Policy gradient methods are among the best Reinforcement Learning (RL) techniques to solve complex control problems. In real-world RL applications, it is common to have a good initial policy whose performance needs to be improved and it may not be acceptable to try bad policies during the learning process. Although several methods for choosing the step size exist, research paid less attention to determine the batch size, that is the number of samples used to estimate the gradient direction for each update of the policy parameters. In this paper, we propose a set of methods to jointly optimize the step and the batch sizes that guarantee (with high probability) to improve the policy performance after each update. Besides providing theoretical guarantees, we show numerical simulations to analyse the behaviour of our methods.

Background: Deep learning models are typically trained using stochastic gradient descent or one of its variants. These methods update the weights using their gradient, estimated from a small fraction of the training data. It has been observed that when using large batch sizes there is a persistent degradation in generalization performance - known as the generalization gap phenomenon. Identifying the origin of this gap and closing it had remained an open problem. Contributions: We examine the initial high learning rate training phase.

As an indispensable component, Batch Normalization (BN) has successfully improved the training of deep neural networks (DNNs) with mini-batches, by normalizing the distribution of the internal representation for each hidden layer. However, the effectiveness of BN would diminish with the scenario of micro-batch (e.g. less than 4 samples in a mini-batch), since the estimated statistics in a mini-batch are not reliable with insufficient samples. This limits BN's room in training larger models on segmentation, detection, and video-related problems, which require small batches constrained by memory consumption. In this paper, we present a novel normalization method, called Kalman Normalization (KN), for improving and accelerating the training of DNNs, particularly under the context of micro-batches. Specifically, unlike the existing solutions treating each hidden layer as an isolated system, KN treats all the layers in a network as a whole system, and estimates the statistics of a certain layer by considering the distributions of all its preceding layers, mimicking the merits of Kalman Filtering. On ResNet50 trained in ImageNet, KN has 3.4% lower error than its BN counterpart when using a batch size of 4; Even when using typical batch sizes, KN still maintains an advantage over BN while other BN variants suffer a performance degradation. Moreover, KN can be naturally generalized to many existing normalization variants to obtain gains, e.g.

At thet-th backward propagation step, we can derive the gradient il(wt)toupdatei-th module inM. The number in the bracket represents the batch size. We see that when the batch size is small (i.e.,32), the gradientvariancesaresimilar. N and K indicate the number of FPN levels and region proposals fed into the detection head. To evaluate this assumption, as shown in Figure 1, we have three observations. As illustrated by the second figure in Figure 1, the gradient misalignment phenomenon between detection head and backbone has been reduced.

We consider the penalized distributionally robust optimization (DRO) problem with a closed, convex uncertainty set, a setting that encompasses learning using f -DRO and spectral/ L-risk minimization.

Our code is available at https://github.com/sail-sg/stde

IMP-MoE-L focusing on video tasks that achieves new state-of-the-art in zero-shot video classification: 77.0% on Kinetics-400, 76.8% on Kinetics-600, and 68.3% on