scholarly journals Multi-fidelity Gaussian Process Bandit Optimisation

2019 ◽  
Vol 66 ◽  
pp. 151-196 ◽  
Author(s):  
Kirthevasan Kandasamy ◽  
Gautam Dasarathy ◽  
Junier Oliva ◽  
Jeff Schneider ◽  
Barnabás Póczos
Keyword(s):  
Computer Simulation ◽  
Theoretical Analysis ◽  
Gaussian Process ◽  
Target Function ◽  
Black Box ◽  
Confidence Bound ◽  
Bandit Problem ◽  
Single Function ◽  
Novel Method ◽  
Upper Confidence Bound

In many scientific and engineering applications, we are tasked with the maximisation of an expensive to evaluate black box function f. Traditional settings for this problem assume just the availability of this single function. However, in many cases, cheap approximations to f may be obtainable. For example, the expensive real world behaviour of a robot can be approximated by a cheap computer simulation. We can use these approximations to eliminate low function value regions cheaply and use the expensive evaluations of f in a small but promising region and speedily identify the optimum. We formalise this task as a multi-fidelity bandit problem where the target function and its approximations are sampled from a Gaussian process. We develop MF-GP-UCB, a novel method based on upper confidence bound techniques. In our theoretical analysis we demonstrate that it exhibits precisely the above behaviour and achieves better bounds on the regret than strategies which ignore multi-fidelity information. Empirically, MF-GP-UCB outperforms such naive strategies and other multi-fidelity methods on several synthetic and real experiments.

scholarly journals Multi-Task Gaussian Process Upper Confidence Bound for Hyperparameter Tuning

2021 ◽  
Author(s):  
Bo Shen ◽  
Raghav Gnanasambandam ◽  
Rongxuan Wang ◽  
Zhenyu Kong
Keyword(s):  
Gaussian Process ◽  
Black Box ◽  
Bayesian Optimization ◽  
Query Point ◽  
Confidence Bound ◽  
Bayesian Optimization Algorithm ◽  
Machine Learning Model ◽  
Step Algorithm ◽  
Upper Confidence Bound ◽  
General Method

In many scientific and engineering applications, Bayesian optimization (BO) is a powerful tool for hyperparameter tuning of a machine learning model, materials design and discovery, etc. BO guides the choice of experiments in a sequential way to find a good combination of design points in as few experiments as possible. It can be formulated as a problem of optimizing a “black-box” function. Different from single-task Bayesian optimization, Multi-task Bayesian optimization is a general method to efficiently optimize multiple different but correlated “black-box” functions. The previous works in Multi-task Bayesian optimization algorithm queries a point to be evaluated for all tasks in each round of search, which is not efficient. For the case where different tasks are correlated, it is not necessary to evaluate all tasks for a given query point. Therefore, the objective of this work is to develop an algorithm for multi-task Bayesian optimization with automatic task selection so that only one task evaluation is needed per query round. Specifically, a new algorithm, namely, multi-task Gaussian process upper confidence bound (MT-GPUCB), is proposed to achieve this objective. The MT-GPUCB is a two-step algorithm, where the first step chooses which query point to evaluate, and the second step automatically selects the most informative task to evaluate. Under the bandit setting, a theoretical analysis is provided to show that our proposed MT-GPUCB is no-regret under some mild conditions. Our proposed algorithm is verified experimentally on a range of synthetic functions as well as real-world problems. The results clearly show the advantages of our query strategy for both design point and task.

scholarly journals Multi-Task Gaussian Process Upper Confidence Bound for Hyperparameter Tuning

2021 ◽  
Author(s):  
Bo Shen ◽  
Raghav Gnanasambandam ◽  
Rongxuan Wang ◽  
Zhenyu Kong
Keyword(s):  
Gaussian Process ◽  
Black Box ◽  
Bayesian Optimization ◽  
Query Point ◽  
Confidence Bound ◽  
Bayesian Optimization Algorithm ◽  
Machine Learning Model ◽  
Step Algorithm ◽  
Upper Confidence Bound ◽  
General Method

In many scientific and engineering applications, Bayesian optimization (BO) is a powerful tool for hyperparameter tuning of a machine learning model, materials design and discovery, etc. BO guides the choice of experiments in a sequential way to find a good combination of design points in as few experiments as possible. It can be formulated as a problem of optimizing a “black-box” function. Different from single-task Bayesian optimization, Multi-task Bayesian optimization is a general method to efficiently optimize multiple different but correlated “black-box” functions. The previous works in Multi-task Bayesian optimization algorithm queries a point to be evaluated for all tasks in each round of search, which is not efficient. For the case where different tasks are correlated, it is not necessary to evaluate all tasks for a given query point. Therefore, the objective of this work is to develop an algorithm for multi-task Bayesian optimization with automatic task selection so that only one task evaluation is needed per query round. Specifically, a new algorithm, namely, multi-task Gaussian process upper confidence bound (MT-GPUCB), is proposed to achieve this objective. The MT-GPUCB is a two-step algorithm, where the first step chooses which query point to evaluate, and the second step automatically selects the most informative task to evaluate. Under the bandit setting, a theoretical analysis is provided to show that our proposed MT-GPUCB is no-regret under some mild conditions. Our proposed algorithm is verified experimentally on a range of synthetic functions as well as real-world problems. The results clearly show the advantages of our query strategy for both design point and task.

scholarly journals Randomised Gaussian Process Upper Confidence Bound for Bayesian Optimisation

2020 ◽  
Author(s):  
Julian Berk ◽  
Sunil Gupta ◽  
Santu Rana ◽  
Svetha Venkatesh
Keyword(s):  
Gaussian Process ◽  
Real World ◽  
Confidence Bound ◽  
Trade Off ◽  
Upper Confidence Bound ◽  
Exploration Exploitation

In order to improve the performance of Bayesian optimisation, we develop a modified Gaussian process upper confidence bound (GP-UCB) acquisition function. This is done by sampling the exploration-exploitation trade-off parameter from a distribution. We prove that this allows the expected trade-off parameter to be altered to better suit the problem without compromising a bound on the function's Bayesian regret. We also provide results showing that our method achieves better performance than GP-UCB in a range of real-world and synthetic problems.

A Note on the Equivalence of Upper Confidence Bounds and Gittins Indices for Patient Agents

2020 ◽  
Author(s):  
Daniel Russo
Keyword(s):  
Posterior Distribution ◽  
Error Term ◽  
Discount Factor ◽  
Gittins Index ◽  
Confidence Bound ◽  
Bandit Problem ◽  
Confidence Bounds ◽  
Upper Confidence Bound ◽  
Gittins Indices ◽  
Multiarmed Bandit

This note gives a short, self-contained proof of a sharp connection between Gittins indices and Bayesian upper confidence bound algorithms. I consider a Gaussian multiarmed bandit problem with discount factor [Formula: see text]. The Gittins index of an arm is shown to equal the [Formula: see text]-quantile of the posterior distribution of the arm's mean plus an error term that vanishes as [Formula: see text]. In this sense, for sufficiently patient agents, a Gittins index measures the highest plausible mean-reward of an arm in a manner equivalent to an upper confidence bound.

A Novel Method of Spike Detection for Interferograms Based on Two-Step Filtering

2014 ◽  
Vol 599-601 ◽  
pp. 1364-1368
Author(s):  
Yao Pu Zou ◽  
Chang Pei Han ◽  
Lei Zhang ◽  
Wen Gui Pan ◽  
Chao Wang
Keyword(s):  
Computer Simulation ◽  
Theoretical Analysis ◽  
Detection Method ◽  
High Accuracy ◽  
Spike Detection ◽  
Novel Method

According to the characteristics of interferogram, we design a new spike detection method, which firstly filters an interferogram with two different ways and then detects spikes based on both results. Theoretical analysis and computer simulation shows that this algorithm performs well in detecting spikes in any position of an interferogram with high accuracy, and can be easily implemented in hardware.

scholarly journals Federated Bandit

2021 ◽  
Vol 5 (1) ◽  
pp. 1-29
Author(s):  
Zhaowei Zhu ◽  
Jingxuan Zhu ◽  
Ji Liu ◽  
Yang Liu
Keyword(s):  
Connected Graph ◽  
Differential Privacy ◽  
Distributed Data ◽  
Confidence Bound ◽  
Bandit Problem ◽  
Local Data ◽  
Largest Eigenvalue ◽  
Upper Confidence Bound ◽  
Second Largest Eigenvalue ◽  
Private Version

In this paper, we study Federated Bandit, a decentralized Multi-Armed Bandit problem with a set of N agents, who can only communicate their local data with neighbors described by a connected graph G. Each agent makes a sequence of decisions on selecting an arm from M candidates, yet they only have access to local and potentially biased feedback/evaluation of the true reward for each action taken. Learning only locally will lead agents to sub-optimal actions while converging to a no-regret strategy requires a collection of distributed data. Motivated by the proposal of federated learning, we aim for a solution with which agents will never share their local observations with a central entity, and will be allowed to only share a private copy of his/her own information with their neighbors. We first propose a decentralized bandit algorithm \textttGossip\_UCB, which is a coupling of variants of both the classical gossiping algorithm and the celebrated Upper Confidence Bound (UCB) bandit algorithm. We show that \textttGossip\_UCB successfully adapts local bandit learning into a global gossiping process for sharing information among connected agents, and achieves guaranteed regret at the order of O(\max\ \textttpoly (N,M) łog T, \textttpoly (N,M)łog_łambda_2^-1 N\ ) for all N agents, where łambda_2\in(0,1) is the second largest eigenvalue of the expected gossip matrix, which is a function of G. We then propose \textttFed\_UCB, a differentially private version of \textttGossip\_UCB, in which the agents preserve ε-differential privacy of their local data while achieving O(\max \\frac\textttpoly (N,M) ε łog^2.5 T, \textttpoly (N,M) (łog_łambda_2^-1 N + łog T) \ ) regret.

scholarly journals Sparsifying to optimize over multiple information sources: an augmented Gaussian process based algorithm

2021 ◽  
Author(s):  
Antonio Candelieri ◽  
Francesco Archetti
Keyword(s):  
Gaussian Process ◽  
Information Sources ◽  
Information Source ◽  
Search Space ◽  
Black Box ◽  
Test Problems ◽  
Confidence Bound ◽  
Hyperparameter Optimization ◽  
Large Dataset ◽  
Learning Classifier

AbstractOptimizing a black-box, expensive, and multi-extremal function, given multiple approximations, is a challenging task known as multi-information source optimization (MISO), where each source has a different cost and the level of approximation (aka fidelity) of each source can change over the search space. While most of the current approaches fuse the Gaussian processes (GPs) modelling each source, we propose to use GP sparsification to select only “reliable” function evaluations performed over all the sources. These selected evaluations are used to create an augmented Gaussian process (AGP), whose name is implied by the fact that the evaluations on the most expensive source are augmented with the reliable evaluations over less expensive sources. A new acquisition function, based on confidence bound, is also proposed, including both cost of the next source to query and the location-dependent approximation of that source. This approximation is estimated through a model discrepancy measure and the prediction uncertainty of the GPs. MISO-AGP and the MISO-fused GP counterpart are compared on two test problems and hyperparameter optimization of a machine learning classifier on a large dataset.

scholarly journals Bayesian Optimization using Pseudo-Points

2020 ◽  
Author(s):  
Chao Qian ◽  
Hang Xiong ◽  
Ke Xue
Keyword(s):  
Parameter Tuning ◽  
Black Box ◽  
Bayesian Optimization ◽  
Confidence Bound ◽  
Data Points ◽  
Upper Confidence Bound ◽  
Gp Model ◽  
Probability Of Improvement ◽  
And Robotics ◽  
Real World Problems

Bayesian optimization (BO) is a popular approach for expensive black-box optimization, with applications including parameter tuning, experimental design, and robotics. BO usually models the objective function by a Gaussian process (GP), and iteratively samples the next data point by maximizing an acquisition function. In this paper, we propose a new general framework for BO by generating pseudo-points (i.e., data points whose objective values are not evaluated) to improve the GP model. With the classic acquisition function, i.e., upper confidence bound (UCB), we prove that the cumulative regret can be generally upper bounded. Experiments using UCB and other acquisition functions, i.e., probability of improvement (PI) and expectation of improvement (EI), on synthetic as well as real-world problems clearly show the advantage of generating pseudo-points.

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