Timezone: »

 
Poster
Instance Dependent Regret Analysis of Kernelized Bandits
Shubhanshu Shekhar · Tara Javidi

Thu Jul 21 03:00 PM -- 05:00 PM (PDT) @ Hall E #720
We study the problem of designing an adaptive strategy for querying a noisy zeroth-order-oracle to efficiently learn about the optimizer of an unknown function $f$. To make the problem tractable, we assume that $f$ lies in the reproducing kernel Hilbert space (RKHS) associated with a known kernel $K$, with its norm bounded by $M<\infty$. Prior results, working in a \emph{minimax framework}, have characterized the worst-case~(over all functions in the problem class) limits on regret achievable by \emph{any} algorithm, and have constructed algorithms with matching~(modulo polylogarithmic factors) worst-case performance for the Matern family of kernels. These results suffer from two drawbacks. First, the minimax lower bound gives limited information about the limits of regret achievable by commonly used algorithms on a specific problem instance $f$. Second, the existing upper bound analysis fails to adapt to easier problem instances within the function class. Our work takes steps to address both these issues. First, we derive \emph{instance-dependent} regret lower bounds for algorithms with uniformly~(over the function class) vanishing normalized cumulative regret. Our result, valid for several practically relevant kernelized bandits algorithms, such as, GP-UCB, GP-TS and SupKernelUCB, identifies a fundamental complexity measure associated with every problem instance. We then address the second issue, by proposing a new minimax near-optimal algorithm that also adapts to easier problem instances.

Author Information

Shubhanshu Shekhar (University of California, San Diego)
Tara Javidi (University of California San Diego)

Related Events (a corresponding poster, oral, or spotlight)

More from the Same Authors

  • 2023 Poster: Sequential Changepoint Detection via Backward Confidence Sequences »
    Shubhanshu Shekhar · Aaditya Ramdas
  • 2020 Poster: Adaptive Sampling for Estimating Probability Distributions »
    Shubhanshu Shekhar · Tara Javidi · Mohammad Ghavamzadeh
  • 2019 : Poster Session 1 (all papers) »
    Matilde Gargiani · Yochai Zur · Chaim Baskin · Evgenii Zheltonozhskii · Liam Li · Ameet Talwalkar · Xuedong Shang · Harkirat Singh Behl · Atilim Gunes Baydin · Ivo Couckuyt · Tom Dhaene · Chieh Lin · Wei Wei · Min Sun · Orchid Majumder · Michele Donini · Yoshihiko Ozaki · Ryan P. Adams · Christian Geißler · Ping Luo · zhanglin peng · · Ruimao Zhang · John Langford · Rich Caruana · Debadeepta Dey · Charles Weill · Xavi Gonzalvo · Scott Yang · Scott Yak · Eugen Hotaj · Vladimir Macko · Mehryar Mohri · Corinna Cortes · Stefan Webb · Jonathan Chen · Martin Jankowiak · Noah Goodman · Aaron Klein · Frank Hutter · Mojan Javaheripi · Mohammad Samragh · Sungbin Lim · Taesup Kim · SUNGWOONG KIM · Michael Volpp · Iddo Drori · Yamuna Krishnamurthy · Kyunghyun Cho · Stanislaw Jastrzebski · Quentin de Laroussilhe · Mingxing Tan · Xiao Ma · Neil Houlsby · Andrea Gesmundo · Zalán Borsos · Krzysztof Maziarz · Felipe Petroski Such · Joel Lehman · Kenneth Stanley · Jeff Clune · Pieter Gijsbers · Joaquin Vanschoren · Felix Mohr · Eyke Hüllermeier · Zheng Xiong · Wenpeng Zhang · Wenwu Zhu · Weijia Shao · Aleksandra Faust · Michal Valko · Michael Y Li · Hugo Jair Escalante · Marcel Wever · Andrey Khorlin · Tara Javidi · Anthony Francis · Saurajit Mukherjee · Jungtaek Kim · Michael McCourt · Saehoon Kim · Tackgeun You · Seungjin Choi · Nicolas Knudde · Alexander Tornede · Ghassen Jerfel
  • 2019 Tutorial: Active Hypothesis Testing: An Information Theoretic (re)View »
    Tara Javidi
  • 2018 Poster: Active Learning with Logged Data »
    Songbai Yan · Kamalika Chaudhuri · Tara Javidi
  • 2018 Oral: Active Learning with Logged Data »
    Songbai Yan · Kamalika Chaudhuri · Tara Javidi