UDQL: Bridging The Gap between MSE Loss and The Optimal Value Function in Offline Reinforcement Learning

The Mean Square Error (MSE) is commonly utilized to estimate the solution of the optimal value function in the vast majority of offline reinforcement learning (RL) models and has achieved outstanding performance. However, we find that its principle can lead to overestimation phenomenon for the value function. In this paper, we first theoretically analyze overestimation phenomenon led by MSE and provide the theoretical upper bound of the overestimated error. Furthermore, to address it, we propose a novel Bellman underestimated operator to counteract overestimation phenomenon and then prove its contraction characteristics. At last, we propose the offline RL algorithm based on underestimated operator and diffusion policy model. Extensive experimental results on D4RL tasks show that our method can outperform state-of-the-art offline RL algorithms, which demonstrates that our theoretical analysis and underestimation way are effective for offline RL tasks.

Signal Processing Meets SGD: From Momentum to Filter

In the field of deep learning, Stochastic Gradient Descent (SGD) and its momentum-based variants are the predominant choices for optimization algorithms. Despite all that, these momentum strategies, which accumulate historical gradients by using a fixed $\beta$ hyperparameter to smooth the optimization processing, often neglect the potential impact of the variance of historical gradients on the current gradient estimation. In the gradient variance during training, fluctuation indicates the objective function does not meet the Lipschitz continuity condition at all time, which raises the troublesome optimization problem. This paper aims to explore the potential benefits of reducing the variance of historical gradients to make optimizer converge to flat solutions. Moreover, we proposed a new optimization method based on reducing the variance. We employed the Wiener filter theory to enhance the first moment estimation of SGD, notably introducing an adaptive weight to optimizer. Specifically, the adaptive weight dynamically changes along with temporal fluctuation of gradient variance during deep learning model training. Experimental results demonstrated our proposed adaptive weight optimizer, SGDF (Stochastic Gradient Descent With Filter), can achieve satisfactory performance compared with state-of-the-art optimizers.