We study deterministic adaptive optimization of globally $\beta$-smooth, $\mu$-strongly convex functions using exact scalar function values. Queries and outputs lie in $B_2^d(R)$, and the minimizer lies in $B_2^d(R/2)$. Set $\kappa=\beta/\mu$, $Q=\beta R^2/\epsilon$, and $D_d=(d/\log(ed))^{1/3}$. For sufficiently large...
Wen-Dao Wu, Hai-Han Zhang, Chen-Heng Zhang et al.· 0 citations
We establish a randomized first-order lower bound for finding an $\epsilon$-stationary point, $\|\nabla f(x)\|\le \epsilon$, of a nonconvex function with initial gap at most $\Delta$, $L_1$-Lipschitz gradient, and $L_2$-Lipschitz Hessian. Each oracle call returns the exact function value and gradient. Let $Q_{\mathrm{r...
Hai-Han Zhang, Wen-Dao Wu, Chen-Heng Zhang et al.· 0 citations
We prove a joint stochastic zeroth-order lower bound for Goldstein stationarity on a Euclidean query ball, even when the ball is guaranteed to contain a stationary point. In dimension $d$, let $f=\mathbb{E}[F(\cdot;\xi)]$, assume $\mathbb{E}[\operatorname{Lip}(F(\cdot;\xi))^2]\le L_0^2$, and bound the initial objective...
Hai-Han Zhang, Wen-Dao Wu, Chen-Heng Zhang et al.· 0 citations
We establish tight randomized higher-order oracle complexity for finding first-order stationary points of nonconvex finite sums. Let $n$ be the number of components, $\Delta>0$ the initial objective-gap bound, $L_p>0$ an individual $p$-th derivative Lipschitz bound, and $\epsilon>0$ the target gradient norm. For every...
Wen-Dao Wu, Hai-Han Zhang, Chen-Heng Zhang et al.· 0 citations
We characterize the fresh-gradient oracle complexity of smooth nonconvex-strongly-concave minimax optimization, with matching upper and lower bounds up to logarithmic factors. Let $\Phi(x)=\max_y f(x,y)$, where $f$ is jointly $L$-smooth and $\mu$-strongly concave in $y$ on unconstrained Euclidean domains, and set $\kap...
Wen-Dao Wu, Hai-Han Zhang, Chen-Heng Zhang et al.· 0 citations
We establish matching polynomial query bounds for low-rank approximation from exact matrix--vector products. Given an unknown matrix $A\in\mathbb{R}^{m\times n}$, at each step a randomized algorithm chooses either $v\in\mathbb{R}^n$ and receives $Av$, or $u\in\mathbb{R}^m$ and receives $A^\top u$. The choice may depend...
Hai-Han Zhang, Wen-Dao Wu, Chen-Heng Zhang et al.· 0 citations
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 single fixed smooth convex hard instance is constructed using a Moreau-smoothed biased max chain, an exact prefix-shielding mechanism, and batched delayed rotations to preserve consistency with the full adaptive transcript and establish the optimality of the square-root complexity branch for deterministic bounded-que...
Wen-Dao Wu, Hai-Han Zhang, Chen-Heng Zhang et al.· 0 citations
Push notification is a critical recommendation scenario on large-scale platforms, allowing the system to proactively reach users outside the application to improve long-term re-engagement. However, designing an optimal push system requires handling a complex action space for the"whether and when"delivery problem under...
Zhao-Yu Zhang, Qingying Chen, Chunyuan Zheng et al.· 0 citations
In marketing, optimizing subsidy allocation to maximize overall profits is of substantial economic importance. Prior research has employed treatment effect estimation techniques to identify subsidy-sensitive items and design corresponding allocation strategies. However, more accurate treatment effect estimations do not...
Xiang Li, Yanghao Xiao, Chun-Yuan Zheng et al.· Annual International ACM SIG...· 2 citations
Collected data with non-random missing labels poses a widely recognized challenge for unbiased learning. For example, in recommender systems, users are free to choose whether or not to rate an item. To achieve unbiased learning under MNAR data, a variety of methods have been proposed, such as reweighting and imputation...
Chunyuan Zheng, Xiang Li, Hang Pan et al.· Proceedings of the 32nd ACM...· 0 citations
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