Asymptotically optimal strategies for online prediction with history-dependent experts

• URL: http://arxiv.org/abs/2008.13703v1
• Date: Mon, 31 Aug 2020 16:00:42 GMT
• Title: Asymptotically optimal strategies for online prediction with history-dependent experts
• Authors: Jeff Calder and Nadejda Drenska
• Abstract summary: We establish sharpally optimal strategies for the problem of online prediction with history dependent experts. We show that the optimality conditions over the de Bruijn graph correspond to a graph Poisson equation.
• Score: 1.52292571922932
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We establish sharp asymptotically optimal strategies for the problem of online prediction with history dependent experts. The prediction problem is played (in part) over a discrete graph called the $d$ dimensional de Bruijn graph, where $d$ is the number of days of history used by the experts. Previous work [11] established $O(\varepsilon)$ optimal strategies for $n=2$ experts and $d\leq 4$ days of history, while [10] established $O(\varepsilon^{1/3})$ optimal strategies for all $n\geq 2$ and all $d\geq 1$, where the game is played for $N$ steps and $\varepsilon=N^{-1/2}$. In this paper, we show that the optimality conditions over the de Bruijn graph correspond to a graph Poisson equation, and we establish $O(\varepsilon)$ optimal strategies for all values of $n$ and $d$.

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