Online Learning with Bounded Recall
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910466061631488 |
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| author | Schneider, Jon Vodrahalli, Kiran |
| author_facet | Schneider, Jon Vodrahalli, Kiran |
| contents | We study the problem of full-information online learning in the "bounded recall" setting popular in the study of repeated games. An online learning algorithm $\mathcal{A}$ is $M$-$\textit{bounded-recall}$ if its output at time $t$ can be written as a function of the $M$ previous rewards (and not e.g. any other internal state of $\mathcal{A}$). We first demonstrate that a natural approach to constructing bounded-recall algorithms from mean-based no-regret learning algorithms (e.g., running Hedge over the last $M$ rounds) fails, and that any such algorithm incurs constant regret per round. We then construct a stationary bounded-recall algorithm that achieves a per-round regret of $Θ(1/\sqrt{M})$, which we complement with a tight lower bound. Finally, we show that unlike the perfect recall setting, any low regret bound bounded-recall algorithm must be aware of the ordering of the past $M$ losses -- any bounded-recall algorithm which plays a symmetric function of the past $M$ losses must incur constant regret per round. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_14519 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Online Learning with Bounded Recall Schneider, Jon Vodrahalli, Kiran Machine Learning Computer Science and Game Theory We study the problem of full-information online learning in the "bounded recall" setting popular in the study of repeated games. An online learning algorithm $\mathcal{A}$ is $M$-$\textit{bounded-recall}$ if its output at time $t$ can be written as a function of the $M$ previous rewards (and not e.g. any other internal state of $\mathcal{A}$). We first demonstrate that a natural approach to constructing bounded-recall algorithms from mean-based no-regret learning algorithms (e.g., running Hedge over the last $M$ rounds) fails, and that any such algorithm incurs constant regret per round. We then construct a stationary bounded-recall algorithm that achieves a per-round regret of $Θ(1/\sqrt{M})$, which we complement with a tight lower bound. Finally, we show that unlike the perfect recall setting, any low regret bound bounded-recall algorithm must be aware of the ordering of the past $M$ losses -- any bounded-recall algorithm which plays a symmetric function of the past $M$ losses must incur constant regret per round. |
| title | Online Learning with Bounded Recall |
| topic | Machine Learning Computer Science and Game Theory |
| url | https://arxiv.org/abs/2205.14519 |