Deep reinforcement learning(DRL) has shown significant promise in a wide range of applications including computer games and robotics. Yet, training DRL policies consume extraordinary computing resources resulting in dense policies which are prone to overfitting. Moreover, inference with dense DRL policies limit their practical applications, especially in edge computing. Techniques such as pruning and singular value decomposition have been used with deep learning models to achieve sparsification and model compression to limit overfitting and reduce memory consumption. However, these techniques resulted in sub-optimal performance with notable decay in rewards. $L_1$ and $L_2$ regularization techniques have been proposed for neural network sparsification and sparse auto-encoder development, but their implementation in DRL environments has not been apparent. We propose a novel $L_0$-norm-regularization technique using an optimal sparsity map to sparsify DRL policies and promote their decomposition to a lower rank without decay in rewards. We evaluated our $L_0$-norm-regularization technique across five different environments (Cartpole-v1, Acrobat-v1, LunarLander-v2, SuperMarioBros-7.1.v0 and Surgical Robot Learning) using several on-policy and off-policy algorithms. We demonstrated that the $L_0$-norm-regularized DRL policy in the SuperMarioBros environment achieved 93% sparsity and gained 70% compression when subjected to low-rank decomposition, while significantly outperforming the dense policy. Additionally, the $L_0$-norm-regularized DRL policy in the Surgical Robot Learning environment achieved a 36% sparsification and gained 46% compression when decomposed to a lower rank, while being performant. The results suggest that our custom $L_0$-norm-regularization technique for sparsification of DRL policies is a promising avenue to reduce computational resources and limit overfitting.

We propose a general method called truncated gradient to induce sparsity in the weights of online learning algorithms with convex loss functions. This method has several essential properties: The degree of sparsity is continuous -- a parameter controls the rate of sparsification from no sparsification to total sparsification. The approach is theoretically motivated, and an instance of it can be regarded as an online counterpart of the popular $L_1$-regularization method in the batch setting. We prove that small rates of sparsification result in only small additional regret with respect to typical online learning guarantees. The approach works well empirically. We apply the approach to several datasets and find that for datasets with large numbers of features, substantial sparsity is discoverable.