Title: WaveCorr: Deep Reinforcement Learning with Permutation Invariant Policy Networks for Portfolio Management. Abstract: The problem of portfolio management represents an important and challenging class of dynamic decision making problems, where rebalancing decisions need to be made over time with the consideration of many factors such as investors’ preferences, trading environment, and market conditions. In this paper, we present a new portfolio policy network architecture for deep reinforcement learning (DRL) that can exploit more effectively cross-asset dependency information and achieve better performance than  state-of-the-art architectures. In doing so, we introduce a new form of permutation invariance property for policy networks and derive general theory for verifying its applicability. Our portfolio policy network, named WaveCorr, is the first convolutional neural network architecture that preserves this invariance property when treating asset correlation information. Finally, in a set of experiments conducted using data from both Canadian (TSX) and American stock markets (S\&P 500), WaveCorr consistently outperforms other architectures with an impressive 3\%-25\% absolute improvement in terms of average annual return, and up to more than 200\% relative improvement in average Sharpe ratio. We also measured an improvement of a factor of up to 5 in the stability of performance under random choices of initial asset ordering and weights. The stability of the network has been found as particularly valuable by our industrial partner.