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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 containmentthrough isolation) render such detection as fundamentally different from activesearch detection strategies. In this work, through an active learning approach,we design testing and isolation strategies to contain the spread and minimizethe cumulative infections under a given test budget. We prove that theobjective can be optimized, with performance guarantees, by greedily selectingthe nodes to test. We further design reward-based methodologies thateffectively minimize an upper bound on the cumulative infections and arecomputationally more tractable in large networks. These policies, however, needknowledge about the nodes' infection probabilities which are dynamicallychanging and have to be learned by sequential testing. We develop amessage-passing framework for this purpose and, building on that, show noveltradeoffs between exploitation of knowledge through reward-based heuristics andexploration of the unknown through a carefully designed probabilistic testing.The tradeoffs are fundamentally distinct from the classical counterparts underactive search or multi-armed bandit problems (MABs). We provably show thenecessity of exploration in a stylized network and show through simulationsthat exploration can outperform exploitation in various synthetic and real-datanetworks depending on the parameters of the network and the spread.

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