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.

Policy gradient methods are among the best Reinforcement Learning (RL) techniques to solve complex control problems.

There is a gap between finding a first-order stationary point (FOSP) and a second-order stationary point (SOSP) under differential privacy constraints, and it remains unclear whether privately finding an SOSP is more challenging than finding an FOSP. Specifically, Ganesh et al. (2023) demonstrated that an $\alpha$-SOSP can be found with $\alpha=O(\frac{1}{n^{1/3}}+(\frac{\sqrt{d}}{n\epsilon})^{3/7})$, where $n$ is the dataset size, $d$ is the dimension, and $\epsilon$ is the differential privacy parameter. Building on the SpiderBoost algorithm framework, we propose a new approach that uses adaptive batch sizes and incorporates the binary tree mechanism. Our method improves the results for privately finding an SOSP, achieving $\alpha=O(\frac{1}{n^{1/3}}+(\frac{\sqrt{d}}{n\epsilon})^{1/2})$. This improved bound matches the state-of-the-art for finding an FOSP, suggesting that privately finding an SOSP may be achievable at no additional cost.

Summary: This paper derives conditions for guaranteed improvement when using policy gradient methods. These conditions are for stochastic gradient estimates and also bound the amount of improvement with high probability. The authors then show how these bounds can be optimized by properly selecting the step size and batch size parameters. This is in contrast to previous work that only considers how the step size can be optimized. The result is an algorithm that can guarantee improvement with high probability.

Stochastic (on-line) learning can be faster than batch learning. However, at late times, the learning rate must be annealed to re(cid:173) move the noise present in the stochastic weight updates. In this annealing phase, the convergence rate (in mean square) is at best proportional to l/T where T is the number of input presentations. An alternative is to increase the batch size to remove the noise. In this paper we explore convergence for LMS using 1) small but fixed batch sizes and 2) an adaptive batch size. We show that the best adaptive batch schedule is exponential and has a rate of conver(cid:173) gence which is the same as for annealing, Le., at best proportional to l/T.

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.

Various schemes for adapting batch size have been recently proposed to accelerate stochastic algorithms. However, existing schemes either apply prescribed batch size adaption or require additional backtracking and condition verification steps to exploit the information along optimization path. In this paper, we propose an easy-to-implement scheme for adapting batch size by exploiting history stochastic gradients, based on which we propose the Adaptive batch size SGD (AbaSGD), AbaSVRG, and AbaSPIDER algorithms. To handle the dependence of the batch size on history stochastic gradients, we develop a new convergence analysis technique, and show that these algorithms achieve improved overall complexity over their vanilla counterparts. Moreover, their convergence rates are adaptive to the optimization landscape that the iterate experiences. Extensive experiments demonstrate that our algorithms substantially outperform existing competitive algorithms.

Mini-batch stochastic gradient descent (SGD) approximates the gradient of an objective function with the average gradient of some batch of constant size. While small batch sizes can yield high-variance gradient estimates that prevent the model from learning a good model, large batches may require more data and computational effort. This work presents a method to change the batch size adaptively with model quality. We show that our method requires the same number of model updates as full-batch gradient descent while requiring the same total number of gradient computations as SGD. While this method requires evaluating the objective function, we present a passive approximation that eliminates this constraint and improves computational efficiency. We provide extensive experiments illustrating that our methods require far fewer model updates without increasing the total amount of computation.

Convolutional Neural Networks (CNNs) are extensively in use due to their excellent results in various machine learning (ML) tasks like image classification and object detection. Recently, Capsule Networks (CapsNets) have shown improved performances compared to the traditional CNNs, by encoding and preserving spatial relationships between the detected features in a better way. This is achieved through the so-called Capsules (i.e., groups of neurons) that encode both the instantiation probability and the spatial information. However, one of the major hurdles in the wide adoption of CapsNets is its gigantic training time, which is primarily due to the relatively higher complexity of its constituting elements. In this paper, we illustrate how can we devise new optimizations in the training process to achieve fast training of CapsNets, and if such optimizations affect the network accuracy or not. Towards this, we propose a novel framework "X-TrainCaps" that employs lightweight software-level optimizations, including a novel learning rate policy called WarmAdaBatch that jointly performs warm restarts and adaptive batch size, as well as weight sharing for capsule layers to reduce the hardware requirements of CapsNets by removing unused/redundant connections and capsules, while keeping high accuracy through tests of different learning rate policies and batch sizes. We demonstrate that one of the solutions generated by X-TrainCaps framework can achieve 58.6% training time reduction while preserving the accuracy (even 0.9% accuracy improvement), compared to the CapsNet in the original paper by Sabour et al. (2017), while other Pareto-optimal solutions can be leveraged to realize trade-offs between training time and achieved accuracy.