Using effective generalization capabilities of vision language models (VLMs) in context-specific dynamic tasks for embodied artificial intelligence remains a significant challenge. Although supervised fine-tuned models can better align with the real physical world, they still exhibit sluggish responses and hallucination issues in dynamically changing environments, necessitating further alignment. Existing post-SFT methods, reliant on reinforcement learning and chain-of-thought (CoT) approaches, are constrained by sparse rewards and action-only optimization, resulting in low sample efficiency, poor consistency, and model degradation. To address these issues, this paper proposes Thought-Centric Preference Optimization (TCPO) for effective embodied decision-making. Specifically, TCPO introduces a stepwise preference-based optimization approach, transforming sparse reward signals into richer step sample pairs. It emphasizes the alignment of the model's intermediate reasoning process, mitigating the problem of model degradation. Moreover, by incorporating Action Policy Consistency Constraint (APC), it further imposes consistency constraints on the model output. Experiments in the ALFWorld environment demonstrate an average success rate of 26.67%, achieving a 6% improvement over RL4VLM and validating the effectiveness of our approach in mitigating model degradation after fine-tuning. These results highlight the potential of integrating preference-based learning techniques with CoT processes to enhance the decision-making capabilities of vision-language models in embodied agents.

Decision-making under uncertainty is often considered in two stages: predicting the unknown parameters, and then optimizing decisions based on predictions. While traditional prediction-focused learning (PFL) treats these two stages separately, decision-focused learning (DFL) trains the predictive model by directly optimizing the decision quality in an end-to-end manner. However, despite using exact or well-approximated gradients, vanilla DFL often suffers from unstable convergence due to its flat-and-sharp loss landscapes. In contrast, PFL yields more stable optimization, but overlooks the downstream decision quality. To address this, we propose a simple yet effective approach: perturbing the decision loss gradient using the prediction loss gradient to construct an update direction. Our method requires no additional training and can be integrated with any DFL solvers. Using the sigmoid-like decaying parameter, we let the prediction loss gradient guide the decision loss gradient to train a predictive model that optimizes decision quality. Also, we provide a theoretical convergence guarantee to Pareto stationary point under mild assumptions. Empirically, we demonstrate our method across three stochastic optimization problems, showing promising results compared to other baselines. We validate that our approach achieves lower regret with more stable training, even in situations where either PFL or DFL struggles.

Mixture-of-Experts (MoE) has emerged as a promising architecture for modern large language models (LLMs). However, massive parameters impose heavy GPU memory (i.e., VRAM) demands, hindering the widespread adoption of MoE LLMs. Offloading the expert parameters to CPU RAM offers an effective way to alleviate the VRAM requirements for MoE inference. Existing approaches typically cache a small subset of experts in VRAM and dynamically prefetch experts from RAM during inference, leading to significant degradation in inference speed due to the poor cache hit rate and substantial expert loading latency. In this work, we propose MoEpic, an efficient MoE inference system with a novel expert split mechanism. Specifically, each expert is vertically divided into two segments: top and bottom. MoEpic caches the top segment of hot experts, so that more experts will be stored under the limited VRAM budget, thereby improving the cache hit rate. During each layer's inference, MoEpic predicts and prefetches the activated experts for the next layer. Since the top segments of cached experts are exempt from fetching, the loading time is reduced, which allows efficient transfer-computation overlap. Nevertheless, the performance of MoEpic critically depends on the cache configuration (i.e., each layer's VRAM budget and expert split ratio). To this end, we propose a divide-and-conquer algorithm based on fixed-point iteration for adaptive cache configuration. Extensive experiments on popular MoE LLMs demonstrate that MoEpic can save about half of the GPU cost, while lowering the inference latency by about 37.51%-65.73% compared to the baselines.

Existing key-value (KV) cache compression methods typically rely on heuristics, such as uniform cache allocation across layers or static eviction policies, however, they ignore the critical interplays among layer-specific feature patterns and task performance, which can lead to degraded generalization. In this paper, we propose EvolKV, an adaptive framework for layer-wise, task-driven KV cache compression that jointly optimizes the memory efficiency and task performance. By reformulating cache allocation as a multi-objective optimization problem, EvolKV leverages evolutionary search to dynamically configure layer budgets while directly maximizing downstream performance. Extensive experiments on 11 tasks demonstrate that our approach outperforms all baseline methods across a wide range of KV cache budgets on long-context tasks and surpasses heuristic baselines by up to 7 percentage points on GSM8K. Notably, EvolKV achieves superior performance over the full KV cache setting on code completion while utilizing only 1.5% of the original budget, suggesting the untapped potential in learned compression strategies for KV cache budget allocation.

Distributed and federated learning are essential paradigms for training models across decentralized data sources while preserving privacy, yet communication overhead remains a major bottleneck. This dissertation explores strategies to improve communication efficiency, focusing on model compression, local training, and personalization. We establish a unified framework for biased and unbiased compression operators with convergence guarantees, then propose adaptive local training strategies that incorporate personalization to accelerate convergence and mitigate client drift. In particular, Scafflix balances global and personalized objectives, achieving superior performance under both IID and non-IID settings. We further introduce privacy-preserving pruning frameworks that optimize sparsity while minimizing communication costs, with Cohort-Squeeze leveraging hierarchical aggregation to reduce cross-device overhead. Finally, SymWanda, a symmetric post-training pruning method, enhances robustness under high sparsity and maintains accuracy without retraining. Extensive experiments on benchmarks and large-scale language models demonstrate favorable trade-offs among accuracy, convergence, and communication, offering theoretical and practical insights for scalable, efficient distributed learning.

A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis introduces robust and computationally efficient methods to address several common challenges associated with high-dimensional data. In my first manuscript, I propose a coherent approach to variable screening that accommodates nonlinear associations. I develop a novel variable screening method that transcends traditional linear assumptions by leveraging mutual information, with an intended application in neuroimaging data. This approach allows for accurate identification of important variables by capturing nonlinear as well as linear relationships between the outcome and covariates. Building on this foundation, I develop new optimization methods for sparse estimation using nonconvex penalties in my second manuscript. These methods address notable challenges in current statistical computing practices, facilitating computationally efficient and robust analyses of complex datasets. The proposed method can be applied to a general class of optimization problems. In my third manuscript, I contribute to robust modeling of high-dimensional correlated observations by developing a mixed-effects model based on Tsallis power-law entropy maximization and discussed the theoretical properties of such distribution. This model surpasses the constraints of conventional Gaussian models by accommodating a broader class of distributions with enhanced robustness to outliers. Additionally, I develop a proximal nonlinear conjugate gradient algorithm that accelerates convergence while maintaining numerical stability, along with rigorous statistical properties for the proposed framework.

Federated Learning (FL) is a novel, multidisciplinary Machine Learning paradigm where multiple clients, such as mobile devices, collaborate to solve machine learning problems. Initially introduced in Kone{č}n{ý} et al. (2016a,b); McMahan et al. (2017), FL has gained further attention through its inclusion in the National AI Research and Development Strategic Plan (2023 Update) of the United States (Science and on Artificial Intelligence, 2023). The FL training process is inherently decentralized and often takes place in less controlled settings compared to data centers, posing unique challenges distinct from those in fully controlled environments. In this thesis, we identify five key challenges in Federated Learning and propose novel approaches to address them. These challenges arise from the heterogeneity of data and devices, communication issues, and privacy concerns for clients in FL training. Moreover, even well-established theoretical advances in FL require diverse forms of practical implementation to enhance their real-world applicability. Our contributions advance FL algorithms and systems, bridging theoretical advancements and practical implementations. More broadly, our work serves as a guide for researchers navigating the complexities of translating theoretical methods into efficient real-world implementations and software. Additionally, it offers insights into the reverse process of adapting practical implementation aspects back into theoretical algorithm design. This reverse process is particularly intriguing, as the practical perspective compels us to examine the underlying mechanics and flexibilities of algorithms more deeply, often uncovering new dimensions of the algorithms under study.

Abstract--Autonomous vehicles must navigate dynamically uncertain environments while balancing the safety and driving efficiency. This challenge is exacerbated by the unpredictable nature of surrounding human-driven vehicles (HVs) and perception inaccuracies, which require planners to adapt to evolving uncertainties while maintaining safe trajectories. Overly conservative planners degrade driving efficiency, while deterministic approaches may encounter serious issues and risks of failure when faced with sudden and unexpected maneuvers. T o address these issues, we propose a real-time contingency trajectory optimization framework in this paper . By employing event-triggered online learning of HV control-intent sets, our method dynamically quantifies multi-modal HV uncertainties and refines the forward reachable set (FRS) incrementally. Crucially, we enforce invariant safety through FRS-based barrier constraints that ensure safety without reliance on accurate trajectory prediction of HVs. These constraints are embedded in contingency trajectory optimization and solved efficiently through consensus alternative direction method of multipliers (ADMM). High-fidelity simulations on highway and urban scenarios, as well as a series of real-world experiments demonstrate significant improvements in driving efficiency and passenger comfort while maintaining safety under uncertainty. The project page is available at https: //pathetiue.github.io/frscp.github.io/.

Self-supervised pre-training using unlabeled data is widely used in automatic speech recognition. In this paper, we propose a new self-supervised pre-training approach to dealing with heterogeneous data. Instead of mixing all the data and minimizing the averaged global loss in the conventional way, we impose additional local constraints to ensure that the model optimizes each source of heterogeneous data to its local optimum after $K$-step gradient descent initialized from the model. We formulate this as a bilevel optimization problem, and use the first-order approximation method to solve the problem. We discuss its connection to model-agnostic meta learning. Experiments are carried out on self-supervised pre-training using multi-domain and multilingual datasets, demonstrating that the proposed approach can significantly improve the adaptivity of the self-supervised pre-trained model for the downstream supervised fine-tuning tasks.

We propose a novel framework for learning time-varying graphs from spatiotemporal measurements. Given an appropriate prior on the temporal behavior of signals, our proposed method can estimate time-varying graphs from a small number of available measurements. To achieve this, we introduce two regularization terms in convex optimization problems that constrain sparseness of temporal variations of the time-varying networks. Moreover, a computationally-scalable algorithm is introduced to efficiently solve the optimization problem. The experimental results with synthetic and real datasets (point cloud and temperature data) demonstrate our proposed method outperforms the existing state-of-the-art methods.