In this paper, we focus on the problem of inferring the underlying reward function of an expert given demonstrations, which is often referred to as inverse reinforcement learning (IRL). In particular, we propose a model-free density-based IRL algorithm, named density matching reward learning (DMRL), which does not require model dynamics. The performance of DMRL is analyzed theoretically and the sample complexity is derived. Furthermore, the proposed DMRL is extended to handle nonlinear IRL problems by assuming that the reward function is in the reproducing kernel Hilbert space (RKHS) and kernel DMRL (KDMRL) is proposed. The parameters for KDMRL can be computed analytically, which greatly reduces the computation time. The performance of KDMRL is extensively evaluated in two sets of experiments: grid world and track driving experiments. In grid world experiments, the proposed KDMRL method is compared with both model-based and model-free IRL methods and shows superior performance on a nonlinear reward setting and competitive performance on a linear reward setting in terms of expected value differences. Then we move on to more realistic experiments of learning different driving styles for autonomous navigation in complex and dynamic tracks using KDMRL and receding horizon control.
A margin based approach aims to maximize the margin between the value of the expert's policy compared to other possible policies. An IRL problem was first introduced by Ng and Russell @cite_23 , where the parameters of the reward function are optimized by maximizing the margin between randomly sampled reward functions. Abbeel and Ng @cite_32 proposed an apprenticeship learning algorithm, which minimizes the difference between the empirical distribution of an expert and the distribution induced by the reward function. @cite_25 proposed the maximum margin planning (MMP) algorithm, where Bellman-flow constraints are utilized to maximize the margin between the experts' policy and all other policies.
@cite_25 @cite_32 @cite_23
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The Maximum Margin Planning (MMP) (, 2006) algorithm solves imitation learning problems by learning linear mappings from features to cost functions in a planning domain. The learned policy is the result of minimum-cost planning using these cost functions. These mappings are chosen so that example policies (or trajectories) given by a teacher appear to be lower cost (with a loss-scaled margin) than any other policy for a given planning domain. We provide a novel approach, MMPBOOST, based on the functional gradient descent view of boosting (, 1999; Friedman, 1999a) that extends MMP by "boosting" in new features. This approach uses simple binary classification or regression to improve performance of MMP imitation learning, and naturally extends to the class of structured maximum margin prediction problems. (, 2005) Our technique is applied to navigation and planning problems for outdoor mobile robots and robotic legged locomotion. This paper considers the Inverse Reinforcement Learning (IRL) problem, that is inferring a reward function for which a demonstrated expert policy is optimal. We propose to break the IRL problem down into two generic Supervised Learning steps: this is the Cascaded Supervised IRL (CSI) approach. A classification step that defines a score function is followed by a regression step providing a reward function. A theoretical analysis shows that the demonstrated expert policy is near-optimal for the computed reward function. Not needing to repeatedly solve a Markov Decision Process (MDP) and the ability to leverage existing techniques for classification and regression are two important advantages of the CSI approach. It is furthermore empirically demonstrated to compare positively to state-of-the-art approaches when using only transitions sampled according to the expert policy, up to the use of some heuristics. This is exemplified on two classical benchmarks (the mountain car problem and a highway driving simulator). We present a formulation of deep learning that aims at producing a large margin classifier. The notion of margin, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically successful results for both classification and regression tasks. However, most large margin algorithms are applicable only to shallow models with a preset feature representation; and conventional margin methods for neural networks only enforce margin at the output layer. Such methods are therefore not well suited for deep networks. In this work, we propose a novel loss function to impose a margin on any chosen set of layers of a deep network (including input and hidden layers). Our formulation allows choosing any norm on the metric measuring the margin. We demonstrate that the decision boundary obtained by our loss has nice properties compared to standard classification loss functions. Specifically, we show improved empirical results on the MNIST, CIFAR-10 and ImageNet datasets on multiple tasks: generalization from small training sets, corrupted labels, and robustness against adversarial perturbations. The resulting loss is general and complementary to existing data augmentation (such as random adversarial input transform) and regularization techniques (such as weight decay, dropout, and batch norm). We consider the problem of imitation learning where the examples, demonstrated by an expert, cover only a small part of a large state space. Inverse Reinforcement Learning (IRL) provides an ecient tool for generalizing the demonstration, based on the assumption that the expert is optimally acting in a Markov Decision Process (MDP). Most of the past work on IRL requires that a (near)optimal policy can be computed for dierent reward functions. However, this requirement can hardly be satised in systems with a large, or continuous, state space. In this paper, we propose a model-free IRL algorithm, where the relative entropy between the empirical distribution of the state-action trajectories under a baseline policy and their distribution under the learned policy is minimized by stochastic gradient descent. We compare this new approach to well-known IRL algorithms using learned MDP models. Empirical results on simulated car racing, gridworld and ball-in-a-cup problems show that our approach is able to learn good policies from a small number of demonstrations.