Tutorials

Higher-Order Learning Dynamics in Games

Learning in games, as well as the related topic of evolutionary game theory, concerns how an agent’s strategy in a multi-agent setting evolves in response to the evolving strategies of other agents. The outcome is highly dependent on both the underlying game structure (zero-sum, general sum, two-player, contractive, potential, etc.) and specific learning dynamics (fictitious play, replicator, regret matching, etc.). Long-run behaviors can range from convergence to familiar solution concepts, such as Nash equilibrium, to non-convergent limit cycles or even chaos.

This tutorial will focus on recent developments in “higher-order” learning, where learning dynamics include auxiliary states that can be interpreted as path dependencies, forecasts, or estimates. Higher-order learning dynamics parallel higher-order algorithms in optimization, such as accelerated or optimistic gradient methods. The tutorial will start with an introduction to the learning in games framework, with the emphasis on learning dynamics in matrix games. The presentation will then introduce higher-order learning and show how higher-order learning dynamics can overcome limitations of standard-order learning dynamics, such as bypassing impossibility results, accelerating convergent behavior, or exhibiting equilibrium selection. The tutorial will conclude with an introduction to the control theoretic approach of passivity analysis as a framework for the analysis of higher-order learning.

Neural Networks in the Loop: a Tutorial on Robust Machine Learning for Control

The purpose of this tutorial is to provide a comprehensive and integrated intro- duction to control-theoretic methods for certification of behavioural properties of neural networks. The tutorial will bring together experts who are active in this field, and include material on both theoretical foundations and applications in a variety of domains, along with live coding demonstrations. The intention is that after attending this tutorial, a typical L4DC participant is equipped to do independent research in this area, and contribute to a scientific field which is experiencing rapid growth and can potentially have high impact in industry.

The Scenario Approach: Data Science for Decision and Control

Data are ubiquitous in modern applied sciences. In learning and control, the effective use of data requires frameworks where data not only assist in model construction but also offer guarantees on the quality and robustness of the resulting designs.

In this context, the scenario approach has gained widespread recognition as a framework for data-driven decision-making with rigorous generalization guarantees. Specifically, it provides a way for the user to control the risk, defined as the probability that a decision will underperform when confronted with scenarios outside the training set. This offers a valid support to develop trust in data-driven methodologies, and plays a fundamental role as a tool for hyper-parameter tuning.

This tutorial provides a structured introduction to the scenario approach, starting with essential tools in optimization, encompassing both convex and non-convex cases. The tutorial is divided into two parts: the first part introduces scenario-based optimization techniques, while the second part extends the theory to broader data-driven decision frameworks. The tutorial is designed to be fully accessible for newcomers; no specific prerequisites are required, which makes it suitable for a wide range of conference attendees.

Capabilities of Large Language Models (LLMs) in Control Engineering

This tutorial delves into the intersection of large language models (LLMs) and machine reasoning, focusing on their potential in control engineering. Modern LLMs, which are foundation models with vast knowledge bases, have shown great promise in solving complex reasoning and coding tasks. But how can they benefit control engineers? This tutorial explores LLM reasoning and its applications in control tasks, covering topics including : i) LLM capabilities in answering textbook-level control system questions, ii) review of advanced LLM reasoning methods, iii) integrating LLMs with control/verification toolboxes for automated developments of control systems, iv) limitations of LLMs in control engineering, and v) future directions. Participants will gain insights into LLM reasoning, its applications in control engineering, and emerging opportunities for LLM integration in control systems.