This work establishes a (cid:101) Ω ( 𝑑 5 / 4 √ 𝑇 ) lower bound on the minimax expected regret of stochastic bandit convex optimization of 1-Lipschitz functions on the Euclidean ball, establishing that stochastic bandit convex optimization is fundamentally harder than linear bandits.
The proposed algorithm is the first in the literature that achieves the $O((L/\varepsilon)^{1/3})$ first-order oracle complexity, although its current version is not necessarily practical for implementation.
The same accuracy exponent holds beyond tensor update rules, even for randomized queries and arbitrary feasible outputs, for smooth convex--concave minimax optimization.
Yan-Yi Li, Hai-Han Zhang, Chen-Heng Zhang et al.· 0 citations
A variant of stochastic gradient descent with initial regularization with initial regularization is analyzed and dimension-free upper bounds on its expected excess risk for the squared loss are derived.
We study first-order black-box convex optimization over an $\ell_p$-ball for objectives Lipschitz in the $\ell_q$-norm, solving in the affirmative the nonsmooth version of the COLT open question (Guz15b) on whether the geometry of a smaller feasible set ($p<q$) can improve convergence rates in convex optimization, and...
David Martínez-Rubio, Brian Bullins, Cristóbal Guzmán et al.· 1 citation
An algorithm for composite optimization problems of the form min x f (x) + g(T x), where f is smooth and g may be non-smooth is proposed, which leverages the Moreau envelope to smooth the non-smooth component while adapting to problem geometry through linear minimization oracles.
A global iteration complexity bound is established for the smallest gradient norm among the first $k$ iterates for the smallest gradient norm among the first $k$ iterates when the initial sublevel set is bounded.
Lijun Ding, Jin-Wen Yang, Baoyu Zhou· 0 citations
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