We give improved tradeoffs between space and regret for the online learning with expert advice problem over $T$ days with $n$ experts. Given a space budget of $n^{\delta}$ for $\delta \in (0,1)$, we provide an algorithm achieving regret $\tilde{O}(n^2 T^{1/(1+\delta)})$, improving upon the regret bound $\tilde{O}(n^2 T^{2/(2+\delta)})$ in the recent work of [PZ23]. The improvement is particularly salient in the regime $\delta \rightarrow 1$ where the regret of our algorithm approaches $\tilde{O}_n(\sqrt{T})$, matching the $T$ dependence in the standard online setting without space restrictions.
翻译:我们改进了空间之间的取舍,并对在专家咨询问题上与专家进行在线学习感到遗憾,花费了4美元。鉴于空间预算为0.1美元(0.1美元),我们提供了一种实现遗憾的算法 $tilde{O}(n<unk> 2 T<unk> 1/(1<unk> delta)},改进了[PZ23]最近工作中与专家咨询问题有关的遗憾($2 T<unk> 2/(2<unk> delta)}美元。改进特别突出的是制度$delta\rightrow 1美元,因为对我们的算法的遗憾接近了$tilde{O}(O}(sqrt{T})$,与标准在线设置中无空间限制地依赖$T$相匹配。</s>