Community Exploration: From Offline Optimization to Online Learning
This work addresses resource allocation in dynamic environments such as online advertising, offering incremental improvements in regret bounds for learning-based exploration.
The paper tackles the community exploration problem, which involves allocating limited budget to explore communities to maximize member meetings, with applications like online advertising. For offline optimization with known community sizes, greedy methods are proven optimal, and for online learning with unknown sizes, an upper confidence-like algorithm achieves logarithmic regret bounds, with constant regret possible by combining feedback across rounds.
We introduce the community exploration problem that has many real-world applications such as online advertising. In the problem, an explorer allocates limited budget to explore communities so as to maximize the number of members he could meet. We provide a systematic study of the community exploration problem, from offline optimization to online learning. For the offline setting where the sizes of communities are known, we prove that the greedy methods for both of non-adaptive exploration and adaptive exploration are optimal. For the online setting where the sizes of communities are not known and need to be learned from the multi-round explorations, we propose an `upper confidence' like algorithm that achieves the logarithmic regret bounds. By combining the feedback from different rounds, we can achieve a constant regret bound.