具有历史依赖专家的在线预测的渐近最优策略
Asymptotically optimal strategies for online prediction with history-dependent experts
摘要：
针对专家依赖历史的在线预测问题，建立了精确的渐近最优策略。预测问题（部分）在称为$d$维de Bruijn图的离散图上进行，其中$d$是专家使用的历史天数。以前的工作[11]为$n=2$专家和$d\leq 4$历史日建立了$O(\varepsilon)$最优策略，而[10]为所有$n\geq 2$和所有$d\geq 1$建立了$O(\varepsilon^{1/3})$最优策略，其中游戏针对$N$步骤和$\varepsilon=N^{-1/2}$进行。本文证明了de Bruijn图上的最优性条件对应于一个图Poisson方程，并对$n$和$d$的所有值建立了$O(\varepsilon)$最优策略.
英文摘要：
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 $d$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
