Image-based robot action planning is becoming an active area of research owing to recent advances in deep learning. To evaluate and execute robot actions, recently proposed approaches require the estimation of the optimal cost-minimizing path, such as the shortest distance or time, between two states. To estimate the cost, parametric models consisting of deep neural networks are widely used. However, such parametric models require large amounts of correctly labeled data to accurately estimate the cost. In real robotic tasks, collecting such data is not always feasible, and the robot itself may require collecting it. In this study, we empirically show that when a model is trained with data autonomously collected by a robot, the estimation of such parametric models could be inaccurate to perform a task. Specifically, the higher the maximum predicted distance, the more inaccurate the estimation, and the robot fails navigating in the environment. To overcome this issue, we propose an alternative metric, “task achievability” (TA), which is defined as the probability that a robot will reach a goal state within a specified number of timesteps. Compared to the training of optimal cost estimator, TA can use both optimal and non-optimal trajectories in the training dataset to train, which leads to a stable estimation. We demonstrate the effectiveness of TA through robot navigation experiments in an environment resembling a real living room. We show that TA-based navigation succeeds in navigating a robot to different target positions, even when conventional cost estimator-based navigation fails.