Precision agriculture requires efficient autonomous systems for crop monitoring, where agents must explore large-scale environments while minimizing resource consumption. This work addresses the problem as an active exploration task in a grid environment representing an agricultural field. Each cell may contain targets (e.g., damaged crops) observable from nine predefined points of view (POVs). Agents must infer the number of targets per cell using partial, sequential observations. We propose a two-stage deep learning framework. A pre-trained LSTM serves as a belief model, updating a probabilistic map of the environment and its associated entropy, which defines the expected information gain (IG). This allows agents to prioritize informative regions. A key contribution is the inclusion of a POV visibility mask in the input, preserving the Markov property under partial observability and avoiding revisits to already explored views. Three agent architectures were compared: an untrained IG-based agent selecting actions to maximize entropy reduction; a DQN agent using CNNs over local 3x3 inputs with belief, entropy, and POV mask; and a Double-CNN DQN agent with wider spatial context. Simulations on 20x20 maps showed that the untrained agent performs well despite its simplicity. The DQN agent matches this performance when the POV mask is included, while the Double-CNN agent consistently achieves superior exploration efficiency, especially in larger environments. Results show that uncertainty-aware policies leveraging entropy, belief states, and visibility tracking lead to robust and scalable exploration. Future work includes curriculum learning, multi-agent cooperation with shared rewards, transformer-based models, and intrinsic motivation mechanisms to further enhance learning efficiency and policy generalization.

Computing expected information gain (EIG) from prior to posterior (equivalently, mutual information between candidate observations and model parameters or other quantities of interest) is a fundamental challenge in Bayesian optimal experimental design. We formulate flexible transport-based schemes for EIG estimation in general nonlinear/non-Gaussian settings, compatible with both standard and implicit Bayesian models. These schemes are representative of two-stage methods for estimating or bounding EIG using marginal and conditional density estimates. In this setting, we analyze the optimal allocation of samples between training (density estimation) and approximation of the outer prior expectation. We show that with this optimal sample allocation, the MSE of the resulting EIG estimator converges more quickly than that of a standard nested Monte Carlo scheme. We then address the estimation of EIG in high dimensions, by deriving gradient-based upper bounds on the mutual information lost by projecting the parameters and/or observations to lower-dimensional subspaces. Minimizing these upper bounds yields projectors and hence low-dimensional EIG approximations that outperform approximations obtained via other linear dimension reduction schemes. Numerical experiments on a PDE-constrained Bayesian inverse problem also illustrate a favorable trade-off between dimension truncation and the modeling of non-Gaussianity, when estimating EIG from finite samples in high dimensions.