Exploration by Optimization with Hybrid Regularizers: Logarithmic Regret with Adversarial Robustness in Partial Monitoring
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909494860054528 |
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| author | Tsuchiya, Taira Ito, Shinji Honda, Junya |
| author_facet | Tsuchiya, Taira Ito, Shinji Honda, Junya |
| contents | Partial monitoring is a generic framework of online decision-making problems with limited feedback. To make decisions from such limited feedback, it is necessary to find an appropriate distribution for exploration. Recently, a powerful approach for this purpose, \emph{exploration by optimization} (ExO), was proposed, which achieves optimal bounds in adversarial environments with follow-the-regularized-leader for a wide range of online decision-making problems. However, a naive application of ExO in stochastic environments significantly degrades regret bounds. To resolve this issue in locally observable games, we first establish a new framework and analysis for ExO with a hybrid regularizer. This development allows us to significantly improve existing regret bounds of best-of-both-worlds (BOBW) algorithms, which achieves nearly optimal bounds both in stochastic and adversarial environments. In particular, we derive a stochastic regret bound of $O(\sum_{a \neq a^*} k^2 m^2 \log T / Δ_a)$, where $k$, $m$, and $T$ are the numbers of actions, observations and rounds, $a^*$ is an optimal action, and $Δ_a$ is the suboptimality gap for action $a$. This bound is roughly $Θ(k^2 \log T)$ times smaller than existing BOBW bounds. In addition, for globally observable games, we provide a new BOBW algorithm with the first $O(\log T)$ stochastic bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08321 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exploration by Optimization with Hybrid Regularizers: Logarithmic Regret with Adversarial Robustness in Partial Monitoring Tsuchiya, Taira Ito, Shinji Honda, Junya Machine Learning Partial monitoring is a generic framework of online decision-making problems with limited feedback. To make decisions from such limited feedback, it is necessary to find an appropriate distribution for exploration. Recently, a powerful approach for this purpose, \emph{exploration by optimization} (ExO), was proposed, which achieves optimal bounds in adversarial environments with follow-the-regularized-leader for a wide range of online decision-making problems. However, a naive application of ExO in stochastic environments significantly degrades regret bounds. To resolve this issue in locally observable games, we first establish a new framework and analysis for ExO with a hybrid regularizer. This development allows us to significantly improve existing regret bounds of best-of-both-worlds (BOBW) algorithms, which achieves nearly optimal bounds both in stochastic and adversarial environments. In particular, we derive a stochastic regret bound of $O(\sum_{a \neq a^*} k^2 m^2 \log T / Δ_a)$, where $k$, $m$, and $T$ are the numbers of actions, observations and rounds, $a^*$ is an optimal action, and $Δ_a$ is the suboptimality gap for action $a$. This bound is roughly $Θ(k^2 \log T)$ times smaller than existing BOBW bounds. In addition, for globally observable games, we provide a new BOBW algorithm with the first $O(\log T)$ stochastic bound. |
| title | Exploration by Optimization with Hybrid Regularizers: Logarithmic Regret with Adversarial Robustness in Partial Monitoring |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2402.08321 |