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Maximum Causal Tsallis Entropy Imitation Learning

Neural Information Processing Systems

In this paper, we propose a novel maximum causal Tsallis entropy (MCTE) framework for imitation learning which can efficiently learn a sparse multi-modal policy distribution from demonstrations. We provide the full mathematical analysis of the proposed framework. First, the optimal solution of an MCTE problem is shown to be a sparsemax distribution, whose supporting set can be adjusted. The proposed method has advantages over a softmax distribution in that it can exclude unnecessary actions by assigning zero probability. Second, we prove that an MCTE problem is equivalent to robust Bayes estimation in the sense of the Brier score. Third, we propose a maximum causal Tsallis entropy imitation learning (MCTEIL) algorithm with a sparse mixture density network (sparse MDN) by modeling mixture weights using a sparsemax distribution. In particular, we show that the causal Tsallis entropy of an MDN encourages exploration and efficient mixture utilization while Boltzmann Gibbs entropy is less effective. We validate the proposed method in two simulation studies and MCTEIL outperforms existing imitation learning methods in terms of average returns and learning multi-modal policies.


Maximum Causal Tsallis Entropy Imitation Learning

Neural Information Processing Systems

In this paper, we propose a novel maximum causal Tsallis entropy (MCTE) framework for imitation learning which can efficiently learn a sparse multi-modal policy distribution from demonstrations. We provide the full mathematical analysis of the proposed framework. First, the optimal solution of an MCTE problem is shown to be a sparsemax distribution, whose supporting set can be adjusted. The proposed method has advantages over a softmax distribution in that it can exclude unnecessary actions by assigning zero probability. Second, we prove that an MCTE problem is equivalent to robust Bayes estimation in the sense of the Brier score.


Sparse Markov Decision Processes with Causal Sparse Tsallis Entropy Regularization for Reinforcement Learning

arXiv.org Machine Learning

In this paper, a sparse Markov decision process (MDP) with novel causal sparse Tsallis entropy regularization is proposed.The proposed policy regularization induces a sparse and multi-modal optimal policy distribution of a sparse MDP. The full mathematical analysis of the proposed sparse MDP is provided.We first analyze the optimality condition of a sparse MDP. Then, we propose a sparse value iteration method which solves a sparse MDP and then prove the convergence and optimality of sparse value iteration using the Banach fixed point theorem. The proposed sparse MDP is compared to soft MDPs which utilize causal entropy regularization. We show that the performance error of a sparse MDP has a constant bound, while the error of a soft MDP increases logarithmically with respect to the number of actions, where this performance error is caused by the introduced regularization term. In experiments, we apply sparse MDPs to reinforcement learning problems. The proposed method outperforms existing methods in terms of the convergence speed and performance.


Multi-task Maximum Entropy Inverse Reinforcement Learning

arXiv.org Artificial Intelligence

Multi-task Inverse Reinforcement Learning (IRL) is the problem of inferring multiple reward functions from expert demonstrations. Prior work, built on Bayesian IRL, is unable to scale to complex environments due to computational constraints. This paper contributes the first formulation of multi-task IRL in the more computationally efficient Maximum Causal Entropy (MCE) IRL framework. Experiments show our approach can perform one-shot imitation learning in a gridworld environment that single-task IRL algorithms require hundreds of demonstrations to solve. Furthermore, we outline how our formulation can be applied to state-of-the-art MCE IRL algorithms such as Guided Cost Learning. This extension, based on meta-learning, could enable multi-task IRL to be performed for the first time in high-dimensional, continuous state MDPs with unknown dynamics as commonly arise in robotics.


Multi-Modal Imitation Learning from Unstructured Demonstrations using Generative Adversarial Nets

Neural Information Processing Systems

Imitation learning has traditionally been applied to learn a single task from demonstrations thereof. The requirement of structured and isolated demonstrations limits the scalability of imitation learning approaches as they are difficult to apply to real-world scenarios, where robots have to be able to execute a multitude of tasks. In this paper, we propose a multi-modal imitation learning framework that is able to segment and imitate skills from unlabelled and unstructured demonstrations by learning skill segmentation and imitation learning jointly. The extensive simulation results indicate that our method can efficiently separate the demonstrations into individual skills and learn to imitate them using a single multi-modal policy.