[2309.06548] On-line Infinite-Dimensional Regression: Studying Linear Operators


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Summary:We contemplate the issue of studying linear operators below squared loss between two infinite-dimensional Hilbert areas within the on-line setting. We present that the category of linear operators with uniformly bounded $p$-Schatten norm is on-line learnable for any $p in [1, infty)$. On the other hand, we prove an impossibility result by showing that the class of uniformly bounded linear operators with respect to the operator norm is textit{not} online learnable. Moreover, we show a separation between sequential uniform convergence and online learnability by identifying a class of bounded linear operators that is online learnable but uniform convergence does not hold. Finally, we prove that the impossibility result and the separation between uniform convergence and learnability also hold in the batch setting.

Submission history

From: Unique Subedi [view email]
Fri, 8 Sep 2023 21:34:52 UTC (27 KB)
Thu, 21 Sep 2023 21:45:28 UTC (27 KB)
Thu, 25 Jan 2024 01:25:33 UTC (40 KB)

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