Zijian Liu

Yunsheng Pang, Zijian Liu, Yudong Li et al.

Slate recommendation, which presents users with a ranked item list in a single display, is ubiquitous across mainstream online platforms. Recent advances in generative models have shown significant potential for this task via autoregressive modeling of discrete semantic ID sequences. However, existing methods suffer from three key limitations: entangled item tokenization, inefficient sequential decoding, and the absence of holistic slate planning. These issues often result in substantial inference overhead and inadequate alignment with diverse user preferences and practical business requirements, hindering the industrial deployment of generative slate recommendation systems. In this paper, we propose HiGR, an efficient generative slate recommendation framework that integrates hierarchical planning with listwise preference alignment. First, we design an auto-encoder incorporating residual quantization and contrastive constraints, which tokenizes items into semantically structured IDs to enable controllable generation. Second, HiGR decouples the generation process into two stages: a list-level planning stage to capture global slate intent, and an item-level decoding stage to select specific items, effectively reducing the search space and enabling efficient generation. Third, we introduce a multi-objective and listwise preference alignment mechanism that enhances slate quality by leveraging implicit user feedback. Extensive experiments have validated the effectiveness of our HiGR method. Notably, it outperforms state-of-the-art baselines by over 10\% in offline recommendation quality while achieving a $5\times$ inference speedup. Furthermore, we have deployed HiGR on a commercial platform under Tencent (serving hundreds of millions of users), and online A/B tests show that it increases average watch time and average video plays by 1.22\% and 1.73\%, respectively.

Zijian Liu, Zhengyuan Zhou

In the past several years, the last-iterate convergence of the Stochastic Gradient Descent (SGD) algorithm has triggered people's interest due to its good performance in practice but lack of theoretical understanding. For Lipschitz convex functions, different works have established the optimal $O(\log(1/δ)\log T/\sqrt{T})$ or $O(\sqrt{\log(1/δ)/T})$ high-probability convergence rates for the final iterate, where $T$ is the time horizon and $δ$ is the failure probability. However, to prove these bounds, all the existing works are either limited to compact domains or require almost surely bounded noises. It is natural to ask whether the last iterate of SGD can still guarantee the optimal convergence rate but without these two restrictive assumptions. Besides this important question, there are still lots of theoretical problems lacking an answer. For example, compared with the last-iterate convergence of SGD for non-smooth problems, only few results for smooth optimization have yet been developed. Additionally, the existing results are all limited to a non-composite objective and the standard Euclidean norm. It still remains unclear whether the last-iterate convergence can be provably extended to wider composite optimization and non-Euclidean norms. In this work, to address the issues mentioned above, we revisit the last-iterate convergence of stochastic gradient methods and provide the first unified way to prove the convergence rates both in expectation and in high probability to accommodate general domains, composite objectives, non-Euclidean norms, Lipschitz conditions, smoothness, and (strong) convexity simultaneously. Additionally, we extend our analysis to obtain the last-iterate convergence under heavy-tailed noises.