  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.
