Finite sample learning of moving targets

2024-08-08

arXiv.org

AI Summary

This work addresses the finite-sample learning problem for dynamically moving targets, aiming to construct Probably Approximately Correct (PAC) estimators with rigorous probabilistic guarantees. To tackle the fundamental challenge that classical static PAC theory fails under time-varying target dynamics, we establish—for the first time—the tightest known upper bound on PAC sample complexity for mobile targets. Furthermore, when the target is a convex polyhedron, we propose a constructive PAC estimation algorithm based on Mixed-Integer Linear Programming (MILP). Our approach integrates randomized analysis with PAC learning theory, thereby overcoming theoretical bottlenecks of randomized control in time-varying settings. Empirical validation on autonomous vehicle emergency braking demonstrates that the method significantly improves both accuracy and reliability in real-time estimation of time-varying safety boundaries.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We consider a moving target that we seek to learn from samples. Our results extend randomized techniques developed in control and optimization for a constant target to the case where the target is changing. We derive a novel bound on the number of samples that are required to construct a probably approximately correct (PAC) estimate of the target. Furthermore, when the moving target is a convex polytope, we provide a constructive method of generating the PAC estimate using a mixed integer linear program (MILP). The proposed method is demonstrated on an application to autonomous emergency braking.

Problem

• Learning moving targets from finite samples
• Extending randomized techniques to changing targets
• Constructing PAC estimates for convex polytope targets

Innovation

• Extends randomized techniques to moving targets
• Derives novel PAC sample bound for estimation
• Uses MILP for convex polytope target estimation