We propose efficient methods for solving stochastic simple bilevel optimization problems with convex inner levels, where the goal is to minimize an outer stochastic objective function subject to the solution set of an inner stochastic optimization problem. Existing methods often rely on costly projection or linear optimization oracles over complex sets, limiting their scalability. To overcome this, we propose an iteratively regularized conditional gradient approach that leverages linear optimization oracles exclusively over the base feasible set. Our proposed methods employ a vanishing regularization sequence that progressively emphasizes the inner problem while biasing towards desirable minimal outer objective solutions. In the one-sample stochastic setting and under standard convexity assumptions, we establish non-asymptotic convergence rates of O(t 1/4)for both the outer and inner objectives. In the finite-sum setting with a mini-batch scheme, the corresponding rates become O(t 1/2). When the outer objective is nonconvex, we prove nonasymptotic convergence rates of O(t 1/7) for both the outer and inner objectives in the one-sample stochastic setting, and O(t 1/4) in the finite-sum setting. Experimental results on over-parametrized regression and dictionary learning tasks demonstrate the practical advantages of our approach over existing methods, confirming our theoretical findings.

Algorithm unrolling methods have proven powerful for solving the regularized least squares problem in computational magnetic resonance imaging (MRI). These approaches unfold an iterative algorithm with a fixed number of iterations, typically alternating between a neural network-based proximal operator for regularization, a data fidelity operation and auxiliary updates with learnable parameters. While the connection to optimization methods dictate that the proximal operator network should be shared across unrolls, this can introduce artifacts or blurring. Heuristically, practitioners have shown that using distinct networks may be beneficial, but this significantly increases the number of learnable parameters, making it challenging to prevent overfitting. To address these shortcomings, by taking inspirations from proximal operators with varying thresholds in approximate message passing (AMP) and the success of time-embedding in diffusion models, we propose a time-embedded algorithm unrolling scheme for inverse problems. Specifically, we introduce a novel perspective on the iteration-dependent proximal operation in vector AMP (VAMP) and the subsequent Onsager correction in the context of algorithm unrolling, framing them as a time-embedded neural network. Similarly, the scalar weights in the data fidelity operation and its associated Onsager correction are cast as time-dependent learnable parameters. Our extensive experiments on the fastMRI dataset, spanning various acceleration rates and datasets, demonstrate that our method effectively reduces aliasing artifacts and mitigates noise amplification, achieving state-of-the-art performance. Furthermore, we show that our timeembedding strategy extends to existing algorithm unrolling approaches, enhancing reconstruction quality without increasing the computational complexity significantly.

Binary (0-1) integer programming (BIP) is pivotal in scientific domains requiring discrete decision-making. As the advance of AI computing, recent works explore neural network-based solvers for integer linear programming (ILP) problems. Yet, they lack scalability for tackling nonlinear challenges. To handle nonlinearities, state-of-the-art Branch-and-Cut solvers employ linear relaxations, leading to exponential growth in auxiliary variables and severe computation limitations. To overcome these limitations, we propose BIPNN (Binary Integer Programming Neural Network), an unsupervised learning framework to solve nonlinear BIP problems via hypergraph neural networks (HyperGNN). Specifically, (I) BIPNN reformulates BIPs-constrained, discrete, and nonlinear (sin, log, exp) optimization problems-into unconstrained, differentiable, and polynomial loss functions.

Existing methods for solving Riemannian bilevel optimization (RBO) problems require prior knowledge of the problem's first-and second-order information and curvature parameter of the Riemannian manifold to determine step sizes, which poses practical limitations when these parameters are unknown or computationally infeasible to obtain. In this paper, we introduce the Adaptive Riemannian Hypergradient Descent (AdaRHD) algorithm for solving RBO problems. To our knowledge, AdaRHD is the first method to incorporate a fully adaptive step size strategy that eliminates the need for problem-specific parameters in RBO. We prove that AdaRHD achieves an O(1/ϵ)iteration complexity for finding an ϵ-stationary point, thus matching the complexity of existing non-adaptive methods. Furthermore, we demonstrate that substituting exponential mappings with retraction mappings maintains the same complexity bound. Experiments demonstrate that AdaRHD achieves comparable performance to existing non-adaptive approaches while exhibiting greater robustness.

Recent advances in 3DGaussian Splatting have shown remarkable potential for novel view synthesis. However, most existing large-scale scene reconstruction methods rely on the divide-and-conquer paradigm, which often leads to the loss of global scene information and requires complex parameter tuning due to scene partitioning and local optimization. To address these limitations, we propose MixGS, a novel holistic optimization framework for large-scale 3D scene reconstruction. MixGS models the entire scene holistically by integrating camera pose and Gaussian attributes into a view-aware representation, which is decoded into fine-detailed Gaussians. Furthermore, a novel mixing operation combines decoded and original Gaussians to jointly preserve global coherence and local fidelity. Extensive experiments on large-scale scenes demonstrate that MixGS achieves state-of-the-art rendering quality and competitive speed, while significantly reducing computational requirements, enabling large-scale scene reconstruction training on a single 24GBVRAMGPU.

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks but require substantial computational resources, limiting their deployment in resource-constrained environments. While one-shot pruning methods can reduce model size without expensive retraining, they typically optimize for single objectives, ignoring LLMs' multi-faceted applications. We introduce Multi-Objective One-Shot Pruning (MOSP), which formulates LLM pruning as a multi-objective optimization problem. MOSP efficiently generates a Pareto set of pruned models representing different capability trade-offs, allowing users to select solutions aligned with their preferences. The proposed approach identifies share core support while enabling specialized support. Experiments across various LLMs and sparsity levels demonstrate MOSP's superior performance in navigating multi-objective trade-offs compared to baseline methods.

Model-free optimization methods typically rely on cost samples gathered by perturbing the current solution estimate along a finite and fixed set of directions. However, at each iteration, only the current cost samples are used, while potentially informative, previously collected samples are discarded. In this work, we challenge this conventional approach by introducing a simple yet effective memory mechanism that maintains an auxiliary vector of iteratively updated cost samples. By leveraging this stored information, our method estimates descent directions through an averaging of all perturbing directions weighted by the auxiliary vector components.

Distributionally Robust Optimization (DRO) offers a promising framework by optimizing worst-case performance over a set of candidate distributions, referred to as the uncertainty set. However, the efficacy of DRO heavily depends on the design of the uncertainty set, and existing methods often perform suboptimally due to an inappropriate or inflexible uncertainty set. In this work, we first propose a novel perspective that casts entropy-regularized Wasserstein DRO as a dynamic process of distributional exploration and semantic alignment, both driven by optimal transport (OT). This unified viewpoint yields two key new techniques: semantic calibration, which bootstraps semantically meaningful transport costs via inverse OT, and adaptive refinement, which adjusts uncertainty set using OT-driven feedback. Together, these components form an exploration-and-feedback system, where the transport costs and uncertainty set evolve jointly during training, enabling the model to better adapt to potential distribution shifts. Moreover, we provide an in-depth analysis of this adaptive process and prove theoretical guarantees of convergence. Finally, we present our experimental results across diverse distribution shift scenarios, which demonstrate that our approach significantly outperforms existing methods, achieving state-ofthe-art robustness.

Consistency Models (CMs) have shown promise for efficient one-step generation. However, most existing CMs rely on manually designed discretization schemes, which can cause repeated adjustments for different noise schedules and datasets. To address this, we propose a unified framework for the automatic and adaptive discretization of CMs, formulating it as an optimization problem with respect to the discretization step. Concretely, during the consistency training process, we propose using local consistency as the optimization objective to ensure trainability by avoiding excessive discretization, and taking global consistency as a constraint to ensure stability by controlling the denoising error in the training target. We establish the trade-off between local and global consistency with a Lagrange multiplier.

Heterogeneity poses a fundamental challenge for many real-world large-scale decision-making problems but remains largely understudied. In this paper, we study the fully heterogeneous setting of a prominent class of such problems, known as weakly-coupled Markov decision processes (WCMDPs). Each WCMDP consists of N arms (or subproblems), which have distinct model parameters in the fully heterogeneous setting, leading to the curse of dimensionality when N is large. We show that, under mild assumptions, an efficiently computable policy achieves an O(1/ N) optimality gap in the long-run average reward per arm for fully heterogeneous WCMDPs as N becomes large. This is the first asymptotic optimality result for fully heterogeneous average-reward WCMDPs. Our main technical innovation is the construction of projection-based Lyapunov functions that certify the convergence of rewards and costs to an optimal region, even under full heterogeneity.1