Recent advances in policy gradient methods and deep learning have demonstrated their applicability for complex reinforcement learning problems. However, the variance of the performance gradient estimates obtained from the simulation is often excessive, leading to poor sample efficiency. In this paper, we apply the stochastic variance reduced gradient descent (SVRG) to model-free policy gradient to significantly improve the sample-efficiency. The SVRG estimation is incorporated into a trust-region Newton conjugate gradient framework for the policy optimization. On several Mujoco tasks, our method achieves significantly better performance compared to the state-of-the-art model-free policy gradient methods in robotic continuous control such as trust region policy optimization (TRPO)
Optimization methods @cite_7 @cite_23 @cite_25 play a key role in the policy search, especially for nonlinear policies in continuous high-dimensional parameter space. For example, the well-known @cite_2 is simply a (stochastic) gradient descent method. To accelerate the convergence rates, Fisher information is adopted in Natural Gradient @cite_1 @cite_27 and TRPO @cite_19 . Stochastic Variance Reduction @cite_14 is proposed under the mechanics of control variates @cite_36 to accelerate the convergence of SGD by dramatic variance reduction. Recently, second order statistics and stochastic curvature information are adopted @cite_29 @cite_3 @cite_18 @cite_35 to improve the convergence while achieving the good trade-off between computations and accuracy for the large-scale machine learning problems. The stochastic and approximated curvature information is also useful to further accelerate the variance reduction methods @cite_11 @cite_10 .
@cite_35 @cite_18 @cite_14 @cite_7 @cite_36 @cite_29 @cite_1 @cite_3 @cite_19 @cite_27 @cite_23 @cite_2 @cite_10 @cite_25 @cite_11
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Stochastic gradient algorithms have been the main focus of large-scale learning problems and they led to important successes in machine learning. The convergence of SGD depends on the careful choice of learning rate and the amount of the noise in stochastic estimates of the gradients. In this paper, we propose a new adaptive learning rate algorithm, which utilizes curvature information for automatically tuning the learning rates. The information about the element-wise curvature of the loss function is estimated from the local statistics of the stochastic first order gradients. We further propose a new variance reduction technique to speed up the convergence. In our preliminary experiments with deep neural networks, we obtained better performance compared to the popular stochastic gradient algorithms. We consider stochastic strongly convex optimization with a complex inequality constraint. This complex inequality constraint may lead to computationally expensive projections in algorithmic iterations of the stochastic gradient descent (SGD) methods. To reduce the computation costs pertaining to the projections, we propose an Epoch-Projection Stochastic Gradient Descent (Epro-SGD) method. The proposed Epro-SGD method consists of a sequence of epochs; it applies SGD to an augmented objective function at each iteration within the epoch, and then performs a projection at the end of each epoch. Given a strongly convex optimization and for a total number of @math iterations, Epro-SGD requires only @math projections, and meanwhile attains an optimal convergence rate of @math , both in expectation and with a high probability. To exploit the structure of the optimization problem, we propose a proximal variant of Epro-SGD, namely Epro-ORDA, based on the optimal regularized dual averaging method. We apply the proposed methods on real-world applications; the empirical results demonstrate the effectiveness of our methods. Parallel implementations of stochastic gradient descent (SGD) have received significant research attention, thanks to its excellent scalability properties. A fundamental barrier when parallelizing SGD is the high bandwidth cost of communicating gradient updates between nodes; consequently, several lossy compresion heuristics have been proposed, by which nodes only communicate quantized gradients. Although effective in practice, these heuristics do not always guarantee convergence, and it is not clear whether they can be improved. In this paper, we propose Quantized SGD (QSGD), a family of compression schemes for gradient updates which provides convergence guarantees. QSGD allows the user to smoothly trade off and : nodes can adjust the number of bits sent per iteration, at the cost of possibly higher variance. We show that this trade-off is inherent, in the sense that improving it past some threshold would violate information-theoretic lower bounds. QSGD guarantees convergence for convex and non-convex objectives, under asynchrony, and can be extended to stochastic variance-reduced techniques. When applied to training deep neural networks for image classification and automated speech recognition, QSGD leads to significant reductions in end-to-end training time. For example, on 16GPUs, we can train the ResNet152 network to full accuracy on ImageNet 1.8x faster than the full-precision variant. We study optimization algorithms based on variance reduction for stochastic gradient descent (SGD). Remarkable recent progress has been made in this direction through development of algorithms like SAG, SVRG, SAGA. These algorithms have been shown to outperform SGD, both theoretically and empirically. However, asynchronous versions of these algorithms—a crucial requirement for modern large-scale applications—have not been studied. We bridge this gap by presenting a unifying framework for many variance reduction techniques. Subsequently, we propose an asynchronous algorithm grounded in our framework, and prove its fast convergence. An important consequence of our general approach is that it yields asynchronous versions of variance reduction algorithms such as SVRG and SAGA as a byproduct. Our method achieves near linear speedup in sparse settings common to machine learning. We demonstrate the empirical performance of our method through a concrete realization of asynchronous SVRG.