Hongcheng Liu

Hongcheng Liu, Jindong Tong

This paper studies sample average approximation (SAA) in solving convex or strongly convex stochastic programming (SP) problems. In estimating SAA's sample efficiency, the state-of-the-art sample complexity bounds entail metric entropy terms (such as the logarithm of the feasible region's covering number), which often grow polynomially with problem dimensionality. While it has been shown that metric entropy-free complexity rates are attainable under a uniform Lipschitz condition, such an assumption can be overly critical for many important SP problem settings. In response, this paper presents perhaps the first set of metric entropy-free sample complexity bounds for the SAA under standard SP assumptions -- in the absence of the uniform Lipschitz condition. The new results often lead to an $O(d)$-improvement in the complexity rate than the state-of-the-art. From the newly established complexity bounds, an important revelation is that SAA and the canonical stochastic mirror descent (SMD) method, two mainstream solution approaches to SP, entail almost identical rates of sample efficiency, lifting a theoretical discrepancy of SAA from SMD also by the order of $O(d)$. Furthermore, this paper explores non-Lipschitzian scenarios where SAA maintains provable efficacy but the corresponding results for SMD remain mostly unexplored, indicating the potential of SAA's better applicability in some irregular settings. Our numerical experiment results on SAA for solving a simulated SP problem align with our theoretical findings.

Hongcheng Liu, Yixuan Hou, Heyang Liu et al.

While Speech Large Language Models (Speech-LLMs) show strong performance in many applications, their robustness is critically under-tested, especially to speech disfluency. Existing evaluations often rely on idealized inputs, overlooking common disfluencies, particularly those associated with conditions like Parkinson's disease. This work investigates whether current Speech-LLMs can maintain performance when interacting with users who have speech impairments. To facilitate this inquiry, we introduce VocalBench-DF, a framework for the systematic evaluation of disfluency across a multi-dimensional taxonomy. Our evaluation of 22 mainstream Speech-LLMs reveals substantial performance degradation, indicating that their real-world readiness is limited. Further analysis identifies phoneme-level processing and long-context modeling as primary bottlenecks responsible for these failures. Strengthening recognition and reasoning capability from components and pipelines can substantially improve robustness. These findings highlight the urgent need for new methods to improve disfluency handling and build truly inclusive Speech-LLMs

Yuhao Wang, Zhiyuan Zhu, Heyang Liu et al.

Multimodal large language models (MLLMs) excel at multimodal perception and understanding, yet their tendency to generate hallucinated or inaccurate responses undermines their trustworthiness. Existing methods have largely overlooked the importance of refusal responses as a means of enhancing MLLMs reliability. To bridge this gap, we present the Information Boundary-aware Learning Framework (InBoL), a novel approach that empowers MLLMs to refuse to answer user queries when encountering insufficient information. To the best of our knowledge, InBoL is the first framework that systematically defines the conditions under which refusal is appropriate for MLLMs using the concept of information boundaries proposed in our paper. This framework introduces a comprehensive data generation pipeline and tailored training strategies to improve the model's ability to deliver appropriate refusal responses. To evaluate the trustworthiness of MLLMs, we further propose a user-centric alignment goal along with corresponding metrics. Experimental results demonstrate a significant improvement in refusal accuracy without noticeably compromising the model's helpfulness, establishing InBoL as a pivotal advancement in building more trustworthy MLLMs.

Hongcheng Liu, Yu Yang

This paper concerns a convex, stochastic zeroth-order optimization (S-ZOO) problem. The objective is to minimize the expectation of a cost function whose gradient is not directly accessible. For this problem, traditional optimization algorithms mostly yield query complexities that grow polynomially with dimensionality (the number of decision variables). Consequently, these methods may not perform well in solving massive-dimensional problems arising in many modern applications. Although more recent methods can be provably dimension-insensitive, almost all of them require arguably more stringent conditions such as everywhere sparse or compressible gradient. In this paper, we propose a sparsity-inducing stochastic gradient-free (SI-SGF) algorithm, which provably yields a dimension-free (up to a logarithmic term) query complexity in both convex and strongly convex cases. Such insensitivity to the dimensionality growth is proven, for the first time, to be achievable when neither gradient sparsity nor gradient compressibility is satisfied. Our numerical results demonstrate a consistency between our theoretical prediction and the empirical performance.

Yunmei Chen, Hongcheng Liu, Xiaojing Ye et al.

We propose a general learning based framework for solving nonsmooth and nonconvex image reconstruction problems. We model the regularization function as the composition of the $l_{2,1}$ norm and a smooth but nonconvex feature mapping parametrized as a deep convolutional neural network. We develop a provably convergent descent-type algorithm to solve the nonsmooth nonconvex minimization problem by leveraging the Nesterov's smoothing technique and the idea of residual learning, and learn the network parameters such that the outputs of the algorithm match the references in training data. Our method is versatile as one can employ various modern network structures into the regularization, and the resulting network inherits the guaranteed convergence of the algorithm. We also show that the proposed network is parameter-efficient and its performance compares favorably to the state-of-the-art methods in a variety of image reconstruction problems in practice.

Qingchao Zhang, Xiaojing Ye, Hongcheng Liu et al.

Optimization algorithms for solving nonconvex inverse problem have attracted significant interests recently. However, existing methods require the nonconvex regularization to be smooth or simple to ensure convergence. In this paper, we propose a novel gradient descent type algorithm, by leveraging the idea of residual learning and Nesterov's smoothing technique, to solve inverse problems consisting of general nonconvex and nonsmooth regularization with provable convergence. Moreover, we develop a neural network architecture intimating this algorithm to learn the nonlinear sparsity transformation adaptively from training data, which also inherits the convergence to accommodate the general nonconvex structure of this learned transformation. Numerical results demonstrate that the proposed network outperforms the state-of-the-art methods on a variety of different image reconstruction problems in terms of efficiency and accuracy.