Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study fast learning rates when the losses are not necessarily bounded and may have a distribution with heavy tails. To enable such analyses,  introduce two new conditions: (i) the envelope function $\sup_{f \in \mathcal{F}}|\ell \circ f|$, where $\ell$ is the loss function and $\mathcal{F}$ is the hypothesis class, exists and is $L^r$-integrable, and (ii) $\ell$ satisfies the multi-scale Bernstein's condition on $\mathcal{F}$. Under these assumptions,  prove that learning rate faster than $O(n^{-1/2})$ can be obtained and, depending on $r$ and the multi-scale Bernstein's pors, can be arbitrarily close to $O(n^{-1})$.  then verify these assumptions and derive fast learning rates for the problem of vector quantization by $k$-means clustering with heavy-tailed distributions. The analyses enable us to obtain novel learning rates that extend and complement existing results in the literature from both theoretical and practical viewpoints.
['Vu Dinh', 'Lam Si Tung Ho', 'Duy Nguyen', 'Binh T. Nguyen']
I am writing a research paper on a idea Fast learning rates with heavy-tailed losses
[{"from": "human", "value": "I am writing a research paper on a idea Fast learning rates with heavy-tailed losses"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study fast learning rates when the losses are not necessarily bounded and may have a distribution with heavy tails. To enable such analyses,  introduce two new conditions: (i) the envelope function $\\sup_{f \\in \\mathcal{F}}|\\ell \\circ f|$, where $\\ell$ is the loss function and $\\mathcal{F}$ is the hypothesis class, exists and is $L^r$-integrable, and (ii) $\\ell$ satisfies the multi-scale Bernstein's condition on $\\mathcal{F}$. Under these assumptions,  prove that learning rate faster than $O(n^{-1/2})$ can be obtained and, depending on $r$ and the multi-scale Bernstein's pors, can be arbitrarily close to $O(n^{-1})$.  then verify these assumptions and derive fast learning rates for the problem of vector quantization by $k$-means clustering with heavy-tailed distributions. The analyses enable us to obtain novel learning rates that extend and complement existing results in the literature from both theoretical and practical viewpoints."}]