Luxuan Li

Luxuan Li, Chunfeng Cui, Xiao Wang

In this paper, we study a structured class of nonconvex constrained stochastic problems with difference-of-convex (DC) regularization, where the feasible set is possibly nonconvex and the concave part of the DC regularizer is allowed to be nonsmooth. The fundamental challenge lies in maintaining feasibility for nonconvex constraints while achieving favorable oracle complexity. Although single-loop algorithms efficiently solve unconstrained DC optimization problems, their potential for constrained optimization with DC structure remains largely unexplored. To address this gap, we develop MoSSP, a Momentum-based Single-loop Stochastic Penalty method for such problems with provable complexity guarantees. The key idea is to apply a single stochastic proximal-gradient step to the Moreau envelope of the penalty plus the convex DC part, with the concave part's proximal mapping computed in parallel. We derive two algorithm variants: a Polyak-momentum version with $O(\varepsilon^{-4})$ oracle complexity for finding stochastic $\varepsilon$-KKT points, and an improved $O(\varepsilon^{-3})$ version incorporating recursive momentum. Experimental results demonstrate the effectiveness of the proposed algorithms.

Luxuan Li, Tao Kong, Fuchun Sun et al.

Detecting actions in videos is an important yet challenging task. Previous works usually utilize (a) sliding window paradigms, or (b) per-frame action scoring and grouping to enumerate the possible temporal locations. Their performances are also limited to the designs of sliding windows or grouping strategies. In this paper, we present a simple and effective method for temporal action proposal generation, named Deep Point-wise Prediction (DPP). DPP simultaneously predicts the action existing possibility and the corresponding temporal locations, without the utilization of any handcrafted sliding window or grouping. The whole system is end-to-end trained with joint loss of temporal action proposal classification and location prediction. We conduct extensive experiments to verify its effectiveness, generality and robustness on standard THUMOS14 dataset. DPP runs more than 1000 frames per second, which largely satisfies the real-time requirement. The code is available at https://github.com/liluxuan1997/DPP.

Luxuan Li, Xiao Wang, Chunfeng Cui

Deep hashing converts high-dimensional feature vectors into compact binary codes, enabling efficient large-scale retrieval. A fundamental challenge in deep hashing stems from the discrete nature of quantization in generating the codes. W-type regularizations, such as $||z|-1|$, have been proven effective as they encourage variables toward binary values. However, existing methods often directly optimize these regularizations without convergence guarantees. While proximal gradient methods offer a promising solution, the coupling between W-type regularizers and neural network outputs results in composite forms that generally lack closed-form proximal solutions. In this paper, we present a stochastic primal-dual hashing algorithm, referred to as DualHash, that provides rigorous complexity bounds. Using Fenchel duality, we partially transform the nonconvex W-type regularization optimization into the dual space, which results in a proximal operator that admits closed-form solutions. We derive two algorithm instances: a momentum-accelerated version with $\mathcal{O}(\varepsilon^{-4})$ complexity and an improved $\mathcal{O}(\varepsilon^{-3})$ version using variance reduction. Experiments on three image retrieval databases demonstrate the superior performance of DualHash.