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Michele Giordano

Publications and source records attributed to Michele Giordano.

5 recordsLinked to original sources

ELEVATE: Designing Human-Centered GenAI Virtual Tutors for Scalable and Inclusive Education

The advent of Generative Artificial Intelligence (GenAI), and in particular Large Language Models (LLMs), is reshaping educational practice, while intensifying ethical debate about its adoption. To date, the dominant paradigm remains cloud-based and text-only chatbot: a centralized service that offers limited pedagogical control, weak transparency over knowledge sources, and non-trivial risks for privacy and regulatory compliance. This model also presumes continuous connectivity and recurring API costs, creating structural barriers for many institutions, reinforcing existing digital divides. At the same time, educational interaction with LLM can benefit from multimodal cues and embodied presence, requiring interfaces that move beyond text-only tutoring. In this work, we propose ELEVATE (Efficient LLM Education with Virtual Avatar Teaching Engine), a framework to develop efficient GenAI-driven avatar tutors governed by epistemic infrastructures. ELEVATE integrates LLM-driven dialogue with embodied 3D avatars for multimodal interaction and adopts a local-first execution model enabling deployment on consumer-grade hardware. The framework formalizes a three-stratum design that separates (i) a student-facing virtual avatar interaction layer, (ii) a local GenAI execution and multimodal synthesis core, and (iii) a teacher-facing governance layer. We implemented and evaluated a working prototype deployed in a real-world educational curriculum. The system runs on standard PCs and smartphones, and we provide system-level performance evidence to show responsive interaction under realistic hardware constraints. Finally, we discuss sociotechnical and pedagogical implications for responsible adoption, positioning ELEVATE as a scalable pathway for privacy-preserving and inclusive GenAI tutoring across heterogeneous school environments.

cs.CY

Lifting of Volterra processes: optimal control in UMD Banach spaces

We study a stochastic control problem for a Volterra-type controlled forward equation with past dependence obtained via convolution with a deterministic kernel. To be able to apply dynamic programming to solve the problem, we lift it to infinite dimensions and we formulate a UMD Banach-valued Markovian problem, which is shown to be equivalent to the original finite-dimensional non-Markovian one. We characterize the optimal control for the infinite dimensional problem and show that this also characterizes the optimal control for the finite dimensional problem.

math.OC

Stochastic Volterra equations with time-changed Lévy noise and maximum principles

Motivated by a problem of optimal harvesting of natural resources, we study a control problem for Volterra type dynamics driven by time-changed Lévy noises, which are in general not Markovian. To exploit the nature of the noise, we make use of different kind of information flows within a maximum principle approach. For this we work with backward stochastic differential equations (BSDE) with time-change and exploit the non-anticipating stochastic derivative introduced in [15]. We prove both a sufficient and necessary stochastic maximum principle.

math.PR

Maximum principles for stochastic time-changed Volterra games

We study a stochastic differential game between two players, controlling a forward stochastic Volterra integral equation (FSVIE). Each player has to optimize his own performance functional which includes a backward stochastic differential equation (BSDE). The dynamics considered are driven by time-changed Lévy noises, with absolutely continuous time-change process. We prove a sufficient maximum principle to characterize Nash equilibria and the related optimal strategies. For this we use techniques of control under partial information, and the non-anticipating stochastic derivative. The zero-sum game is presented as a particular case.

math.PR

Optimal control in linear stochastic advertising models with memory

This paper deals with a class of optimal control problems which arises in advertising models with Volterra Ornstein-Uhlenbeck process representing the product goodwill. Such choice of the model can be regarded as a stochastic modification of the classical Nerlove-Arrow model that allows to incorporate both presence of uncertainty and empirically observed memory effects such as carryover or distributed forgetting. We present an approach to solve such optimal control problems based on an infinite dimensional lift which allows us to recover Markov properties by formulating a optimization problem equivalent to the original one in a Hilbert space. Such technique, however, requires the Volterra kernel from the forward equation to have a representation of a particular form that may be challenging to obtain in practice. We overcome this issue for Hölder continuous kernels by approximating them with Bernstein polynomials (which turn out to enjoy a simple representation of the required type) and then solving the optimal control problem for the forward process with approximated kernel instead of the original one. The approach is illustrated with simulations.

math.OC