This paper presents a new human activity recognition method that uses a camera mounted on a mobile robot. We assume that the robot's camera captures images of a person and recognizes his/her activities based on skeletal and visual features extracted from the images. A key issue encountered with this method for activity recognition is that it requires the robot to position itself so that it has an adequate field of view of the activities being conducted. For example, if the robot is directly behind a person while observing that person making tea, it will be difficult for the robot to distinguish that activity from other similar activities such as preparing a meal or washing dishes. Our method employs deep reinforcement learning to control the movements of the mobile robot that is observing the activities in order to maximize its recognition accuracy while minimizing its energy consumption related to its movement. We propose effective action- and state-space designs that can achieve early training convergence and highly accurate activity recognition by: (i) incorporating the confidence of the activity recognition output when evaluating the quality of the current state (position), (ii) incorporating the costs of subsequent actions when estimating values for those actions, and (iii) designing an effective action space that accelerates reinforcement learning by restricting the movement space of the robot to the circumference of a circle with a predefined radius centered on the person.