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.
On the other hand, probabilistic model based methods aim to find the reward function which maximizes the likelihood or posterior distribution. @cite_2 proposed maximum entropy IRL (MaxEnt) using the principle of maximum entropy to alleviate the inherent ambiguity problem of the reward function. In @cite_20 , proposed Bayesian IRL (BIRL), where the Bayesian probabilistic model was defined and effectively solved by using a Metropolis-Hastings sampling method. Levine and Koltun @cite_14 proposed Gaussian process inverse reinforcement learning (GPIRL), where a nonlinear reward function is effectively modeled by a sparse Gaussian process with inducing inputs.
@cite_14 @cite_20 @cite_2
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We present a probabilistic algorithm for nonlinear inverse reinforcement learning. The goal of inverse reinforcement learning is to learn the reward function in a Markov decision process from expert demonstrations. While most prior inverse reinforcement learning algorithms represent the reward as a linear combination of a set of features, we use Gaussian processes to learn the reward as a nonlinear function, while also determining the relevance of each feature to the expert's policy. Our probabilistic algorithm allows complex behaviors to be captured from suboptimal stochastic demonstrations, while automatically balancing the simplicity of the learned reward structure against its consistency with the observed actions. Inverse Reinforcement Learning (IRL) is the problem of learning the reward function underlying a Markov Decision Process given the dynamics of the system and the behaviour of an expert. IRL is motivated by situations where knowledge of the rewards is a goal by itself (as in preference elicitation) and by the task of apprenticeship learning (learning policies from an expert). In this paper we show how to combine prior knowledge and evidence from the expert's actions to derive a probability distribution over the space of reward functions. We present efficient algorithms that find solutions for the reward learning and apprenticeship learning tasks that generalize well over these distributions. Experimental results show strong improvement for our methods over previous heuristic-based approaches. Recent research has shown the benefit of framing problems of imitation learning as solutions to Markov Decision Problems. This approach reduces learning to the problem of recovering a utility function that makes the behavior induced by a near-optimal policy closely mimic demonstrated behavior. In this work, we develop a probabilistic approach based on the principle of maximum entropy. Our approach provides a well-defined, globally normalized distribution over decision sequences, while providing the same performance guarantees as existing methods. We develop our technique in the context of modeling real-world navigation and driving behaviors where collected data is inherently noisy and imperfect. Our probabilistic approach enables modeling of route preferences as well as a powerful new approach to inferring destinations and routes based on partial trajectories.