We study constructive discrete multimarginal optimal transport (MOT) among $m$ distributions on $n$ points, where the cost tensor $C$ has $N=n^m$ entries. For additive accuracy $\varepsilon$, let $\kappa=\max\{1,(\max C-\min C)/\varepsilon\}$. Classically, we give two algorithms that return exactly feasible additive-$\...
Brandon Augustino, Yue Sun, Atithi Acharya et al.· 0 citations
SF-NorMuon, a schedule-free spectral optimizer that closes the performance gap with tuned AdamW baselines, makes horizon-free optimization more practical, taking a step towards truly open-ended, continual learning.
We establish a near-linear quantum query lower bound for high-accuracy convex optimization over an explicit family of $n$-dimensional ellipsoids. We focus on linear optimization with an explicitly given objective, where the feasible set is accessed through a membership oracle. We show that any algorithm that, for every...
Brandon Augustino, Shouvanik Chakrabarti, Enrico Fontana et al.· 1 citation
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