Learning on the Edge: Online Learning with Stochastic Feedback Graphs
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913236612284416 |
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| author | Esposito, Emmanuel Fusco, Federico van der Hoeven, Dirk Cesa-Bianchi, Nicolò |
| author_facet | Esposito, Emmanuel Fusco, Federico van der Hoeven, Dirk Cesa-Bianchi, Nicolò |
| contents | The framework of feedback graphs is a generalization of sequential decision-making with bandit or full information feedback. In this work, we study an extension where the directed feedback graph is stochastic, following a distribution similar to the classical Erdős-Rényi model. Specifically, in each round every edge in the graph is either realized or not with a distinct probability for each edge. We prove nearly optimal regret bounds of order $\min\bigl\{\min_{\varepsilon} \sqrt{(α_\varepsilon/\varepsilon) T},\, \min_{\varepsilon} (δ_\varepsilon/\varepsilon)^{1/3} T^{2/3}\bigr\}$ (ignoring logarithmic factors), where $α_{\varepsilon}$ and $δ_{\varepsilon}$ are graph-theoretic quantities measured on the support of the stochastic feedback graph $\mathcal{G}$ with edge probabilities thresholded at $\varepsilon$. Our result, which holds without any preliminary knowledge about $\mathcal{G}$, requires the learner to observe only the realized out-neighborhood of the chosen action. When the learner is allowed to observe the realization of the entire graph (but only the losses in the out-neighborhood of the chosen action), we derive a more efficient algorithm featuring a dependence on weighted versions of the independence and weak domination numbers that exhibits improved bounds for some special cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_04229 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Learning on the Edge: Online Learning with Stochastic Feedback Graphs Esposito, Emmanuel Fusco, Federico van der Hoeven, Dirk Cesa-Bianchi, Nicolò Machine Learning Data Structures and Algorithms The framework of feedback graphs is a generalization of sequential decision-making with bandit or full information feedback. In this work, we study an extension where the directed feedback graph is stochastic, following a distribution similar to the classical Erdős-Rényi model. Specifically, in each round every edge in the graph is either realized or not with a distinct probability for each edge. We prove nearly optimal regret bounds of order $\min\bigl\{\min_{\varepsilon} \sqrt{(α_\varepsilon/\varepsilon) T},\, \min_{\varepsilon} (δ_\varepsilon/\varepsilon)^{1/3} T^{2/3}\bigr\}$ (ignoring logarithmic factors), where $α_{\varepsilon}$ and $δ_{\varepsilon}$ are graph-theoretic quantities measured on the support of the stochastic feedback graph $\mathcal{G}$ with edge probabilities thresholded at $\varepsilon$. Our result, which holds without any preliminary knowledge about $\mathcal{G}$, requires the learner to observe only the realized out-neighborhood of the chosen action. When the learner is allowed to observe the realization of the entire graph (but only the losses in the out-neighborhood of the chosen action), we derive a more efficient algorithm featuring a dependence on weighted versions of the independence and weak domination numbers that exhibits improved bounds for some special cases. |
| title | Learning on the Edge: Online Learning with Stochastic Feedback Graphs |
| topic | Machine Learning Data Structures and Algorithms |
| url | https://arxiv.org/abs/2210.04229 |