# Containing a spread through sequential learning: to exploit or to explore?

## TL;DR

This paper develops active learning strategies for testing and isolating infected nodes in a network to contain disease spread, balancing exploration and exploitation with performance guarantees and practical algorithms.

## Contribution

It introduces novel tradeoffs between exploration and exploitation in sequential testing for epidemic containment, with theoretical guarantees and scalable algorithms.

## Key findings

- Greedy testing strategies optimize containment with performance guarantees.
- Reward-based methods effectively minimize upper bounds on infections.
- Exploration can outperform exploitation depending on network parameters.

## Abstract

The spread of an undesirable contact process, such as an infectious disease (e.g. COVID-19), is contained through testing and isolation of infected nodes. The temporal and spatial evolution of the process (along with containment through isolation) render such detection as fundamentally different from active search detection strategies. In this work, through an active learning approach, we design testing and isolation strategies to contain the spread and minimize the cumulative infections under a given test budget. We prove that the objective can be optimized, with performance guarantees, by greedily selecting the nodes to test. We further design reward-based methodologies that effectively minimize an upper bound on the cumulative infections and are computationally more tractable in large networks. These policies, however, need knowledge about the nodes' infection probabilities which are dynamically changing and have to be learned by sequential testing. We develop a message-passing framework for this purpose and, building on that, show novel tradeoffs between exploitation of knowledge through reward-based heuristics and exploration of the unknown through a carefully designed probabilistic testing. The tradeoffs are fundamentally distinct from the classical counterparts under active search or multi-armed bandit problems (MABs). We provably show the necessity of exploration in a stylized network and show through simulations that exploration can outperform exploitation in various synthetic and real-data networks depending on the parameters of the network and the spread.