In [AS21], Axiotis and Sviridenko conjectured that the linear dependence on the restricted condition number in sparse convex optimization cannot be improved by a polynomial-time algorithm. We establish their conjectured lower bound for least-squares objectives, conditional on the randomized exact-volume Small-Set Expansion Hypothesis in the weighted regular-graph formulation of Raghavendra, Steurer, and Tulsiani [RST12].
arXiv:2511.02821v2 Announce Type: replace-cross
Abstract: We develop new accelerated first-order algorithms in the Frank-Wolfe (FW) family for minimizing smooth convex functions over compact convex s...
By Dan Garber
arXiv:2609.38375v1 Announce Type: new
Abstract: Can a constant number of linear minimizations per round improve on the $T^{3/4}$ regret rate of online Frank-Wolfe on general convex sets? Weibel et al...
By Mohit Sinha
arXiv:2602. 20376v3 Announce Type: replace-cross Abstract: We study the problem of maximizing a complex-valued quadratic form over the $K^{\text{th}}$ roots of unity.
By Ria Stevens, Fangshuo Liao, Barbara Su, Thanasis Hadjidimoulas, Jianqiang Li, Anastasios Kyrillidis
The paper establishes the optimal incremental first‑order oracle (IFO) complexity for nonconvex finite‑sum optimization under individual smoothness, proving a matching lower bound that closes a previously missing √{n} factor. It also refines the analysis of the PAGE algorithm under the global Polyak‑Lojasiewicz condition, providing tighter guarantees for different ranges of the condition number. The authors introduce a novel dense weak hiding construction that yields these lower bounds and demonstrates the limits of existing methods.
By Yuxing Peng, Zhiqing Tang, Weijia Jia
arXiv:2610. 00545v1 Announce Type: new Abstract: We study adversarial online maximization of nonnegative, non-monotone DR-submodular functions over compact convex down-closed sets.
By Vaneet Aggarwal
arXiv:2608. 26552v1 Announce Type: cross Abstract: Randomized sketch-and-solve algorithms accelerate overconstrained $\ell_2$ regression by replacing the input with a smaller problem.
By Zhao Song, Lichen Zhang
arXiv:2609.09524v1 Announce Type: cross
Abstract: We study the oracle complexity of computing a point with small fixed-point residual $\|T(x)-x\| \leq \epsilon$, for a general norm $\|\cdot\|$ and a...
By Jelena Diakonikolas, Crist\'obal Guzm\'an, David Mart\'inez-Rubio
The paper studies online convex optimization when the learner can only query an exact linear optimization oracle. It establishes a dimension‑free minimax expected regret bound of θ(GD max{√T, T/(1+min{Q,BT})^{1/4}}) for convex G‑Lipschitz losses, where Q is the total oracle budget and B the per‑round limit. The authors provide matching lower and upper bounds, showing how strict per‑round or total‑budget constraints affect the achievable regret, and extend the analysis to smooth losses with curvature‑dependent bounds.
By Vaneet Aggarwal
arXiv:2609. 30877v1 Announce Type: cross Abstract: We study whether the linear condition-number dependence in the stochastic complexity of SAPD+ is necessary for nonconvex-strongly-concave minimax optimization.
By Qihao Zhou
arXiv:2609. 20687v1 Announce Type: cross Abstract: 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 matching prior lower bounds up to logarithmic factors.
By David Mart\'inez-Rubio, Brian Bullins, Crist\'obal Guzm\'an, Mathieu Molina
Randomized sketch-and-solve algorithms accelerate overconstrained $\ell_2$ regression by replacing the input with a smaller problem. Standard subspace embeddings guarantee that the cost of the regress...