Mingyi Li

Mingyi Li, Michael R. Metel, Akiko Takeda

The K-means algorithm is one of the most widely studied clustering algorithms in machine learning. While extensive research has focused on its ability to achieve a globally optimal solution, there still lacks a rigorous analysis of its local optimality guarantees. In this paper, we first present conditions under which the K-means algorithm converges to a locally optimal solution. Based on this, we propose simple modifications to the K-means algorithm which ensure local optimality in both the continuous and discrete sense, with the same computational complexity as the original K-means algorithm. As the dissimilarity measure, we consider a general Bregman divergence, which is an extension of the squared Euclidean distance often used in the K-means algorithm. Numerical experiments confirm that the K-means algorithm does not always find a locally optimal solution in practice, while our proposed methods provide improved locally optimal solutions with reduced clustering loss. Our code is available at https://github.com/lmingyi/LO-K-means.

Mingyi Li, Taira Tsuchiya, Kenji Yamanishi

This work studies online episodic tabular Markov decision processes (MDPs) with known transitions and develops best-of-both-worlds algorithms that achieve refined data-dependent regret bounds in the adversarial regime and variance-dependent regret bounds in the stochastic regime. We quantify MDP complexity using a first-order quantity and several new data-dependent measures for the adversarial regime, including a second-order quantity and a path-length measure, as well as variance-based measures for the stochastic regime. To adapt to these measures, we develop algorithms based on global optimization and policy optimization, both built on optimistic follow-the-regularized-leader with log-barrier regularization. For global optimization, our algorithms achieve first-order, second-order, and path-length regret bounds in the adversarial regime, and in the stochastic regime, they achieve a variance-aware gap-independent bound and a variance-aware gap-dependent bound that is polylogarithmic in the number of episodes. For policy optimization, our algorithms achieve the same data- and variance-dependent adaptivity, up to a factor of the episode horizon, by exploiting a new optimistic $Q$-function estimator. Finally, we establish regret lower bounds in terms of data-dependent complexity measures for the adversarial regime and a variance measure for the stochastic regime, implying that the regret upper bounds achieved by the global-optimization approach are nearly optimal.

Xiao Zhang, Qi Wang, Mingyi Li et al.

Implementing large language models (LLMs)-driven root cause analysis (RCA) in cloud-native systems has become a key topic of modern software operations and maintenance. However, existing LLM-based approaches face three key challenges: multi-modality input constraint, context window limitation, and dynamic dependence graph. To address these issues, we propose a tool-assisted LLM agent with multi-modality observation data for fine-grained RCA, namely TAMO, including multimodality alignment tool, root cause localization tool, and fault types classification tool. In detail, TAMO unifies multi-modal observation data into time-aligned representations for cross-modal feature consistency. Based on the unified representations, TAMO then invokes its specialized root cause localization tool and fault types classification tool for further identifying root cause and fault type underlying system context. This approach overcomes the limitations of LLMs in processing real-time raw observational data and dynamic service dependencies, guiding the model to generate repair strategies that align with system context through structured prompt design. Experiments on two benchmark datasets demonstrate that TAMO outperforms state-of-the-art (SOTA) approaches with comparable performance.

Yan Li, Xiao Zhang, Mingyi Li et al.

In this work, we study to release the potential of massive heterogeneous weak computing power to collaboratively train large-scale models on dispersed datasets. In order to improve both efficiency and accuracy in resource-adaptive collaborative learning, we take the first step to consider the \textit{unstructured pruning}, \textit{varying submodel architectures}, \textit{knowledge loss}, and \textit{straggler} challenges simultaneously. We propose a novel semi-asynchronous collaborative training framework, namely ${Co\text{-}S}^2{P}$, with data distribution-aware structured pruning and cross-block knowledge transfer mechanism to address the above concerns. Furthermore, we provide theoretical proof that ${Co\text{-}S}^2{P}$ can achieve asymptotic optimal convergence rate of $O(1/\sqrt{N^*EQ})$. Finally, we conduct extensive experiments on two types of tasks with a real-world hardware testbed including diverse IoT devices.The experimental results demonstrate that $Co\text{-}S^2P$ improves accuracy by up to 8.8\% and resource utilization by up to 1.2$\times$ compared to state-of-the-art methods, while reducing memory consumption by approximately 22\% and training time by about 24\% on all resource-limited devices.

Ji Li, Jing Xia, Mingyi Li et al.

Deploying Multimodal Large Language Models as the brain of embodied agents remains challenging, particularly under long-horizon observations and limited context budgets. Existing memory assisted methods often rely on textual summaries, which discard rich visual and spatial details and remain brittle in non-stationary environments. In this work, we propose a non-parametric memory framework that explicitly disentangles episodic and semantic memory for embodied exploration and question answering. Our retrieval-first, reasoning-assisted paradigm recalls episodic experiences via semantic similarity and verifies them through visual reasoning, enabling robust reuse of past observations without rigid geometric alignment. In parallel, we introduce a program-style rule extraction mechanism that converts experiences into structured, reusable semantic memory, facilitating cross-environment generalization. Extensive experiments demonstrate state-of-the-art performance on embodied question answering and exploration benchmarks, yielding a 7.3% gain in LLM-Match and an 11.4% gain in LLM MatchXSPL on A-EQA, as well as +7.7% success rate and +6.8% SPL on GOAT-Bench. Analyses reveal that our episodic memory primarily improves exploration efficiency, while semantic memory strengthens complex reasoning of embodied agents.