A Bandit Approach to Maximum Inner Product Search

There has been substantial research on sub-linear time approximate algorithms for Maximum Inner Product Search (MIPS). To achieve fast query time, state-of-the-art techniques require significant preprocessing, which can be a burden when the number of subsequent queries is not sufficiently large to amortize the cost. Furthermore, existing methods do not have the ability to directly control the suboptimality of their approximate results with theoretical guarantees. In this paper, we propose the first approximate algorithm for MIPS that does not require any preprocessing, and allows users to control and bound the suboptimality of the results. We cast MIPS as a Best Arm Identification problem, and introduce a new bandit setting that can fully exploit the special structure of MIPS. Our approach outperforms state-of-the-art methods on both synthetic and real-world datasets.

[1]  Parikshit Ram,et al.  Improved maximum inner product search with better theoretical guarantees , 2017, 2017 International Joint Conference on Neural Networks (IJCNN).

[2]  Patrick Seemann,et al.  Matrix Factorization Techniques for Recommender Systems , 2014 .

[3]  Michael J. Cafarella,et al.  Neighbor-Sensitive Hashing , 2015, Proc. VLDB Endow..

[4]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[5]  Pascal Vincent,et al.  Clustering is Efficient for Approximate Maximum Inner Product Search , 2015, ArXiv.

[6]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[7]  Robert D. Nowak,et al.  Best-arm identification algorithms for multi-armed bandits in the fixed confidence setting , 2014, 2014 48th Annual Conference on Information Sciences and Systems (CISS).

[8]  Thorsten Joachims,et al.  Cutting-plane training of structural SVMs , 2009, Machine Learning.

[9]  Barzan Mozafari,et al.  A Handbook for Building an Approximate Query Engine , 2015, IEEE Data Eng. Bull..

[10]  Martin Jaggi,et al.  A Unified Optimization View on Generalized Matching Pursuit and Frank-Wolfe , 2017, AISTATS.

[11]  Ulrich Paquet,et al.  Speeding up the Xbox recommender system using a euclidean transformation for inner-product spaces , 2014, RecSys '14.

[12]  Oren Somekh,et al.  Almost Optimal Exploration in Multi-Armed Bandits , 2013, ICML.

[13]  Gábor Lugosi,et al.  Concentration Inequalities - A Nonasymptotic Theory of Independence , 2013, Concentration Inequalities.

[14]  Martin Jaggi,et al.  Revisiting Frank-Wolfe: Projection-Free Sparse Convex Optimization , 2013, ICML.

[15]  Danna Zhou,et al.  d. , 1934, Microbial pathogenesis.

[16]  Ion Stoica,et al.  BlinkDB: queries with bounded errors and bounded response times on very large data , 2012, EuroSys '13.

[17]  Shie Mannor,et al.  PAC Bounds for Multi-armed Bandit and Markov Decision Processes , 2002, COLT.

[18]  Jonathon Shlens,et al.  Fast, Accurate Detection of 100,000 Object Classes on a Single Machine , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[19]  Rui Liu,et al.  Robust Multi-Network Clustering via Joint Cross-Domain Cluster Alignment , 2015, 2015 IEEE International Conference on Data Mining.

[20]  Thorsten Joachims,et al.  Training linear SVMs in linear time , 2006, KDD '06.

[21]  Rémi Munos,et al.  Pure Exploration in Multi-armed Bandits Problems , 2009, ALT.

[22]  Inderjit S. Dhillon,et al.  A Greedy Approach for Budgeted Maximum Inner Product Search , 2016, NIPS.

[23]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[24]  Ashish Kapoor,et al.  Active learning for large multi-class problems , 2009, 2009 IEEE Conference on Computer Vision and Pattern Recognition.

[25]  Ameet Talwalkar,et al.  Knowing when you're wrong: building fast and reliable approximate query processing systems , 2014, SIGMOD Conference.

[26]  Barzan Mozafari,et al.  BlinkML : Approximate Machine Learning with Probabilistic Guarantees , 2018 .

[27]  Ameet Talwalkar,et al.  Non-stochastic Best Arm Identification and Hyperparameter Optimization , 2015, AISTATS.

[28]  Nathan Srebro,et al.  On Symmetric and Asymmetric LSHs for Inner Product Search , 2014, ICML.

[29]  Stefano Ermon,et al.  Best arm identification in multi-armed bandits with delayed feedback , 2018, AISTATS.

[30]  Edith Cohen,et al.  Approximating matrix multiplication for pattern recognition tasks , 1997, SODA '97.

[31]  Ping Li,et al.  Asymmetric LSH (ALSH) for Sublinear Time Maximum Inner Product Search (MIPS) , 2014, NIPS.

[32]  Roberto Turrin,et al.  Performance of recommender algorithms on top-n recommendation tasks , 2010, RecSys '10.

[33]  Shie Mannor,et al.  Action Elimination and Stopping Conditions for the Multi-Armed Bandit and Reinforcement Learning Problems , 2006, J. Mach. Learn. Res..

[34]  Odalric-Ambrym Maillard,et al.  Concentration inequalities for sampling without replacement , 2013, 1309.4029.

[35]  Ambuj Tewari,et al.  PAC Subset Selection in Stochastic Multi-armed Bandits , 2012, ICML.