Overview

The discovery of rare events is crucial to many applications, ranging from the verification of mission-critical systems to the collection of training data for machine learning. Discovering rare events is particularly challenging because alternative approaches, such as Monte Carlo methods and their randomized field-testing counterparts, are inefficient and expensive.

Some of the course topics that will be discussed include:

• The Cross Entropy search method identifies statistical distributions of rare events of interest, thereby enabling a range of specific application use cases: Runtime Verification and Validation of mission-critical systems, Autonomous Vehicles, Autonomous Drones, Air Traffic Control, and Nuclear Plants.
• Pathfinding for complex multi-agent applications in the presence of uncertainties.
• Pathfinding for applications where the underlying map changes during navigation.
• Pathfinding solutions where traditional dynamic programming methods (such as A*) fail.
• Fast generation of high-quality, high-variance synthetic data for machine learning classifiers.
• Generation of machine learning training data that enables uncertainty estimation for classifiers.
• Synthesis of rare events.

This course covers the principles and applications of the Cross Entropy search method, providing students with the tools and knowledge needed to effectively discover and utilize rare events in various high-stakes scenarios.

Learning Outcomes

Upon successful completion of this short course, participants will be able to:

1. Determine if a problem satisfies the optimal substructure property.
2. Assess whether a pathfinding problem can be solved using the A* algorithm.
3. Define, in clear English, the constraints associated with one of the rare-event discovery problems covered in the course.
4. Identify two cost functions – one for the Vanilla sample and one for the Perturbation sample – when employing the HybridPair method.