Learning Optimal Search Strategies

TL;DR

This paper develops a learning algorithm for optimal search strategies in parking problems modeled by unknown inhomogeneous Poisson processes, achieving near-optimal regret bounds.

Contribution

It introduces a novel algorithm that estimates the integrated jump intensity to learn the optimal threshold policy with logarithmic regret growth.

Findings

Algorithm achieves logarithmic regret growth.

Proves a matching logarithmic minimax regret lower bound.

Demonstrates effectiveness across broad environments.

Abstract

We explore the question of how to learn an optimal search strategy within the example of a parking problem where parking opportunities arrive according to an unknown inhomogeneous Poisson process. The optimal policy is a threshold-type stopping rule characterized by an indifference position. We propose an algorithm that learns this threshold by estimating the integrated jump intensity rather than the intensity function itself. We show that our algorithm achieves a logarithmic regret growth, uniformly over a broad class of environments. Moreover, we prove a logarithmic minimax regret lower bound, establishing the growth optimality of the proposed approach.