  In this paper, we consider improving the efficiency of information-based
autonomous robot exploration in unknown and complex environments. We first
utilize Gaussian process (GP) regression to learn a surrogate model to infer
the confidence-rich mutual information (CRMI) of querying control actions, then
adopt an objective function consisting of predicted CRMI values and prediction
uncertainties to conduct Bayesian optimization (BO), i.e., GP-based BO (GPBO).
The trade-off between the best action with the highest CRMI value
(exploitation) and the action with high prediction variance (exploration) can
be realized. To further improve the efficiency of GPBO, we propose a novel
lightweight information gain inference method based on Bayesian kernel
inference and optimization (BKIO), achieving an approximate logarithmic
complexity without the need for training. BKIO can also infer the CRMI and
generate the best action using BO with bounded cumulative regret, which ensures
its comparable accuracy to GPBO with much higher efficiency. Extensive
numerical and real-world experiments show the desired efficiency of our
proposed methods without losing exploration performance in different
unstructured, cluttered environments. We also provide our open-source
implementation code at https://github.com/Shepherd-Gregory/BKIO-Exploration.
