Timezone: »
Poster
Nearly Optimal Best-of-Both-Worlds Algorithms for Online Learning with Feedback Graphs
Shinji Ito · Taira Tsuchiya · Junya Honda
This study considers online learning with general directed feedback graphs. For this problem, we present best-of-both-worlds algorithms that achieve nearly tight regret bounds for adversarial environments as well as poly-logarithmic regret bounds for stochastic environments. As Alon et al. [2015] have shown, tight regret bounds depend on the structure of the feedback graph: strongly observable graphs yield minimax regret of $\tilde{\Theta}( \alpha^{1/2} T^{1/2} )$, while weakly observable graphs induce minimax regret of $\tilde{\Theta}( \delta^{1/3} T^{2/3} )$, where $\alpha$ and $\delta$, respectively, represent the independence number of the graph and the domination number of a certain portion of the graph. Our proposed algorithm for strongly observable graphs has a regret bound of $\tilde{O}( \alpha^{1/2} T^{1/2} )$ for adversarial environments, as well as of $ {O} ( \frac{\alpha (\ln T)^3 }{\Delta_{\min}} ) $ for stochastic environments, where $\Delta_{\min}$ expresses the minimum suboptimality gap. This result resolves an open question raised by Erez and Koren [2021]. We also provide an algorithm for weakly observable graphs that achieves a regret bound of $\tilde{O}( \delta^{1/3}T^{2/3} )$ for adversarial environments and poly-logarithmic regret for stochastic environments. The proposed algorithms are based on the follow-the-regularized-leader approach combined with newly designed update rules for learning rates.
Author Information
Shinji Ito (NEC Corporation)
Taira Tsuchiya (Kyoto University)
Junya Honda (Kyoto University / RIKEN)
More from the Same Authors
-
2022 Poster: Average Sensitivity of Euclidean k-Clustering »
Yuichi Yoshida · Shinji Ito -
2022 Poster: Single Loop Gaussian Homotopy Method for Non-convex Optimization »
Hidenori Iwakiri · Yuhang Wang · Shinji Ito · Akiko Takeda -
2022 Poster: Minimax Optimal Algorithms for Fixed-Budget Best Arm Identification »
Junpei Komiyama · Taira Tsuchiya · Junya Honda -
2021 Poster: On Optimal Robustness to Adversarial Corruption in Online Decision Problems »
Shinji Ito -
2021 Poster: Hybrid Regret Bounds for Combinatorial Semi-Bandits and Adversarial Linear Bandits »
Shinji Ito -
2020 Poster: Tight First- and Second-Order Regret Bounds for Adversarial Linear Bandits »
Shinji Ito · Shuichi Hirahara · Tasuku Soma · Yuichi Yoshida -
2020 Poster: A Tight Lower Bound and Efficient Reduction for Swap Regret »
Shinji Ito -
2020 Poster: Delay and Cooperation in Nonstochastic Linear Bandits »
Shinji Ito · Daisuke Hatano · Hanna Sumita · Kei Takemura · Takuro Fukunaga · Naonori Kakimura · Ken-Ichi Kawarabayashi -
2020 Poster: Analysis and Design of Thompson Sampling for Stochastic Partial Monitoring »
Taira Tsuchiya · Junya Honda · Masashi Sugiyama -
2020 Spotlight: A Tight Lower Bound and Efficient Reduction for Swap Regret »
Shinji Ito -
2020 Spotlight: Delay and Cooperation in Nonstochastic Linear Bandits »
Shinji Ito · Daisuke Hatano · Hanna Sumita · Kei Takemura · Takuro Fukunaga · Naonori Kakimura · Ken-Ichi Kawarabayashi -
2020 Spotlight: Tight First- and Second-Order Regret Bounds for Adversarial Linear Bandits »
Shinji Ito · Shuichi Hirahara · Tasuku Soma · Yuichi Yoshida -
2019 Poster: Improved Regret Bounds for Bandit Combinatorial Optimization »
Shinji Ito · Daisuke Hatano · Hanna Sumita · Kei Takemura · Takuro Fukunaga · Naonori Kakimura · Ken-Ichi Kawarabayashi -
2019 Poster: Submodular Function Minimization with Noisy Evaluation Oracle »
Shinji Ito -
2019 Poster: Oracle-Efficient Algorithms for Online Linear Optimization with Bandit Feedback »
Shinji Ito · Daisuke Hatano · Hanna Sumita · Kei Takemura · Takuro Fukunaga · Naonori Kakimura · Ken-Ichi Kawarabayashi