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Abstract:
Inhomogeneous Poisson point processes are widely used models of event occurrences. We address \emphadaptive sensing of Poisson Point processes, namely, maximizing the number of captured events subject to sensing costs. We encode prior assumptions on the rate function by modeling it as a member of a known \emphreproducing kernel Hilbert space (RKHS). By partitioning the domain into separate small regions, and using heteroscedastic linear regression, we propose a tractable estimator of Poisson process rates for two feedback models: \emphcount-record, where exact locations of events are observed, and \emphhistogram feedback, where only counts of events are observed. We derive provably accurate anytime confidence estimates for our estimators for sequentially acquired Poisson count data. Using these, we formulate algorithms based on optimism that provably incur sublinear count-regret. We demonstrate the practicality of the method on problems from crime modeling, revenue maximization as well as environmental monitoring.
Reference:
No-regret Algorithms for Capturing Events in Poisson Point Processes M. ír Mutný, A. KrauseIn Proc. International Conference for Machine Learning (ICML), 2021
Bibtex Entry:
@InProceedings{Mutny2021a,
    author    = {Mutn\'{y},Mojm\'{i}r and Krause, Andreas},
  booktitle = {Proc. International Conference for Machine Learning (ICML)},
  title     = {No-regret Algorithms for Capturing Events in Poisson Point Processes},
  year      = {2021},
  month     = jul,
  number    = {38}, namely, maximizing the number of captured events subject to sensing costs. We encode prior assumptions on the rate function by modeling it as a member of a known \emph{reproducing kernel Hilbert space} (RKHS). By partitioning the domain into separate small regions, and using heteroscedastic linear regression, we propose a tractable estimator of Poisson process rates for two feedback models: \emph{count-record}, where exact locations of events are observed, and \emph{histogram} feedback, where only counts of events are observed. We derive provably accurate anytime confidence estimates for our estimators for sequentially acquired Poisson count data. Using these, we formulate algorithms based on optimism that provably incur sublinear count-regret. We demonstrate the practicality of the method on problems from crime modeling, revenue maximization as well as environmental monitoring.}}