Li Shen

Parvin Nazari, Bojian Hou, Davoud Ataee Tarzanagh et al.

Online bilevel optimization (OBO) is a powerful framework for machine learning problems where both outer and inner objectives evolve over time, requiring dynamic updates. Current OBO approaches rely on deterministic \textit{window-smoothed} regret minimization, which may not accurately reflect system performance when functions change rapidly. In this work, we introduce a novel search direction and show that both first- and zeroth-order (ZO) stochastic OBO algorithms leveraging this direction achieve sublinear {stochastic bilevel regret without window smoothing}. Beyond these guarantees, our framework enhances efficiency by: (i) reducing oracle dependence in hypergradient estimation, (ii) updating inner and outer variables alongside the linear system solution, and (iii) employing ZO-based estimation of Hessians, Jacobians, and gradients. Experiments on online parametric loss tuning and black-box adversarial attacks validate our approach.

Anke Tang, Li Shen, Yong Luo et al.

Solving multi-objective optimization problems for large deep neural networks is a challenging task due to the complexity of the loss landscape and the expensive computational cost of training and evaluating models. Efficient Pareto front approximation of large models enables multi-objective optimization for various tasks such as multi-task learning and trade-off analysis. Existing algorithms for learning Pareto set, including (1) evolutionary, hypernetworks, and hypervolume-maximization methods, are computationally expensive and have restricted scalability to large models; (2) Scalarization algorithms, where a separate model is trained for each objective ray, which is inefficient for learning the entire Pareto set and fails to capture the objective trade-offs effectively. Inspired by the recent success of model merging, we propose a practical and scalable approach to Pareto set learning problem via mixture of experts (MoE) based model fusion. By ensembling the weights of specialized single-task models, the MoE module can effectively capture the trade-offs between multiple objectives and closely approximate the entire Pareto set of large neural networks. Once the routers are learned and a preference vector is set, the MoE module can be unloaded, thus no additional computational cost is introduced during inference. We conduct extensive experiments on vision and language tasks using large-scale models such as CLIP-ViT and GPT-2. The experimental results demonstrate that our method efficiently approximates the entire Pareto front of large models. Using only hundreds of trainable parameters of the MoE routers, our method even has lower memory usage compared to linear scalarization and algorithms that learn a single Pareto optimal solution, and are scalable to both the number of objectives and the size of the model.