a method to leverage descriptor information about AutoML production tasks to select a filtered subset of the most relevant development tasks. Empirical studies show that our filtering strategy improves the ability to assess AutoML system changes on holdout tasks with different distributions than development.

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arXiv2022

Pre-training helps Bayesian optimization too

Bayesian optimization (BO) has become a popular strategy for global optimization of many expensive real-world functions. Contrary to a common belief that BO is suited to optimizing black-box functions, it actually requires domain knowledge on characteristics of those functions to deploy BO successfully. Such domain knowledge often manifests in Gaussian process priors that specify initial beliefs on functions. However, even with expert knowledge, it is not an easy task to select a prior. This is especially true for hyperparameter tuning problems on complex machine learning models, where landscapes of tuning objectives are often difficult to comprehend. We seek an alternative practice for setting these functional priors. In particular, we consider the scenario where we have data from similar functions that allow us to pre-train a tighter distribution a priori. To verify our approach in realistic model training setups, we collected a large multi-task hyperparameter tuning dataset by training tens of thousands of configurations of near-state-of-the-art models on popular image and text datasets, as well as a protein sequence dataset. Our results show that on average, our method is able to locate good hyperparameters at least 3 times more efficiently than the best competing methods.

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arXiv2021

Pre-trained Gaussian Processes for Bayesian Optimization

Bayesian optimization (BO) has become a popular strategy for global optimization of expensive real-world functions. Contrary to a common expectation that BO is suited to optimizing black-box functions, it actually requires domain knowledge about those functions to deploy BO successfully. Such domain knowledge often manifests in Gaussian process (GP) priors that specify initial beliefs on functions. However, even with expert knowledge, it is non-trivial to quantitatively define a prior. This is especially true for hyperparameter tuning problems on complex machine learning models, where landscapes of tuning objectives are often difficult to comprehend. We seek an alternative practice for setting these functional priors. In particular, we consider the scenario where we have data from similar functions that allow us to pre-train a tighter distribution a priori. We detail what pre-training entails for GPs using a KL divergence based loss function, and propose a new pre-training based BO framework named HyperBO. Theoretically, we show bounded posterior predictions and near-zero regrets for HyperBO without assuming the "ground truth" GP prior is known. To verify our approach in realistic setups, we collect a large multi-task hyperparameter tuning dataset by training tens of thousands of configurations of near-state-of-the-art deep learning models on popular image and text datasets, as well as a protein sequence dataset. Our results show that on average, HyperBO is able to locate good hyperparameters at least 3 times more efficiently than the best competing methods on both our new tuning dataset and existing multi-task BO benchmarks.

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arXiv2020

Gradientless Descent: High-Dimensional Zeroth-Order Optimization

Zeroth-order optimization is the process of minimizing an objective $f(x)$, given oracle access to evaluations at adaptively chosen inputs $x$. In this paper, we present two simple yet powerful GradientLess Descent (GLD) algorithms that do not rely on an underlying gradient estimate and are numerically stable. We analyze our algorithm from a novel geometric perspective and present a novel analysis that shows convergence within an $ε$-ball of the optimum in $O(kQ\log(n)\log(R/ε))$ evaluations, for any monotone transform of a smooth and strongly convex objective with latent dimension $k < n$, where the input dimension is $n$, $R$ is the diameter of the input space and $Q$ is the condition number. Our rates are the first of its kind to be both 1) poly-logarithmically dependent on dimensionality and 2) invariant under monotone transformations. We further leverage our geometric perspective to show that our analysis is optimal. Both monotone invariance and its ability to utilize a low latent dimensionality are key to the empirical success of our algorithms, as demonstrated on BBOB and MuJoCo benchmarks.

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arXiv2019

Online Learning via the Differential Privacy Lens

In this paper, we use differential privacy as a lens to examine online learning in both full and partial information settings. The differential privacy framework is, at heart, less about privacy and more about algorithmic stability, and thus has found application in domains well beyond those where information security is central. Here we develop an algorithmic property called one-step differential stability which facilitates a more refined regret analysis for online learning methods. We show that tools from the differential privacy literature can yield regret bounds for many interesting online learning problems including online convex optimization and online linear optimization. Our stability notion is particularly well-suited for deriving first-order regret bounds for follow-the-perturbed-leader algorithms, something that all previous analyses have struggled to achieve. We also generalize the standard max-divergence to obtain a broader class called Tsallis max-divergences. These define stronger notions of stability that are useful in deriving bounds in partial information settings such as multi-armed bandits and bandits with experts.

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arXiv2017

Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences

The Stern diatomic sequence is closely linked to continued fractions via the Gauss map on the unit interval, which in turn can be understood via systematic subdivisions of the unit interval. Higher dimensional analogues of continued fractions, called multidimensional continued fractions, can be produced through various subdivisions of a triangle. We define triangle partition-Stern sequences (TRIP-Stern sequences for short), higher-dimensional generalizations of the Stern diatomic sequence, from the method of subdividing a triangle via various triangle partition algorithms. We then explore several combinatorial results about TRIP-Stern sequences, which may be used to give rise to certain well-known sequences. We finish by generalizing TRIP-Stern sequences and presenting analogous results for these generalizations.

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arXiv2016

Hardness of Online Sleeping Combinatorial Optimization Problems

We show that several online combinatorial optimization problems that admit efficient no-regret algorithms become computationally hard in the sleeping setting where a subset of actions becomes unavailable in each round. Specifically, we show that the sleeping versions of these problems are at least as hard as PAC learning DNF expressions, a long standing open problem. We show hardness for the sleeping versions of Online Shortest Paths, Online Minimum Spanning Tree, Online $k$-Subsets, Online $k$-Truncated Permutations, Online Minimum Cut, and Online Bipartite Matching. The hardness result for the sleeping version of the Online Shortest Paths problem resolves an open problem presented at COLT 2015 (Koolen et al., 2015).

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arXiv2015

Spectral Smoothing via Random Matrix Perturbations

We consider stochastic smoothing of spectral functions of matrices using perturbations commonly studied in random matrix theory. We show that a spectral function remains spectral when smoothed using a unitarily invariant perturbation distribution. We then derive state-of-the-art smoothing bounds for the maximum eigenvalue function using the Gaussian Orthogonal Ensemble (GOE). Smoothing the maximum eigenvalue function is important for applications in semidefinite optimization and online learning. As a direct consequence of our GOE smoothing results, we obtain an $O((N \log N)^{1/4} \sqrt{T})$ expected regret bound for the online variance minimization problem using an algorithm that performs only a single maximum eigenvector computation per time step. Here $T$ is the number of rounds and $N$ is the matrix dimension. Our algorithm and its analysis also extend to the more general online PCA problem where the learner has to output a rank $k$ subspace. The algorithm just requires computing $k$ maximum eigenvectors per step and enjoys an $O(k (N \log N)^{1/4} \sqrt{T})$ expected regret bound.

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arXiv2015

Fighting Bandits with a New Kind of Smoothness

We define a novel family of algorithms for the adversarial multi-armed bandit problem, and provide a simple analysis technique based on convex smoothing. We prove two main results. First, we show that regularization via the \emph{Tsallis entropy}, which includes EXP3 as a special case, achieves the $Θ(\sqrt{TN})$ minimax regret. Second, we show that a wide class of perturbation methods achieve a near-optimal regret as low as $O(\sqrt{TN \log N})$ if the perturbation distribution has a bounded hazard rate. For example, the Gumbel, Weibull, Frechet, Pareto, and Gamma distributions all satisfy this key property.

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arXiv2014

Online Linear Optimization via Smoothing

We present a new optimization-theoretic approach to analyzing Follow-the-Leader style algorithms, particularly in the setting where perturbations are used as a tool for regularization. We show that adding a strongly convex penalty function to the decision rule and adding stochastic perturbations to data correspond to deterministic and stochastic smoothing operations, respectively. We establish an equivalence between "Follow the Regularized Leader" and "Follow the Perturbed Leader" up to the smoothness properties. This intuition leads to a new generic analysis framework that recovers and improves the previous known regret bounds of the class of algorithms commonly known as Follow the Perturbed Leader.

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arXiv2014

Cubic Irrationals and Periodicity via a Family of Multi-dimensional Continued Fraction Algorithms

We construct a countable family of multi-dimensional continued fraction algorithms, built out of five specific multidimensional continued fractions, and find a wide class of cubic irrational real numbers a so that either (a, a^2) or (a, a-a^2) is purely periodic with respect to an element in the family. These cubic irrationals seem to be quite natural, as we show that, for every cubic number field, there exists a pair (u,u') with u a unit in the cubic number field (or possibly the quadratic extension of the cubic number field by the square root of the discriminant) such that (u,u') has a periodic multidimensional continued fraction expansion under one of the maps in the family generated by the initial five maps. Thus these results are built on a careful technical analysis of certain units in cubic number fields and our family of multi-dimensional continued fractions. We then recast the linking of cubic irrationals with periodicity to the linking of cubic irrationals with the construction of a matrix with nonnegative integer entries for which at least one row is eventually periodic.

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arXiv2012

A Generalized Family of Multidimensional Continued Fractions: TRIP Maps

Most well-known multidimensional continued fractions, including the Mönkemeyer map and the triangle map, are generated by repeatedly subdividing triangles. This paper constructs a family of multidimensional continued fractions by permuting the vertices of these triangles before and after each subdivision. We obtain an even larger class of multidimensional continued fractions by composing the maps in the family. These include the algorithms of Brun, Parry-Daniels and Güting. We give criteria for when multidimensional continued fractions associate sequences to unique points, which allows us to determine when periodicity of the corresponding multidimensional continued fraction corresponds to pairs of real numbers being cubic irrationals in the same number field.

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