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Exhaustive optimistic scoring can make action selection costly in linear bandits with a large fixed set of $K$ actions, requiring $\mathcal{O}(K)$ score evaluations per round. We introduce Persistent Candidate LinUCB (\textsc{PC-LinUCB}), which maintains $k$ active actions and samples $q$ challengers uniformly from the...
We prove that, over any field, the bilinear complexity of multiplying a $3\times 2$ matrix by a $2\times m$ matrix is strictly greater than $24m/5$. In particular, every exact bilinear algorithm for multiplying a $3\times 2$ matrix by a $2\times 5$ matrix requires at least $25$ multiplications. Together with the Hopcro...
We present a fully GPU-oriented SVD pipeline based on polar decomposition, motivated by iterative methods that rely solely on matrix multiplications, such as the Newton-Schulz iteration. We show that this approach enables up to a $2\times$ speedup compared to standard implementations. Furthermore, we derive a numerical...
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