We consider the problem of estimation of an unknown real valued function with real valued input by an agent. The agent exists in 3D Euclidean space. It is able to traverse in a 2D plane while the function is depicted in a 2D plane perpendicular to the plane of traversal. By viewing the function from a given position, the agent is able to collect a data point lying on the function. By traversing through the plane while paying a control cost, the agent collects a finite set of data points. The set of data points are used by the agent to estimate the function. The objective of the agent is to find a control law which minimizes the control cost while estimating the function optimally. We formulate a control problem for the agent incorporating an inference cost and the control cost. The control problem is relaxed by finding a lower bound for the cost function. We present a kernel based linear regression model to approximate the cost-to-go and use the same in a control algorithm to solve the relaxed optimization problem. We present simulation results comparing the proposed approach with greedy algorithm based exploration.