Fixed-Dimensional and Permutation Invariant State Representation of Autonomous Driving

In this paper, we propose a new state representation method, called encoding sum and concatenation (ESC), to describe the environment observation for decision-making in autonomous driving. Unlike existing state representation methods, ESC is applicable to the situation where the number of surrounding vehicles is variable and eliminates the need for manually pre-designed sorting rules, leading to higher representation ability and generality. The proposed ESC method introduces a feature neural network (NN) to encode the real-valued feature of each surrounding vehicle into an encoding vector, and then adds these vectors up to obtain the representation vector of the set of surrounding vehicles. Then, a fixed-dimensional and permutation-invariance state representation can be obtained by concatenating the set representation with other variables, such as indicators of the ego vehicle and road. By introducing the sum-of-power mapping, this paper has further proved that the injectivity of the ESC state representation can be guaranteed if the output dimension of the feature NN is greater than the number of variables of all surrounding vehicles. This means that the ESC representation can be used to describe the environment and taken as the inputs of learning-based policy functions. Experiments demonstrate that compared with the fixed-permutation representation method, the policy learning accuracy based on ESC representation is improved by 62.2%.