High-Order Error Bounds for Markovian LSA with Richardson-Romberg Extrapolation

In this paper, we study the bias and high-order error bounds of the Linear Stochastic Approximation (LSA) algorithm with Polyak-Ruppert (PR) averaging under Markovian noise. We focus on the version of the algorithm with constant step size $\alpha$ and propose a novel decomposition of the bias via a linearization technique. We analyze the structure of the bias and show that the leading-order term is linear in $\alpha$ and cannot be eliminated by PR averaging. To address this, we apply the Richardson-Romberg (RR) extrapolation procedure, which effectively cancels the leading bias term. We derive high-order moment bounds for the RR iterates and show that the leading error term aligns with the asymptotically optimal covariance matrix of the vanilla averaged LSA iterates.

Smart Learning in the 21st Century: Advancing Constructionism Across Three Digital Epochs

This article explores the evolution of constructionism as an educational framework, tracing its relevance and transformation across three pivotal eras: the advent of personal computing, the networked society, and the current era of generative AI. Rooted in Seymour Papert constructionist philosophy, this study examines how constructionist principles align with the expanding role of digital technology in personal and collective learning. We discuss the transformation of educational environments from hierarchical instructionism to constructionist models that emphasize learner autonomy and interactive, creative engagement. Central to this analysis is the concept of an expanded personality, wherein digital tools and AI integration fundamentally reshape individual self-perception and social interactions. By integrating constructionism into the paradigm of smart education, we propose it as a foundational approach to personalized and democratized learning. Our findings underscore constructionism enduring relevance in navigating the complexities of technology-driven education, providing insights for educators and policymakers seeking to harness digital innovations to foster adaptive, student-centered learning experiences.

SCAFFLSA: Quantifying and Eliminating Heterogeneity Bias in Federated Linear Stochastic Approximation and Temporal Difference Learning

In this paper, we perform a non-asymptotic analysis of the federated linear stochastic approximation (FedLSA) algorithm. We explicitly quantify the bias introduced by local training with heterogeneous agents, and investigate the sample complexity of the algorithm. We show that the communication complexity of FedLSA scales polynomially with the desired precision $\epsilon$, which limits the benefits of federation. To overcome this, we propose SCAFFLSA, a novel variant of FedLSA, that uses control variates to correct the bias of local training, and prove its convergence without assumptions on statistical heterogeneity. We apply the proposed methodology to federated temporal difference learning with linear function approximation, and analyze the corresponding complexity improvements.