  This paper proposes a Deep Reinforcement Learning algorithm for financial
portfolio trading based on Deep Q-learning. The algorithm is capable of trading
high-dimensional portfolios from cross-sectional datasets of any size which may
include data gaps and non-unique history lengths in the assets. We sequentially
set up environments by sampling one asset for each environment while rewarding
investments with the resulting asset's return and cash reservation with the
average return of the set of assets. This enforces the agent to strategically
assign capital to assets that it predicts to perform above-average. We apply
our methodology in an out-of-sample analysis to 48 US stock portfolio setups,
varying in the number of stocks from ten up to 500 stocks, in the selection
criteria and in the level of transaction costs. The algorithm on average
outperforms all considered passive and active benchmark investment strategies
by a large margin using only one hyperparameter setup for all portfolios.
