Paper ID: 2303.01453

Improved Space Bounds for Learning with Experts

Anders Aamand, Justin Y. Chen, Huy Lê Nguyen, Sandeep Silwal

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.

Submitted: Mar 2, 2023