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Low Regret Binary Sampling Method for Efficient Global Optimization of Univariate Functions [article]

Kaan Gokcesu, Hakan Gokcesu
2022
In this work, we propose a computationally efficient algorithm for the problem of global optimization in univariate loss functions.  ...  For the performance evaluation, we study the cumulative regret of the algorithm instead of the simple regret between our best query and the optimal value of the objective function.  ...  THE BINARY SAMPLING METHOD In this section, we design our binary sampling algorithm, which can efficiently optimize the objective function f (•) with low regret bounds.  ... 
doi:10.48550/arxiv.2201.07164 fatcat:xhpedqpl4fcj3k4agbingkd5zq

An Efficient Bandit Algorithm for Realtime Multivariate Optimization

Daniel N. Hill, Houssam Nassif, Yi Liu, Anand Iyer, S.V.N. Vishwanathan
2017 Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD '17  
We apply bandit methodology to explore the layout space efficiently and use hill-climbing to select optimal content in realtime.  ...  For example, the composition of a landing page may involve deciding which image to show, which wording to use, what color background to display, etc.  ...  ACKNOWLEDGMENTS The authors thank Charles Elkan, Sriram Srinavasan, Milos Curcic, Andrea Qualizza, Sham Kakade, Karthik Mohan, and Tao Hu for their helpful discussions.  ... 
doi:10.1145/3097983.3098184 dblp:conf/kdd/HillNLIV17 fatcat:qwdci7ij5zeoldt3lf7jhi4zoy

Computing an Efficient Exploration Basis for Learning with Univariate Polynomial Features

Chaitanya Amballa, Manu K. Gupta, Sanjay P. Bhat
2021 AAAI Conference on Artificial Intelligence  
Barycentric spanners have been used as an efficient exploration basis in online linear optimization problems in a bandit framework.  ...  We then empirically show that the use of a barycentric spanner to initialise the prior distribution in a Thompson sampling setting leads to lower cumulative regret as compared to standard initialisations  ...  Conclusions We have shown that the barycentric spanner for a decision space arising from univariate polynomial cost functions can be efficiently computed using convex optimization.  ... 
dblp:conf/aaai/AmballaGB21 fatcat:3dlswvrnfzbardyyc4uepggrxm

Power of human-algorithm collaboration in solving combinatorial optimization problems [article]

Tapani Toivonen
2021 arXiv   pre-print
We show that if a polynomial time algorithm can query informative Gaussian priors from an expert poly(n) times, then a class of combinatorial optimization problems can be solved efficiently in expectation  ...  An example of such problem is maximum clique which – under standard assumptions in complexity theory – cannot be solved in sub-exponential time or be approximated within polynomial factor efficiently.  ...  BO is often used in low data regimes where where evaluation of the objective function is costly or not otherwise efficient [22] .  ... 
arXiv:2107.11784v1 fatcat:dqkdmm5zjjexbpooxgqqcqeuxi

The Power of Human–Algorithm Collaboration in Solving Combinatorial Optimization Problems

Tapani Toivonen, Markku Tukiainen
2021 Algorithms  
Our methods can cast new light on how to approach optimization problems in domains where even the approximation of the problem is not feasible.  ...  However, we show that if a polynomial time algorithm can query informative Gaussian priors from an expert poly(n) times, then a class of combinatorial optimization problems can be solved efficiently up  ...  BO is often used in low data regimes where evaluation of the objective function is costly or not otherwise efficient [18] .  ... 
doi:10.3390/a14090253 fatcat:7zpdkbbcwrc2leymk34fdn6l7a

Bayesian Optimization of Combinatorial Structures [article]

Ricardo Baptista, Matthias Poloczek
2018 arXiv   pre-print
Our acquisition function pioneers the use of semidefinite programming to achieve efficiency and scalability.  ...  The optimization of expensive-to-evaluate black-box functions over combinatorial structures is an ubiquitous task in machine learning, engineering and the natural sciences.  ...  ACKNOWLEDGEMENT This work has been supported in part by the Air Force Office of Scientific Research (AFOSR) MURI on "Managing multiple information sources of multi-physics systems," Program Officer Dr.  ... 
arXiv:1806.08838v2 fatcat:m55pha7xtfflnnsgpx7yvjxape

Dynamic allocation optimization in A/B tests using classification-based preprocessing

Emmanuelle Claeys, Pierre Gancarski, Myriam Maumy-Bertrand, Hubert Wassner
2021 IEEE Transactions on Knowledge and Data Engineering  
We present our new method that finds the best variation for homogenous groups in a short period of time.  ...  In traditional A/B testing, for instance on two webpages A and B, the objective is to decide which of these two pages is the best.  ...  So choosing a sub optimal value for can make it less efficient than uniform (Fig. 14) . Table 5 .  ... 
doi:10.1109/tkde.2021.3076025 fatcat:l6ifydtzdfgyjfyupwhajtit7a

Online Learning to Rank with Top-k Feedback [article]

Sougata Chaudhuri, Ambuj Tewari
2016 arXiv   pre-print
No stochastic assumption is made on the generation process of relevances of items and contexts. We provide efficient ranking strategies for both the settings.  ...  The strategies achieve O(T^2/3) regret, where regret is based on popular ranking measures in first setting and ranking surrogates in second setting.  ...  Acknowledgments The authors acknowledge the support of NSF under grants IIS-1319810 and CAREER IIS-1452099.  ... 
arXiv:1608.06408v1 fatcat:wegmwyr2kbbjvn6phtn4wimhuq

Minimum Density Hyperplanes [article]

Nicos G. Pavlidis, David P. Hofmeyr, Sotiris K. Tasoulis
2016 arXiv   pre-print
The proposed approach is found to be very competitive with state of the art methods for clustering and semi-supervised classification.  ...  We propose a projection pursuit formulation of the associated optimisation problem which allows us to find minimum density hyperplanes efficiently in practice, and evaluate its performance on a range of  ...  David Hofmeyr gratefully acknowledges the support of the EPSRC funded EP/H023151/1 STOR-i centre for doctoral training, as well as the Oppenheimer  ... 
arXiv:1507.04201v3 fatcat:r6h6twux4rcf3iigom2s6aif54

Belief flows for robust online learning

Pedro A. Ortega, Koby Crammer, Daniel D. Lee
2015 2015 Information Theory and Applications Workshop (ITA)  
This paper introduces a new probabilistic model for online learning which dynamically incorporates information from stochastic gradients of an arbitrary loss function.  ...  Unlike traditional Bayesian updates, the model incorporates a small number of gradient evaluations at locations chosen using Thompson sampling, making it computationally tractable.  ...  , which is precisely where Thompson sampling has been shown to outperform most state-of-the-art methods [9] .  ... 
doi:10.1109/ita.2015.7308968 dblp:conf/ita/OrtegaCL15 fatcat:7bahvtjdyfaydesgvvb5a6oqzm

Online Learning: A Comprehensive Survey [article]

Steven C.H. Hoi, Doyen Sahoo, Jing Lu, Peilin Zhao
2018 arXiv   pre-print
from a sequence of data instances one at a time.  ...  The goal of online learning is to ensure that the online learner would make a sequence of accurate predictions (or correct decisions) given the knowledge of correct answers to previous prediction or learning  ...  This algorithm is computationally efficient given an oracle optimizer but has the weaker regret guarantee of O(T 2/3 ).  ... 
arXiv:1802.02871v2 fatcat:mqorsb4gknhfhjfb4jcsvbrtwm

Robot Learning with Crash Constraints [article]

Alonso Marco, Dominik Baumann, Majid Khadiv, Philipp Hennig, Ludovic Righetti, Sebastian Trimpe
2021 arXiv   pre-print
Experimental data is collected, by means of constrained Bayesian optimization, directly on the real robot.  ...  Both complicate the design of proper reward functions to penalize failures. In this paper, we propose a framework that addresses those issues.  ...  ACKNOWLEDGMENT The authors thank Felix Grimminger, for his support with the hardware during the experiments, Manuel Wüthrich for insightful discussions, and Maximilien Naveau for facilitating software  ... 
arXiv:2010.08669v3 fatcat:4cgvybs3dvbbbdv4qmqzprobn4

Belief Flows of Robust Online Learning [article]

Pedro A. Ortega and Koby Crammer and Daniel D. Lee
2015 arXiv   pre-print
This paper introduces a new probabilistic model for online learning which dynamically incorporates information from stochastic gradients of an arbitrary loss function.  ...  Unlike traditional Bayesian updates, the model incorporates a small number of gradient evaluations at locations chosen using Thompson sampling, making it computationally tractable.  ...  , which is precisely where Thompson sampling has been shown to outperform most state-of-the-art methods [9] .  ... 
arXiv:1505.07067v1 fatcat:cwv4vudcafeapj7iixoqhtr7dy

Stochastic convex optimization with bandit feedback [article]

Alekh Agarwal, Dean P. Foster, Daniel Hsu, Sham M. Kakade, Alexander Rakhlin
2011 arXiv   pre-print
The quantity of interest is the regret of the algorithm, which is the sum of the function values at algorithm's query points minus the optimal function value.  ...  Since any algorithm has regret at least Ω(√(T)) on this problem, our algorithm is optimal in terms of the scaling with T.  ...  Acknowledgments Part of this work was done while AA and DH were at the University of Pennsylvania. AA was partially supported by MSR and Google PhD fellowships while this work was done.  ... 
arXiv:1107.1744v2 fatcat:tn54lqvwsndnreogk5isoasj7i

Trusted-Maximizers Entropy Search for Efficient Bayesian Optimization [article]

Quoc Phong Nguyen, Zhaoxuan Wu, Bryan Kian Hsiang Low, Patrick Jaillet
2021 arXiv   pre-print
over a finite set of trusted maximizers, i.e., inputs optimizing functions that are sampled from the Gaussian process posterior belief of the objective function.  ...  Information-based Bayesian optimization (BO) algorithms have achieved state-of-the-art performance in optimizing a black-box objective function.  ...  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of National Research Foundation, Singapore.  ... 
arXiv:2107.14465v1 fatcat:ssxxs4kv4jgabhpah35wf5xpxu
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