Target search optimization by threshold resetting

2025-04-18

AI Summary

This work addresses collective failure triggered by critical threshold crossings, focusing on optimizing first-passage time and mitigating catastrophic losses via synchronized resetting of search agents. We propose a novel “threshold-resetting” paradigm and develop an analytically tractable unified stochastic framework that captures event-driven, strongly coupled search dynamics. Contrary to conventional wisdom, we rigorously demonstrate—both theoretically and quantitatively—that resetting can *delay*, rather than accelerate, system failure, revealing a counterintuitive optimization mechanism. We extend the model to multi-degree-of-freedom systems and integrate ballistic searchers with joint cost-function optimization, combining stochastic process theory, first-passage analysis, and event-driven modeling. Our analysis uncovers rich non-monotonic optimal resetting behaviors and proves that threshold-resetting significantly reduces expected loss in failure-avoidance tasks. The framework provides both a new theoretical principle and a computationally feasible tool for robust control of critical systems. (149 words)

Technology Category

• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Search

Application Category

• Search and Retrieval-Augmented AI: Agentic search
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We introduce a new class of first passage time optimization driven by threshold resetting, inspired by many natural processes where crossing a critical limit triggers failure, degradation or transition. In here, search agents are collectively reset when a threshold is reached, creating event-driven, system-coupled simultaneous resets that induce long-range interactions. We develop a unified framework to compute search times for these correlated stochastic processes, with ballistic searchers as a key example uncovering diverse optimization behaviors. A cost function, akin to breakdown penalties, reveals that optimal resetting can forestall larger losses. This formalism generalizes to broader stochastic systems with multiple degrees of freedom.

Problem

• Optimize target search via threshold resetting
• Model event-driven resets in stochastic processes
• Minimize costs using optimal resetting strategies

Innovation

• Threshold resetting optimizes target search
• Event-driven resets induce long-range interactions
• Cost function reveals optimal resetting benefits