Shuai Zhang

Hongkang Li, Shuai Zhang, Meng Wang

This paper analyzes the convergence and generalization of training a one-hidden-layer neural network when the input features follow the Gaussian mixture model consisting of a finite number of Gaussian distributions. Assuming the labels are generated from a teacher model with an unknown ground truth weight, the learning problem is to estimate the underlying teacher model by minimizing a non-convex risk function over a student neural network. With a finite number of training samples, referred to the sample complexity, the iterations are proved to converge linearly to a critical point with guaranteed generalization error. In addition, for the first time, this paper characterizes the impact of the input distributions on the sample complexity and the learning rate.

Shuai Zhang, Hongkang Li, Meng Wang et al.

This paper provides a theoretical understanding of Deep Q-Network (DQN) with the $\varepsilon$-greedy exploration in deep reinforcement learning. Despite the tremendous empirical achievement of the DQN, its theoretical characterization remains underexplored. First, the exploration strategy is either impractical or ignored in the existing analysis. Second, in contrast to conventional Q-learning algorithms, the DQN employs the target network and experience replay to acquire an unbiased estimation of the mean-square Bellman error (MSBE) utilized in training the Q-network. However, the existing theoretical analysis of DQNs lacks convergence analysis or bypasses the technical challenges by deploying a significantly overparameterized neural network, which is not computationally efficient. This paper provides the first theoretical convergence and sample complexity analysis of the practical setting of DQNs with $ε$-greedy policy. We prove an iterative procedure with decaying $ε$ converges to the optimal Q-value function geometrically. Moreover, a higher level of $ε$ values enlarges the region of convergence but slows down the convergence, while the opposite holds for a lower level of $ε$ values. Experiments justify our established theoretical insights on DQNs.

Guanwen Xie, Jingzehua Xu, Yiyuan Yang et al.

Achieving the effective design and improvement of reward functions in reinforcement learning (RL) tasks with complex custom environments and multiple requirements presents considerable challenges. In this paper, we propose ERFSL, an efficient reward function searcher using LLMs, which enables LLMs to be effective white-box searchers and highlights their advanced semantic understanding capabilities. Specifically, we generate reward components for each numerically explicit user requirement and employ a reward critic to identify the correct code form. Then, LLMs assign weights to the reward components to balance their values and iteratively adjust the weights without ambiguity and redundant adjustments by flexibly adopting directional mutation and crossover strategies, similar to genetic algorithms, based on the context provided by the training log analyzer. We applied the framework to an underwater data collection RL task without direct human feedback or reward examples (zero-shot learning). The reward critic successfully corrects the reward code with only one feedback instance for each requirement, effectively preventing unrectifiable errors. The initialization of weights enables the acquisition of different reward functions within the Pareto solution set without the need for weight search. Even in cases where a weight is 500 times off, on average, only 5.2 iterations are needed to meet user requirements. The ERFSL also works well with most prompts utilizing GPT-4o mini, as we decompose the weight searching process to reduce the requirement for numerical and long-context understanding capabilities

Ruihan Jin, Pengpeng Shao, Zhengqi Wen et al.

The rapid advancements in large language models (LLMs) have led to the emergence of routing techniques, which aim to efficiently select the optimal LLM from diverse candidates to tackle specific tasks, optimizing performance while reducing costs. Current LLM routing methods are limited in effectiveness due to insufficient exploration of the intrinsic connection between user queries and the characteristics of LLMs. To address this issue, in this paper, we present RadialRouter, a novel framework for LLM routing which employs a lightweight Transformer-based backbone with a radial structure named RadialFormer to articulate the query-LLMs relationship. The optimal LLM selection is performed based on the final states of RadialFormer. The pipeline is further refined by an objective function that combines Kullback-Leibler divergence with the query-query contrastive loss to enhance robustness. Experimental results on RouterBench show that RadialRouter significantly outperforms existing routing methods by 9.2\% and 5.8\% in the Balance and Cost First scenarios, respectively. Additionally, its adaptability toward different performance-cost trade-offs and the dynamic LLM pool demonstrates practical application potential.

Eyasu Mequanint, Shuai Zhang, Bijan Forutanpour et al.

Following recent technological advances there is a growing interest in building non-intrusive methods that help us communicate with computing devices. In this regard, accurate information from eye is a promising input medium between a user and computing devices. In this paper we propose a method that captures the degree of eye closeness. Although many methods exist for detection of eyelid openness, they are inherently unable to satisfactorily perform in real world applications. Detailed eye state estimation is more important, in extracting meaningful information, than estimating whether eyes are open or closed. However, learning reliable eye state estimator requires accurate annotations which is cost prohibitive. In this work, we leverage synthetic face images which can be generated via computer graphics rendering techniques and automatically annotated with different levels of eye openness. These synthesized training data images, however, have a domain shift from real-world data. To alleviate this issue, we propose a weakly-supervised method which utilizes the accurate annotation from the synthetic data set, to learn accurate degree of eye openness, and the weakly labeled (open or closed) real world eye data set to control the domain shift. We introduce a data set of 1.3M synthetic face images with detail eye openness and eye gaze information, and 21k real-world images with open/closed annotation. The dataset will be released online upon acceptance. Extensive experiments validate the effectiveness of the proposed approach.

Penghang Yin, Jiancheng Lyu, Shuai Zhang et al.

Training activation quantized neural networks involves minimizing a piecewise constant function whose gradient vanishes almost everywhere, which is undesirable for the standard back-propagation or chain rule. An empirical way around this issue is to use a straight-through estimator (STE) (Bengio et al., 2013) in the backward pass only, so that the "gradient" through the modified chain rule becomes non-trivial. Since this unusual "gradient" is certainly not the gradient of loss function, the following question arises: why searching in its negative direction minimizes the training loss? In this paper, we provide the theoretical justification of the concept of STE by answering this question. We consider the problem of learning a two-linear-layer network with binarized ReLU activation and Gaussian input data. We shall refer to the unusual "gradient" given by the STE-modifed chain rule as coarse gradient. The choice of STE is not unique. We prove that if the STE is properly chosen, the expected coarse gradient correlates positively with the population gradient (not available for the training), and its negation is a descent direction for minimizing the population loss. We further show the associated coarse gradient descent algorithm converges to a critical point of the population loss minimization problem. Moreover, we show that a poor choice of STE leads to instability of the training algorithm near certain local minima, which is verified with CIFAR-10 experiments.