Deep reinforcement learning (deep RL) agents have achieved remarkable success in a broad range of game-playing and continuous control tasks. While these agents are effective at maximizing rewards, it is often unclear what strategies they use to do so. In this paper, we take a step toward explaining deep RL agents through a case study in three Atari 2600 environments. In particular, we focus on understanding agents in terms of their visual attentional patterns during decision making. To this end, we introduce a method for generating rich saliency maps and use it to explain 1) what strong agents attend to 2) whether agents are making decisions for the right or wrong reasons, and 3) how agents evolve during the learning phase. We also test our method on non-expert human subjects and find that it improves their ability to reason about these agents. Our techniques are general and, though we focus on Atari, our long-term objective is to produce tools that explain any deep RL policy.
Gradient methods aim to understand what features of a DNN's input are most salient to its output by using variants of the chain rule. The simplest approach is to take the Jacobian with respect to the output of interest @cite_2 . Unfortunately, the Jacobian does not usually produce human-interpretable saliency maps. Thus several variants have emerged, aimed at modifying gradients to obtain more meaningful saliency. These variants include Guided Backpropagation @cite_12 , Excitation Backpropagation @cite_4 , and DeepLIFT @cite_0 .
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Nesterov's accelerated gradient descent (AGD), an instance of the general family of "momentum methods", provably achieves faster convergence rate than gradient descent (GD) in the convex setting. However, whether these methods are superior to GD in the nonconvex setting remains open. This paper studies a simple variant of AGD, and shows that it escapes saddle points and finds a second-order stationary point in @math iterations, faster than the @math iterations required by GD. To the best of our knowledge, this is the first Hessian-free algorithm to find a second-order stationary point faster than GD, and also the first single-loop algorithm with a faster rate than GD even in the setting of finding a first-order stationary point. Our analysis is based on two key ideas: (1) the use of a simple Hamiltonian function, inspired by a continuous-time perspective, which AGD monotonically decreases per step even for nonconvex functions, and (2) a novel framework called improve or localize, which is useful for tracking the long-term behavior of gradient-based optimization algorithms. We believe that these techniques may deepen our understanding of both acceleration algorithms and nonconvex optimization. Deep artificial neural networks (DNNs) are typically trained via gradient-based learning algorithms, namely backpropagation. Evolution strategies (ES) can rival backprop-based algorithms such as Q-learning and policy gradients on challenging deep reinforcement learning (RL) problems. However, ES can be considered a gradient-based algorithm because it performs stochastic gradient descent via an operation similar to a finite-difference approximation of the gradient. That raises the question of whether non-gradient-based evolutionary algorithms can work at DNN scales. Here we demonstrate they can: we evolve the weights of a DNN with a simple, gradient-free, population-based genetic algorithm (GA) and it performs well on hard deep RL problems, including Atari and humanoid locomotion. The Deep GA successfully evolves networks with over four million free parameters, the largest neural networks ever evolved with a traditional evolutionary algorithm. These results (1) expand our sense of the scale at which GAs can operate, (2) suggest intriguingly that in some cases following the gradient is not the best choice for optimizing performance, and (3) make immediately available the multitude of techniques that have been developed in the neuroevolution community to improve performance on RL problems. To demonstrate the latter, we show that combining DNNs with novelty search, which was designed to encourage exploration on tasks with deceptive or sparse reward functions, can solve a high-dimensional problem on which reward-maximizing algorithms (e.g. DQN, A3C, ES, and the GA) fail. Additionally, the Deep GA parallelizes better than ES, A3C, and DQN, and enables a state-of-the-art compact encoding technique that can represent million-parameter DNNs in thousands of bytes. We propose a partially learned approach for the solution of ill-posed inverse problems with not necessarily linear forward operators. The method builds on ideas from classical regularisation theory and recent advances in deep learning to perform learning while making use of prior information about the inverse problem encoded in the forward operator, noise model and a regularising functional. The method results in a gradient-like iterative scheme, where the 'gradient' component is learned using a convolutional network that includes the gradients of the data discrepancy and regulariser as input in each iteration. We present results of such a partially learned gradient scheme on a non-linear tomographic inversion problem with simulated data from both the Sheep-Logan phantom as well as a head CT. The outcome is compared against filtered backprojection and total variation reconstruction and the proposed method provides a 5.4 dB PSNR improvement over the total variation reconstruction while being significantly faster, giving reconstructions of pixel images in about 0.4 s using a single graphics processing unit (GPU). We propose a very simple modification of gradient descent and stochastic gradient descent. We show that when applied to a variety of machine learning models including softmax regression, convolutional neural nets, generative adversarial nets, and deep reinforcement learning, this very simple surrogate can dramatically reduce the variance and improve the accuracy of the generalization. The new algorithm, (which depends on one nonnegative parameter) when applied to non-convex minimization, tends to avoid sharp local minima. Instead it seeks somewhat flatter local (and often global) minima. The method only involves preconditioning the gradient by the inverse of a tri-diagonal matrix that is positive definite. The motivation comes from the theory of Hamilton-Jacobi partial differential equations. This theory demonstrates that the new algorithm is almost the same as doing gradient descent on a new function which (a) has the same global minima as the original function and (b) is "more convex". Again, the programming effort in doing this is minimal, in cost, complexity and effort. We implement our algorithm into both PyTorch and Tensorflow platforms, which will be made publicly available.