Exploration by Optimization with Hybrid Regularizers: Logarithmic Regret with Adversarial Robustness in Partial Monitoring
<|reference_start|>Exploration by Optimization with Hybrid Regularizers: Logarithmic Regret with Adversarial Robustness in Partial Monitoring: Partial monitoring is a generic framework of online decision-making problems with limited observations. To make decisions from such limited observations, it is necessary to find an appropriate distribution for exploration. Recently, a powerful approach for this purpose, exploration by optimization (ExO), was proposed, which achieves the 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 problem in locally observable games, we first establish a novel framework and analysis for ExO with a hybrid regularizer. This development allows us to significantly improve the 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 $O(\sum_{a \neq a^*} k^2 m^2 \log T / \Delta_a)$, where $k$, $m$, and $T$ are the numbers of actions, observations and rounds, $a^*$ is an optimal action, and $\Delta_a$ is the suboptimality gap for action $a$. This bound is roughly $\Theta(k^2 \log T)$ 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.<|reference_end|>
@article{tsuchiya2024exploration,
    title={Exploration by Optimization with Hybrid Regularizers: Logarithmic Regret
  with Adversarial Robustness in Partial Monitoring},
    author={Taira Tsuchiya, Shinji Ito, Junya Honda},
    journal={arXiv preprint arXiv:2402.08321},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.08321},
    primaryClass={cs.LG stat.ML}
}