arXiv subjects

Qihao Zhou

Publications and source records attributed to Qihao Zhou.

11 recordsLinked to original sources

arXiv2026

Near-Optimal Complexity of Finding Approximate Local Minima of Nonconvex Finite Sums

We study the component-oracle complexity of finding approximate local minima of nonconvex finite sums under mean-squared averaged smoothness with parameter $L$ and a $ρ$-Lipschitz average Hessian. Each query returns the value, gradient, and one Hessian-vector product of a component. We show that the complexity in the high-accuracy regime $\varepsilon\le c_0L^2/(nρ)$ is $\tildeΘ(n^{3/4}L^{1/2}ρ^{1/4}Δ\varepsilon^{-7/4})$ for a sufficiently large initial gap $Δ$. We attain the upper bound by adapting the inverse solver and eigenvector routine of FastCubic to averaged smoothness. Our lower bound assigns the bridge edges of a nested chain to random components; a replicated spectral construction gives the same bound for unrestricted randomized algorithms. Under individual smoothness, a factor of $n^{1/4}$ remains for $\varepsilon\le cL^2/(n^2ρ)$, up to logarithmic factors. In the complementary low-accuracy regime, we propose PathVR, which uses $\tilde O(n+\sqrt{n}LΔ\varepsilon^{-2})$ queries and matches a lower bound from dense weak hiding.

math.OC↗

arXiv2026

Accelerating Finite-Sum Bilevel Optimization with Fully First-Order Oracles

We study nonconvex--strongly-convex bilevel optimization with finite-sum objectives and fully first-order oracles. We propose Sampled Implicit Corrections for Bilevel Optimization (SICBO), which combines a penalty approximation with variance-reduced corrections for the lower-level variables. Under componentwise lower strong convexity, SICBO finds a point $x$ satisfying $\mathbb{E}\|\nablaΦ(x)\|^2\le\varepsilon^2$ within $\tilde{O}(N+\sqrt{N}κ^{7/2}\varepsilon^{-2})$ component-gradient calls, where $N$ is the total number of components and $κ$ is the normalized lower-level condition number. The bound achieves square-root finite-sum dependence using only gradients and preserves the best known deterministic fully first-order condition-number exponent for smooth problems. Our improvement follows from a curvature-dependent bound for nonlinear correction errors, which permits epochs of length $\tildeΘ(\sqrt{N/κ})$ with batches of size $\tildeΘ(\sqrt{Nκ})$. A single-level reduction shows that the dependence on $N$ and $\varepsilon$ is optimal up to logarithmic factors for fixed $κ$.

math.OC↗

arXiv2026

Envelope Cubic Regularized Newton Method for Nonconvex-Strongly-Concave Minimax Optimization

We study nonconvex-strongly-concave minimax problem $\min_{\mathbf{x}\in\mathbb{R}^{d_x}}\max_{\mathbf{y}\in\mathbb{R}^{d_y}}f(\mathbf{x},\mathbf{y})$ in which the objective has $ρ$-Lipschitz Hessian and condition number $κ$. We propose envelope cubic regularized Newton method (ECRN) which applies a refined inexact cubic regularized Newton method to the envelope of the primal function $Φ(\cdot) : = \max_{\mathbf{y}\in\mathbb{R}^{d_y}}f(\cdot,\mathbf{y})$. We show that ECRN finds approximate second-order stationary points of $Φ(\cdot)$ with $\widetilde{\mathcal{O}}(\sqrtρ\,κ^{3/4}\varepsilon^{-3/2})$ second-order oracles, improving the condition number dependence $\mathcal{O}(κ^{2})$ achieved by the best known second-order methods. Our improvement comes from the key observation that the Hessian Lipschitz parameter of the envelope is $\mathcal{O}(ρκ^{3/2})$, which is sharper than the order of $\mathcal{O}(ρκ^{3})$ for the function $Φ(\cdot)$. We also conduct a lower bound on second-order methods to show that our complexity is optimal up to a logarithmic factor.

math.OC↗

arXiv2026

Near-Optimal Complexity of Finite-Sum Nonconvex-Strongly-Concave Minimax Optimization

We characterize, up to logarithmic factors, the minimax expected query complexity of finite-sum nonconvex-strongly-concave optimization under mean-squared averaged smoothness. For randomized zero-respecting incremental first-order algorithms, the complexity is $\tildeΘ(n+\min\{\sqrt{n}\,κ,n^{3/4}\sqrtκ\}\,LΔ\varepsilon^{-2})$ throughout $κ=L/μ\ge1$, under exact dual initialization and for $0<\varepsilon^2\le c_0LΔ$, where $c_0>0$ is universal. This characterization is our main result. A dual-chain construction provides the lower bound and matches the existing Catalyst upper bound for $κ\ge\sqrt{n}$. For $1\leκ\le\sqrt{n}$, we introduce recursive proximal descent-ascent (RPDA), which retains a recursive gradient estimator across proximal subproblems and attains $\tilde{O}(n+\sqrt{n}\,κLΔ\varepsilon^{-2})$ with a fixed query budget. Both upper bounds guarantee an expected squared primal gradient at most $\varepsilon^2$. Under individual smoothness, we also prove $Ω(n+\min\{κ,\sqrt{nκ}\}\,LΔ\varepsilon^{-2})$ for every $κ\ge1$. It matches the polynomial upper rate for a bilinear subclass when $κ\ge n$; the intermediate-condition-number gap remains open.

math.OC↗

arXiv2026

Optimal Oracle Complexity for Finite-Sum Monotone Inclusions

We present an oracle-optimal method for finite-sum monotone inclusions under mean-square Lipschitz continuity. Our switching regularization method finds a point $y$ and a certificate $g\in G(y)$ with $(\mathbb{E}\|F(y)+g\|^2)^{1/2}\le\varepsilon$ using $\mathcal{O}(n+\sqrt{n}LR/\varepsilon)$ expected component evaluations and resolvent evaluations. It removes the additive $n\log n$ cost of restarting a variance-reduced solver at every regularization stage by switching to a centered stochastic proximal iteration at regularization strength $L/\sqrt{n}$. Carrying an operator estimate between the remaining stages limits their total cost to $\mathcal{O}(n)$. A matching $Ω(n+\sqrt{n}LR/\varepsilon)$ lower bound holds for randomized linear-span component-oracle algorithms with adaptive stopping and expected query budgets. Thus, for $0<\varepsilon\le LR/2$, our method attains the optimal worst-case expected component complexity in this oracle model, up to universal constants.

math.OC↗

arXiv2026

Tight Stochastic Condition-Number Dependence in Nonconvex-Strongly-Concave Minimax Optimization

We study whether the linear condition-number dependence in the stochastic complexity of SAPD+ is necessary for nonconvex-strongly-concave minimax optimization. For jointly $L$-smooth objectives with dual strong-concavity parameter $μ$, we prove a lower bound that matches the SAPD+ upper bound under the same Moreau-envelope stationarity criterion and the same primal-dual initialization gap. Specifically, when $σ\ge\varepsilon$, the worst-case complexity of zero-respecting algorithms is $Θ(κLGσ^2\varepsilon^{-4})$ in the stated accuracy regime, where $κ=L/μ$, $G$ bounds the initial primal-dual gap, and $σ^2$ bounds the variance of a general unbiased first-order oracle. The lower bound is realized on a smooth problem class with a bounded dual box. Our construction routes each link of a nonconvex zero-chain through a dual gradient of magnitude proportional to $\varepsilon/\sqrtκ$, while an undiscovered primal coordinate prevents stationarity. It also yields the primal-gradient lower bound $Ω(LΔ(\sqrtκ\varepsilon^{-2}+κσ^2\varepsilon^{-4}))$ after combination with the known deterministic bound, where $Δ$ bounds the initial primal function gap.

math.OC↗

arXiv2026

HFS-TriNet: A Three-Branch Collaborative Feature Learning Network for Prostate Cancer Classification from TRUS Videos

Transrectal ultrasound (TRUS) imaging is a cost-effective and non-invasive modality widely used in the diagnosis of prostate cancer. The computer-aided diagnosis (CAD) relying on TRUS images has been extensively investigated recently. Compared to static images, TRUS video provides richer spatial-temporal information, which make it a promising alternative for improving the accuracy and robustness of CAD systems. However, TRUS video analysis also introduces new challenges. These include information redundancy, which increases computational costs; high intra- and inter-class similarity, which complicates feature extraction; and a low signal-to-noise ratio, which hinders the identification of clinically relevant information. To address these problems, we propose a heuristic frame selection (HFS) and a three-branch collaborative feature learning network (HFS-TriNet) for prostate cancer classification from TRUS videos. Specifically, selecting a clip of video frames at intervals for training can mitigate redundancy. The HFS strategy dynamically initializes the starting point of each training clip, which ensures that the sampled clips span the entire video sequence. For better feature extraction, besides a regular ResNet50 branch, we also utilize 1) a large model branch based a pre-trained medical segment anything model (SAM) to extract deep features of each frame and a normalization-based attention module to explore the temporal consistency; and 2) a wavelet transform convolutional residual (WTCR) branch that extracts lesion edge information in the high-frequency domain and performs denoising in the low-frequency domain.

cs.CV↗

arXiv2024

Near-Optimal Distributed Minimax Optimization under the Second-Order Similarity

This paper considers the distributed convex-concave minimax optimization under the second-order similarity. We propose stochastic variance-reduced optimistic gradient sliding (SVOGS) method, which takes the advantage of the finite-sum structure in the objective by involving the mini-batch client sampling and variance reduction. We prove SVOGS can achieve the $\varepsilon$-duality gap within communication rounds of ${\mathcal O}(δD^2/\varepsilon)$, communication complexity of ${\mathcal O}(n+\sqrt{n}δD^2/\varepsilon)$, and local gradient calls of $\tilde{\mathcal O}(n+(\sqrt{n}δ+L)D^2/\varepsilon\log(1/\varepsilon))$, where $n$ is the number of nodes, $δ$ is the degree of the second-order similarity, $L$ is the smoothness parameter and $D$ is the diameter of the constraint set. We can verify that all of above complexity (nearly) matches the corresponding lower bounds. For the specific $μ$-strongly-convex-$μ$-strongly-convex case, our algorithm has the upper bounds on communication rounds, communication complexity, and local gradient calls of $\mathcal O(δ/μ\log(1/\varepsilon))$, ${\mathcal O}((n+\sqrt{n}δ/μ)\log(1/\varepsilon))$, and $\tilde{\mathcal O}(n+(\sqrt{n}δ+L)/μ)\log(1/\varepsilon))$ respectively, which are also nearly tight. Furthermore, we conduct the numerical experiments to show the empirical advantages of proposed method.

math.OC↗

arXiv2021

Federated Reinforcement Learning: Techniques, Applications, and Open Challenges

This paper presents a comprehensive survey of Federated Reinforcement Learning (FRL), an emerging and promising field in Reinforcement Learning (RL). Starting with a tutorial of Federated Learning (FL) and RL, we then focus on the introduction of FRL as a new method with great potential by leveraging the basic idea of FL to improve the performance of RL while preserving data-privacy. According to the distribution characteristics of the agents in the framework, FRL algorithms can be divided into two categories, i.e. Horizontal Federated Reinforcement Learning (HFRL) and Vertical Federated Reinforcement Learning (VFRL). We provide the detailed definitions of each category by formulas, investigate the evolution of FRL from a technical perspective, and highlight its advantages over previous RL algorithms. In addition, the existing works on FRL are summarized by application fields, including edge computing, communication, control optimization, and attack detection. Finally, we describe and discuss several key research directions that are crucial to solving the open problems within FRL.

cs.LG↗

arXiv2019

Design and Implementation of Open LoRa for IoT

Long Range (LoRa) network is emerging as one of the most promising Low Power Wide Area (LPWA) networks, since it enables the energy-constraint devices distributed over wide areas to establish affordable connectivity. However, how to implement a cost-effective and flexible LoRa network is still an open challenge. This paper aims at exposing a feasible solution of design and implementation, allowing users to conveniently build a private LoRa network for various IoT applications. Firstly, several typical application scenarios of LoRa network are discussed. Then, the LoRa system architecture is presented with the functionality of each component. We address the hardware design and implementation of LoRa Gateway, which is the bridge between LoRa nodes and LoRa network server. Especially, the paper contributes by proposing an improved software architecture of LoRa network server whose source codes are open on GitHub. Under the architecture, LoRa network server is divided into four decoupled modules and uses the messaging system based on streaming data for the interaction between modules to guarantee scalability and flexibility. Finally, extensive experiments are conducted to evaluate the performance of LoRa networks in typical environments.

cs.NI↗

arXiv2019

A Novel Rate and Channel Control Scheme Based on Data Extraction Rate for LoRa Networks

Long Range (LoRa) has become one of the most popular Low Power Wide Area (LPWA) technologies, which provides a desirable trade-off among communication range, battery life, and deployment cost. In LoRa networks, several transmission parameters can be allocated to ensure efficient and reliable communication. For example, the configuration of the spreading factor allows tuning the data rate and the transmission distance. However, how to dynamically adjust the setting that minimizes the collision probability while meeting the required communication performance is an open challenge. This paper proposes a novel Data Rate and Channel Control (DRCC) scheme for LoRa networks so as to improve wireless resource utilization and support a massive number of LoRa nodes. The scheme estimates channel conditions based on the short-term Data Extraction Rate (DER), and opportunistically adjusts the spreading factor to adapt the variation of channel conditions. Furthermore, the channel control is carried out to balance the link load of all available channels with the global information of the channel usage, which is able to lower the access collisions under dense deployments. Our experiments demonstrate that the proposed DRCC performs well on improving the reliability and capacity compared with other spreading factor allocation schemes in dense deployment scenarios.

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