In this paper, we establish tight lower bounds for Byzantine-robust distributed first-order stochastic methods in both strongly convex and non-convex stochastic optimization. We reveal that when the distributed nodes have heterogeneous data, the convergence error comprises two components: a non-vanishing Byzantine error and a vanishing optimization error. We establish the lower bounds on the Byzantine error and on the minimum number of queries to a stochastic gradient oracle for achieving an arbitrarily small optimization error. Nevertheless, we also identify significant discrepancies between our established lower bounds and the existing upper bounds. To fill this gap, we leverage the techniques of Nesterov's acceleration and variance reduction to develop novel Byzantine-robust distributed stochastic optimization methods that provably match these lower bounds, up to at most logarithmic factors, implying that our established lower bounds are tight.

Online Action Detection (OAD), which predicts the ongoing human action from a streaming video, is an important task in multimedia analysis. Compared with offline action detection, OAD only uses historical and current frames without any access to future information, resulting in limited performances. Current OAD methods obtain future information by training an additional future anticipation task and suffer from low efficiency. To address the low efficiency problem, we propose to integrate future information into visual representations for OAD. Specifically, we learn future representations through a contrastive-learning-based method. Further, two novel sampling strategies, multiple scale sampling and timeline overlap sampling, are introduced to enhance our method. The experimental results show that our method significantly improves inference efficiency and achieves promising effectiveness performances on two popular OAD benchmarks.

Identifying user consumption intention from social media is of great interests to downstream applications. Since such task is domain-dependent, deep neural networks have been applied to learn transferable features for adapting models from a source domain to a target domain. A basic idea to solve this problem is reducing the distribution difference between the source domain and the target domain such that the transfer error can be bounded. However, the feature transferability drops dramatically in higher layers of deep neural networks with increasing domain discrepancy. Hence, previous work has to use a few target domain annotated data to train domain-specific layers. In this paper, we propose a deep transfer learning framework for consumption intention identification, to reduce the data bias and enhance the transferability in domain-specific layers. In our framework, the representation of the domain-specific layer is mapped to a reproducing kernel Hilbert space, where the mean embeddings of different domain distributions can be explicitly matched. By using an optimal tree kernel method for measuring the mean embedding matching, the domain discrepancy can be effectively reduced. The framework can learn transferable features in a completely unsupervised manner with statistical guarantees. Experimental results on five different domain datasets show that our approach dramatically outperforms state-of-the-art baselines, and it is general enough to be applied to more scenarios. The source code and datasets can be found at http://ir.hit.edu.cn/$\scriptsize{\sim}$xding/index\_english.htm.