Many of the recent triumphs in machine learning are dependent on well-tuned hyperparameters. This is particularly prominent in reinforcement learning (RL) where a small change in the configuration can lead to failure. Despite the importance of tuning hyperparameters, it remains expensive and is often done in a naive and laborious way. A recent solution to this problem is Population Based Training (PBT) which updates both weights and hyperparameters in a single training run of a population of agents. PBT has been shown to be particularly effective in RL, leading to widespread use in the field. However, PBT lacks theoretical guarantees since it relies on random heuristics to explore the hyperparameter space. This inefficiency means it typically requires vast computational resources, which is prohibitive for many small and medium sized labs. In this work, we introduce the first provably efficient PBT-style algorithm, Population-Based Bandits (PB2). PB2 uses a probabilistic model to guide the search in an efficient way, making it possible to discover high performing hyperparameter configurations with far fewer agents than typically required by PBT. We show in a series of RL experiments that PB2 is able to achieve high performance with a modest computational budget.
We consider the neural contextual bandit problem. In contrast to the existing work which primarily focuses on ReLU neural nets, we consider a general set of smooth activation functions. Under this more general setting, (i) we derive non-asymptotic error bounds on the difference between an overparameterized neural net and its corresponding neural tangent kernel, (ii) we propose an algorithm with a provably sublinear regret bound that is also efficient in the finite regime as demonstrated by empirical studies. The non-asymptotic error bounds may be of broader interest as a tool to establish the …
University of California, Los Angeles（加州大学洛杉矶分校）；Yale University（耶鲁大学）
We study federated contextual linear bandits, where $M$ agents cooperate with each other to solve a global contextual linear bandit problem with the help of a central server. We consider the asynchronous setting, where all agents work independently and the communication between one agent and the server will not trigger other agents' communication. We propose a simple algorithm named \texttt{FedLinUCB} based on the principle of optimism. We prove that the regret of \texttt{FedLinUCB} is bounded by $\tilde{O}(d\sqrt{\sum_{m=1}^M T_m})$ and the communication complexity is $\tilde{O}(dM^2)$, where…
Carnegie Mellon University（卡内基梅隆大学）；University of Washington（华盛顿大学）；Google Research（谷歌研究院）；Determined AI
Performance of machine learning algorithms depends critically on identifying a good set of hyperparameters. While recent approaches use Bayesian optimization to adaptively select configurations, we focus on speeding up random search through adaptive resource allocation and early-stopping. We formulate hyperparameter optimization as a pure-exploration non-stochastic infinite-armed bandit problem where a predefined resource like iterations, data samples, or features is allocated to randomly sampled configurations. We introduce a novel algorithm, Hyperband, for this framework and analyze its theo…
Peking University（北京大学）；ETH Zurich（苏黎世联邦理工学院）；Beijing University of Posts and Telecommunications（北京邮电大学）；Alibaba Group（阿里巴巴集团）
The Combined Algorithm Selection and Hyperparameter optimization (CASH) is one of the most fundamental problems in Automatic Machine Learning (AutoML). The existing Bayesian optimization (BO) based solutions turn the CASH problem into a Hyperparameter Optimization (HPO) problem by combining the hyperparameters of all machine learning (ML) algorithms, and use BO methods to solve it. As a result, these methods suffer from the low-efficiency problem due to the huge hyperparameter space in CASH. To alleviate this issue, we propose the alternating optimization framework, where the HPO problem for e…
Contextual bandits are widely used in Internet services from news recommendation to advertising, and to Web search. Generalized linear models (logistical regression in particular) have demonstrated stronger performance than linear models in many applications where rewards are binary. However, most theoretical analyses on contextual bandits so far are on linear bandits. In this work, we propose an upper confidence bound based algorithm for generalized linear contextual bandits, which achieves an $\tilde{O}(\sqrt{dT})$ regret over $T$ rounds with $d$ dimensional feature vectors. This regret matc…
The evaluation of hyperparameters, neural architectures, or data augmentation policies becomes a critical model selection problem in advanced deep learning with a large hyperparameter search space. In this paper, we propose an efficient and robust bandit-based algorithm called Sub-Sampling (SS) in the scenario of hyperparameter search evaluation. It evaluates the potential of hyperparameters by the sub-samples of observations and is theoretically proved to be optimal under the criterion of cumulative regret. We further combine SS with Bayesian Optimization and develop a novel hyperparameter op…
We introduce the study of fairness in multi-armed bandit problems. Our fairness definition can be interpreted as demanding that given a pool of applicants (say, for college admission or mortgages), a worse applicant is never favored over a better one, despite a learning algorithm's uncertainty over the true payoffs. We prove results of two types. First, in the important special case of the classic stochastic bandits problem (i.e., in which there are no contexts), we provide a provably fair algorithm based on "chained" confidence intervals, and provide a cumulative regret bound with a cubic dep…
Considerable research effort has been guided towards algorithmic fairness but there is still no major breakthrough. In practice, an exhaustive search over all possible techniques and hyperparameters is needed to find optimal fairness-accuracy trade-offs. Hence, coupled with the lack of tools for ML practitioners, real-world adoption of bias reduction methods is still scarce. To address this, we present Fairband, a bandit-based fairness-aware hyperparameter optimization (HO) algorithm. Fairband is conceptually simple, resource-efficient, easy to implement, and agnostic to both the objective met…
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 configuratio…
This work explores adaptations of successful multi-armed bandits policies to the online contextual bandits scenario with binary rewards using binary classification algorithms such as logistic regression as black-box oracles. Some of these adaptations are achieved through bootstrapping or approximate bootstrapping, while others rely on other forms of randomness, resulting in more scalable approaches than previous works, and the ability to work with any type of classification algorithm. In particular, the Adaptive-Greedy algorithm shows a lot of promise, in many cases achieving better performanc…
We propose a new algorithm for hyperparameter selection in machine learning algorithms. The algorithm is a novel modification of Harmonica, a spectral hyperparameter selection approach using sparse recovery methods. In particular, we show that a special encoding of hyperparameter space enables a natural group-sparse recovery formulation, which when coupled with HyperBand (a multi-armed bandit strategy) leads to improvement over existing hyperparameter optimization methods such as Successive Halving and Random Search. Experimental results on image datasets such as CIFAR-10 confirm the benefits …
University of Southampton（南安普顿大学）；IBM Research Ireland（IBM爱尔兰研究院）
We introduce the functional bandit problem, where the objective is to find an arm that optimises a known functional of the unknown arm-reward distributions. These problems arise in many settings such as maximum entropy methods in natural language processing, and risk-averse decision-making, but current best-arm identification techniques fail in these domains. We propose a new approach, that combines functional estimation and arm elimination, to tackle this problem. This method achieves provably efficient performance guarantees. In addition, we illustrate this method on a number of important fu…
Department of Computer Science, ETH Zurich（苏黎世联邦理工学院计算机科学系）
We consider a setting where multiple players sequentially choose among a common set of actions (arms). Motivated by a cognitive radio networks application, we assume that players incur a loss upon colliding, and that communication between players is not possible. Existing approaches assume that the system is stationary. Yet this assumption is often violated in practice, e.g., due to signal strength fluctuations. In this work, we design the first Multi-player Bandit algorithm that provably works in arbitrarily changing environments, where the losses of the arms may even be chosen by an adversar…
University of Massachusetts（马萨诸塞大学）；Microsoft Research（微软研究院）
We study reinforcement learning in continuous state and action spaces endowed with a metric. We provide a refined analysis of a variant of the algorithm of Sinclair, Banerjee, and Yu (2019) and show that its regret scales with the \emph{zooming dimension} of the instance. This parameter, which originates in the bandit literature, captures the size of the subsets of near optimal actions and is always smaller than the covering dimension used in previous analyses. As such, our results are the first provably adaptive guarantees for reinforcement learning in metric spaces.
Multi-armed bandits for resource efficient, online optimization of language model pre-training: the use case of dynamic masking
Basque Center for Applied Mathematics（巴斯克应用数学中心）；IKERBASQUE - Basque Foundation for Science（伊克巴斯克-巴斯克科学基金会）；Columbia University（哥伦比亚大学）；Walmart Global Tech（沃尔玛全球技术）；eBay Inc.（易贝公司）
Duke University（杜克大学）；Carnegie Mellon University（卡内基梅隆大学）；Autodesk, Inc.（欧特克公司）
Stochastic Lipschitz bandit algorithms balance exploration and exploitation, and have been used for a variety of important task domains. In this paper, we present a framework for Lipschitz bandit methods that adaptively learns partitions of context- and arm-space. Due to this flexibility, the algorithm is able to efficiently optimize rewards and minimize regret, by focusing on the portions of the space that are most relevant. In our analysis, we link tree-based methods to Gaussian processes. In light of our analysis, we design a novel hierarchical Bayesian model for Lipschitz bandit problems. …
Algorithm Design and Stronger Guarantees for the Improving Multi-Armed Bandits Problem
Toyota Technological Institute at Chicago（芝加哥丰田技术研究所）；University of Chicago（芝加哥大学）；IDEAL Institute, Toyota Technological Institute at Chicago（IDEAL研究所，芝加哥丰田技术研究所）
Automated algorithm selection and hyperparameter tuning facilitates the application of machine learning. Traditional multi-armed bandit strategies look to the history of observed rewards to identify the most promising arms for optimizing expected total reward in the long run. When considering limited time budgets and computational resources, this backward view of rewards is inappropriate as the bandit should look into the future for anticipating the highest final reward at the end of a specified time budget. This work addresses that insight by introducing HAMLET, which extends the bandit appro…
Despite a series of recent successes in reinforcement learning (RL), many RL algorithms remain sensitive to hyperparameters. As such, there has recently been interest in the field of AutoRL, which seeks to automate design decisions to create more general algorithms. Recent work suggests that population based approaches may be effective AutoRL algorithms, by learning hyperparameter schedules on the fly. In particular, the PB2 algorithm is able to achieve strong performance in RL tasks by formulating online hyperparameter optimization as time varying GP-bandit problem, while also providing theor…
Department of Statistics, Purdue University（普渡大学统计系）；Department of Electrical Engineering, Princeton University（普林斯顿大学电气工程系）；Purdue University（普渡大学）；Princeton University（普林斯顿大学）
In this paper, we propose a novel perturbation-based exploration method in bandit algorithms with bounded or unbounded rewards, called residual bootstrap exploration (\texttt{ReBoot}). The \texttt{ReBoot} enforces exploration by injecting data-driven randomness through a residual-based perturbation mechanism. This novel mechanism captures the underlying distributional properties of fitting errors, and more importantly boosts exploration to escape from suboptimal solutions (for small sample sizes) by inflating variance level in an \textit{unconventional} way. In theory, with appropriate varianc…
Contextual multi-armed bandit problems arise frequently in important industrial applications. Existing solutions model the context either linearly, which enables uncertainty driven (principled) exploration, or non-linearly, by using epsilon-greedy exploration policies. Here we present a deep learning framework for contextual multi-armed bandits that is both non-linear and enables principled exploration at the same time. We tackle the exploration vs. exploitation trade-off through Thompson sampling by exploiting the connection between inference time dropout and sampling from the posterior over …
University of British Columbia（英属哥伦比亚大学）；Adobe Research（Adobe研究）
We investigate the use of bootstrapping in the bandit setting. We first show that the commonly used non-parametric bootstrapping (NPB) procedure can be provably inefficient and establish a near-linear lower bound on the regret incurred by it under the bandit model with Bernoulli rewards. We show that NPB with an appropriate amount of forced exploration can result in sub-linear albeit sub-optimal regret. As an alternative to NPB, we propose a weighted bootstrapping (WB) procedure. For Bernoulli rewards, WB with multiplicative exponential weights is mathematically equivalent to Thompson sampling…
Applied AI Institute（应用人工智能研究所）；Deakin University（迪肯大学）；University of Oxford（牛津大学）
Offline policy learning (OPL) leverages existing data collected a priori for policy optimization without any active exploration. Despite the prevalence and recent interest in this problem, its theoretical and algorithmic foundations in function approximation settings remain under-developed. In this paper, we consider this problem on the axes of distributional shift, optimization, and generalization in offline contextual bandits with neural networks. In particular, we propose a provably efficient offline contextual bandit with neural network function approximation that does not require any func…
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Microsoft Research（微软研究院）
A central problem in sequential decision making is to develop algorithms that are practical and computationally efficient, yet support the use of flexible, general-purpose models. Focusing on the contextual bandit problem, recent progress provides provably efficient algorithms with strong empirical performance when the number of possible alternatives ("actions") is small, but guarantees for decision making in large, continuous action spaces have remained elusive, leading to a significant gap between theory and practice. We present the first efficient, general-purpose algorithm for contextual b…
Motivated by the task of hyperparameter optimization, we introduce the non-stochastic best-arm identification problem. Within the multi-armed bandit literature, the cumulative regret objective enjoys algorithms and analyses for both the non-stochastic and stochastic settings while to the best of our knowledge, the best-arm identification framework has only been considered in the stochastic setting. We introduce the non-stochastic setting under this framework, identify a known algorithm that is well-suited for this setting, and analyze its behavior. Next, by leveraging the iterative nature of s…
Motivated by applications in cognitive radio networks, we consider the decentralized multi-player multi-armed bandit problem, without collision nor sensing information. We propose Randomized Selfish KL-UCB, an algorithm with very low computational complexity, inspired by the Selfish KL-UCB algorithm, which has been abandoned as it provably performs sub-optimally in some cases. We subject Randomized Selfish KL-UCB to extensive numerical experiments showing that it far outperforms state-of-the-art algorithms in almost all environments, sometimes by several orders of magnitude, and without the ad…
Provably Reduced Sample Cost in Prior-Guided Hyperparameter Optimization
Leibniz University Hanover（莱比锡大学汉诺威分校）；University of Bielefeld（比勒菲尔德大学）；Institute of Artificial Intelligence, Leibniz University Hanover（人工智能研究所，莱比锡大学汉诺威分校）；L3S Research Center Hanover（汉诺威L3S研究中心）
Multi-armed bandit problems provide a framework to identify the optimal intervention over a sequence of repeated experiments. Without additional assumptions, minimax optimal performance (measured by cumulative regret) is well-understood. With access to additional observed variables that d-separate the intervention from the outcome (i.e., they are a d-separator), recent "causal bandit" algorithms provably incur less regret. However, in practice it is desirable to be agnostic to whether observed variables are a d-separator. Ideally, an algorithm should be adaptive; that is, perform nearly as wel…
Meta AI；Univ. Lille（里尔大学）；Inria（法国国家信息与自动化研究所）；CNRS（法国国家科学研究中心）；Centrale Lille（里尔中央理工学院）
Elimination algorithms for bandit identification, which prune the plausible correct answers sequentially until only one remains, are computationally convenient since they reduce the problem size over time. However, existing elimination strategies are often not fully adaptive (they update their sampling rule infrequently) and are not easy to extend to combinatorial settings, where the set of answers is exponentially large in the problem dimension. On the other hand, most existing fully-adaptive strategies to tackle general identification problems are computationally demanding since they repeate…
University of California, Irvine（加州大学尔湾分校）；eBay Research Labs（eBay研究实验室）
We describe a general framework for online adaptation of optimization hyperparameters by `hot swapping' their values during learning. We investigate this approach in the context of adaptive learning rate selection using an explore-exploit strategy from the multi-armed bandit literature. Experiments on a benchmark neural network show that the hot swapping approach leads to consistently better solutions compared to well-known alternatives such as AdaDelta and stochastic gradient with exhaustive hyperparameter search.
The stochastic multi-arm bandit problem has been extensively studied under standard assumptions on the arm's distribution (e.g bounded with known support, exponential family, etc). These assumptions are suitable for many real-world problems but sometimes they require knowledge (on tails for instance) that may not be precisely accessible to the practitioner, raising the question of the robustness of bandit algorithms to model misspecification. In this paper we study a generic Dirichlet Sampling (DS) algorithm, based on pairwise comparisons of empirical indices computed with re-sampling of the a…
Dipartimento di Informatica Università degli Studi di Milano（米兰大学信息系）
Motivated by recommendation problems in music streaming platforms, we propose a nonstationary stochastic bandit model in which the expected reward of an arm depends on the number of rounds that have passed since the arm was last pulled. After proving that finding an optimal policy is NP-hard even when all model parameters are known, we introduce a class of ranking policies provably approximating, to within a constant factor, the expected reward of the optimal policy. We show an algorithm whose regret with respect to the best ranking policy is bounded by $\widetilde{\mathcal{O}}\big(\!\sqrt{kT}…
Improved Algorithms for Stochastic Linear Bandits Using Tail Bounds for Martingale Mixtures
Bosch Center for Artificial Intelligence（博世人工智能中心）；Technische Universität Darmstadt（达姆施塔特工业大学）；University of Southern Denmark（南丹麦大学）；Deutsches Forschungszentrum für Künstliche Intelligenz (DFKI)（德国人工智能研究中心）
We consider the problem of stochastic $K$-armed dueling bandit in the contextual setting, where at each round the learner is presented with a context set of $K$ items, each represented by a $d$-dimensional feature vector, and the goal of the learner is to identify the best arm of each context sets. However, unlike the classical contextual bandit setup, our framework only allows the learner to receive item feedback in terms of their (noisy) pariwise preferences--famously studied as dueling bandits which is practical interests in various online decision making scenarios, e.g. recommender systems…
Many algorithms for data analysis exist, especially for classification problems. To solve a data analysis problem, a proper algorithm should be chosen, and also its hyperparameters should be selected. In this paper, we present a new method for the simultaneous selection of an algorithm and its hyperparameters. In order to do so, we reduced this problem to the multi-armed bandit problem. We consider an algorithm as an arm and algorithm hyperparameters search during a fixed time as the corresponding arm play. We also suggest a problem-specific reward function. We performed the experiments on 10 …
This paper considers a multi-armed bandit game where the number of arms is much larger than the maximum budget and is effectively infinite. We characterize necessary and sufficient conditions on the total budget for an algorithm to return an ε-good arm with probability at least 1 - δ. In such situations, the sample complexity depends on ε, δ and the so-called reservoir distribution ν from which the means of the arms are drawn iid. While a substantial literature has developed around analyzing specific cases of ν such as the beta distribution, our analysis makes no assumption about the form of ν…
We consider a Multi-Armed Bandit problem in which the rewards are non-stationary and are dependent on past actions and potentially on past contexts. At the heart of our method, we employ a recurrent neural network, which models these sequences. In order to balance between exploration and exploitation, we present an energy minimization term that prevents the neural network from becoming too confident in support of a certain action. This term provably limits the gap between the maximal and minimal probabilities assigned by the network. In a diverse set of experiments, we demonstrate that our met…
INRIA - DIENS - PSL Research University（法国国家信息与自动化研究所 - 巴黎高等师范学院计算机系 - PSL研究大学）；Toyota Technological Institute at Chicago（芝加哥丰田技术研究所）
We study reward maximisation in a wide class of structured stochastic multi-armed bandit problems, where the mean rewards of arms satisfy some given structural constraints, e.g. linear, unimodal, sparse, etc. Our aim is to develop methods that are flexible (in that they easily adapt to different structures), powerful (in that they perform well empirically and/or provably match instance-dependent lower bounds) and efficient in that the per-round computational burden is small. We develop asymptotically optimal algorithms from instance-dependent lower-bounds using iterative saddle-point solvers. …
University College London（伦敦大学学院）；Usher Institute of Population Health Sciences and Informatics（亚瑟人口健康科学与信息学研究所）；NASA Ames Research Center（美国国家航空航天局艾姆斯研究中心）；University of Manchester（曼彻斯特大学）
Probability estimates generated by boosting ensembles are poorly calibrated because of the margin maximization nature of the algorithm. The outputs of the ensemble need to be properly calibrated before they can be used as probability estimates. In this work, we demonstrate that online boosting is also prone to producing distorted probability estimates. In batch learning, calibration is achieved by reserving part of the training data for training the calibrator function. In the online setting, a decision needs to be made on each round: shall the new example(s) be used to update the parameters o…
Indian Institute of Science（印度科学学院）；Technion, Israel Institute of Technology（以色列理工学院）
We study the problem of best arm identification in linearly parameterised multi-armed bandits. Given a set of feature vectors $\mathcal{X}\subset\mathbb{R}^d,$ a confidence parameter $δ$ and an unknown vector $θ^*,$ the goal is to identify $\arg\max_{x\in\mathcal{X}}x^Tθ^*$, with probability at least $1-δ,$ using noisy measurements of the form $x^Tθ^*.$ For this fixed confidence ($δ$-PAC) setting, we propose an explicitly implementable and provably order-optimal sample-complexity algorithm to solve this problem. Previous approaches rely on access to minimax optimization oracles. The algorithm,…
A stochastic combinatorial semi-bandit is an online learning problem where at each step a learning agent chooses a subset of ground items subject to combinatorial constraints, and then observes stochastic weights of these items and receives their sum as a payoff. In this paper, we consider efficient learning in large-scale combinatorial semi-bandits with linear generalization, and as a solution, propose two learning algorithms called Combinatorial Linear Thompson Sampling (CombLinTS) and Combinatorial Linear UCB (CombLinUCB). Both algorithms are computationally efficient as long as the offline…
In this paper, we consider stochastic multi-armed bandits (MABs) with heavy-tailed rewards, whose $p$-th moment is bounded by a constant $ν_{p}$ for $1<p\leq2$. First, we propose a novel robust estimator which does not require $ν_{p}$ as prior information, while other existing robust estimators demand prior knowledge about $ν_{p}$. We show that an error probability of the proposed estimator decays exponentially fast. Using this estimator, we propose a perturbation-based exploration strategy and develop a generalized regret analysis scheme that provides upper and lower regret bounds by revealin…
