This paper provides a finite-time analysis of linear stochastic approximation (LSA) algorithms with fixed step size, a core method in statistics and machine learning. LSA is used to compute approximate solutions of a d-dimensional linear system [ ] for which [ ] can only be estimated by (asymptotically) unbiased observations [ ]. We consider here the case where [ ] is an a sequence of independent and identically distributed random variables sequence or a uniformly geometrically ergodic Markov chain. We derive pth moment and high-probability deviation bounds for the iterates defined by LSA and its Polyak–Ruppert-averaged version. Our finite-time instance-dependent bounds for the averaged LSA iterates are sharp in the sense that the leading term we obtain coincides with the local asymptotic minimax limit. Moreover, the remainder terms of our bounds admit a tight dependence on the mixing time [ ] of the underlying chain and the norm of the noise variables. We emphasize that our result requires the LSA step size to scale only with logarithm of the problem dimension d. Funding: The work of A. Durmus and E. Moulines was partly supported by [Grant ANR-19-CHIA-0002]. This project received funding from the European Research Council [ERC-SyG OCEAN Grant 101071601]. The research of A. Naumov and S. Samsonov was prepared within the framework of the HSE University Basic Research Program.

With the rise of generative artificial intelligence (AI), the relationship between these emerging technologies and education, as well as educational practices, has become a central topic of scholarly debate. Research in this area is rapidly expanding, particularly regarding the potential benefits and drawbacks of AI use by students in education. However, despite the growing interest, certain gaps remain. Firstly, research often lacks a strong empirical foundation with rigorous hypothesis testing using validated methodologies, especially within the Russian context. Secondly, existing studies tend to focus primarily on opportunities for development rather than potential challenges. The authors believe that identifying these challenges is crucial for effectively managing the integration of AI into education, and this serves as the primary goal of this study. The core objective of this research is to provide empirical evidence supporting the existence of such challenges and to delineate their specific nature. To achieve this, we analyze data from a survey conducted by the authors in 2025, involving students from leading Russian universities (N=4207). One of the most significant challenges identified by the study is the exacerbation of inequality within the educational landscape. This is particularly evident in the disparate AI usage patterns between students in STEM fields and those in non-STEM disciplines. Furthermore, significant heterogeneity exists among students with varying academic performance (GPA). For highachieving students, AI tends to serve as a tool for enhancement, whereas for others, the opposite effect is observed. These findings are partially consistent with existing literature reviews, both domestic and international, as well as other surveys conducted on the topic. However, they contribute to a more defined understanding of the challenges associated with increasing educational inequality due to AI. Addressing the divisions within the educational sphere resulting from unequal levels of AI integration and utilization represents a crucial first step toward developing appropriate educational strategies that leverage AI as a tool to empower students, rather than the contrary.