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We propose a data-driven Neural Network (NN) optimization framework to determine the optimal multi-period dynamic asset allocation strategy for outperforming a general stochastic target. We formulate the problem as an optimal stochastic control with an asymmetric, distribution shaping, objective function. The proposed framework is illustrated with the asset allocation problem in the accumulation phase of a defined contribution pension plan, with the goal of achieving a higher terminal wealth than a stochastic benchmark. We demonstrate that the data-driven approach is capable of learning an adaptive asset allocation strategy directly from historical market returns, without assuming any parametric model of the financial market dynamics. Following the optimal adaptive strategy, investors can make allocation decisions simply depending on the current state of the portfolio. The optimal adaptive strategy outperforms the benchmark constant proportion strategy, achieving a higher terminal wealth with a 90% probability, a 46% higher median terminal wealth, and a significantly more right-skewed terminal wealth distribution. We further demonstrate the robustness of the optimal adaptive strategy by testing the performance of the strategy on bootstrap resampled market data, which has different distributions compared to the training data.