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Motivated by robust and quantile regression problems, we investigate the stochastic gradient descent (SGD) algorithm for minimizing an objective functionfthat is locally strongly convex with a sub--quadratic tail. This setting covers many widely used online statistical methods. We introduce a novel piecewise Lyapunov function that enables us to handle functionsfwith only first-order differentiability, which includes a wide range of popular loss functions such as Huber loss. Leveraging our proposed Lyapunov function, we derive finite-time moment bounds under general diminishing stepsizes, as well as constant stepsizes. We further establish the weak convergence, central limit theorem and bias characterization under constant stepsize, providing the first geometrical convergence result for sub--quadratic SGD. Our results have wide applications, especially in online statistical methods. In particular, we discuss two applications of our results. 1) Online robust regression: We consider a corrupted linear model with sub--exponential covariates and heavy--tailed noise. Our analysis provides convergence rates comparable to those for corrupted models with Gaussian covariates and noise. 2) Online quantile regression: Importantly, our results relax the common assumption in prior work that the conditional density is continuous and provide a more fine-grained analysis for the moment bounds. 

Generative AI (GenAI) has brought opportunities and challenges for higher education as it integrates into teaching and learning environments. As instructors navigate this new landscape, understanding their engagement with and attitudes toward GenAI is crucial. We surveyed 178 instructors from a single U.S. university to examine their current practices, perceptions, trust, and distrust of GenAI in higher education in March 2024. While most surveyed instructors reported moderate to high familiarity with GenAI-related concepts, their actual use of GenAI tools for direct instructional tasks remained limited. Our quantitative results show that trust and distrust in GenAI are related yet distinct; high trust does not necessarily imply low distrust, and vice versa. We also found significant differences in surveyed instructors' familiarity with GenAI across different trust and distrust groups. Our qualitative results show nuanced manifestations of trust and distrust among surveyed instructors and various approaches to support calibrated trust in GenAI. We discuss practical implications focused on (dis)trust calibration among instructors. 

Social anxiety (SA) has become increasingly prevalent. Traditional coping strategies often face accessibility challenges. Generative AI (GenAI), known for their knowledgeable and conversational capabilities, are emerging as alternative tools for mental well-being. With the increased integration of GenAI, it is important to examine individuals’ attitudes and trust in GenAI chatbots’ support for SA. Through a mixed-method approach that involved surveys (n = 159) and interviews (n = 17), we found that individuals with severe symptoms tended to trust and embrace GenAI chatbots more readily, valuing their non-judgmental support and perceived emotional comprehension. However, those with milder symptoms prioritized technical reliability. We identified factors influencing trust, such as GenAI chatbots’ ability to generate empathetic responses and its context-sensitive limitations, which were particularly important among individuals with SA. We also discuss the design implications and use of GenAI chatbots in fostering cognitive and emotional trust, with practical and design considerations. 

Significant advancements have occurred in the application of Large Language Models (LLMs) for social simulations. Despite this, their abilities to perform teaming in task-oriented social events are underexplored. Such capabilities are crucial if LLMs are to effectively mimic human-like social behaviors and form efficient teams to solve tasks. To bridge this gap, we introduce MetaAgents, a social simulation framework populated with LLM-based agents. MetaAgents facilitates agent engagement in conversations and a series of decision making within social contexts, serving as an appropriate platform for investigating interactions and interpersonal decision-making of agents. In particular, we construct a job fair environment as a case study to scrutinize the team assembly and skill-matching behaviors of LLM-based agents. We take advantage of both quantitative metrics evaluation and qualitative text analysis to assess their teaming abilities at the job fair. Our evaluation demonstrates that LLM-based agents perform competently in making rational decisions to develop efficient teams. However, we also identify limitations that hinder their effectiveness in more complex team assembly tasks. Our work provides valuable insights into the role and evolution of LLMs in task-oriented social simulations. 

In this work, we investigate stochastic approximation (SA) with Markovian data and nonlinear updates under constant stepsize. Existing work has primarily focused on either i.i.d. data or linear update rules. We take a new perspective and carefully examine the simultaneous presence of Markovian dependency of data and nonlinear update rules, delineating how the interplay between these two structures leads to complications that are not captured by prior techniques. By leveraging the smoothness and recurrence properties of the SA updates, we develop a fine-grained analysis of the correlation between the SA iterates and Markovian data. This enables us to overcome the obstacles in existing analysis and establish for the first time the weak convergence of the joint process. Furthermore, we present a precise characterization of the asymptotic bias of the SA iterates. As a by-product of our analysis, we derive finite-time bounds on higher moment and present non-asymptotic geometric convergence rates for the iterates, along with a Central Limit Theorem. 

Stochastic Approximation (SA) is a widely used algorithmic approach in various fields, including optimization and reinforcement learning (RL). Among RL algorithms, Q-learning is particularly popular due to its empirical success. In this paper, we study asynchronous Q-learning with constant stepsize, which is commonly used in practice for its fast convergence. By connecting the constant stepsize Q-learning to a time-homogeneous Markov chain, we show the distributional convergence of the iterates in Wasserstein distance and establish its exponential convergence rate. We also establish a Central Limit Theory for Q-learning iterates, demonstrating the asymptotic normality of the averaged iterates. Moreover, we provide an explicit expansion of the asymptotic bias of the averaged iterate in stepsize. Specifically, the bias is proportional to the stepsize up to higher-order terms and we provide an explicit expression for the linear coefficient. This precise characterization of the bias allows the application of Richardson-Romberg (RR) extrapolation technique to construct a new estimate that is provably closer to the optimal Q function. Numerical results corroborate our theoretical finding on the improvement of the RR extrapolation method. 

Motivated by Q-learning, we study nonsmooth contractive stochastic approximation (SA) with constant stepsize. We focus on two important classes of dynamics: 1) nonsmooth contractive SA with additive noise, and 2) synchronous and asynchronous Q-learning, which features both additive and multiplicative noise. For both dynamics, we establish weak convergence of the iterates to a stationary limit distribution in Wasserstein distance. Furthermore, we propose a prelimit coupling technique for establishing steady-state convergence and characterize the limit of the stationary distribution as the stepsize goes to zero. Using this result, we derive that the asymptotic bias of nonsmooth SA is proportional to the square root of the stepsize, which stands in sharp contrast to smooth SA. This bias characterization allows for the use of Richardson-Romberg extrapolation for bias reduction in nonsmooth SA.