We examine the impact of learning Lipschitz continuous models in the context of model-based reinforcement learning. We provide a novel bound on multi-step prediction error of Lipschitz models where we quantify the error using the Wasserstein metric. We go on to prove an error bound for the value-function estimate arising from Lipschitz models and show that the estimated value function is itself Lipschitz. We conclude with empirical results that show the benefits of controlling the Lipschitz constant of neural-network models.
In 35th International Conference on Machine Learning (ICML),
End-to-end learning of recurrent neural networks (RNNs) is an attractive solution for dialog systems; however, current techniques are data-intensive and require thousands of dialogs to learn simple behaviors. We introduce Hybrid Code Networks (HCNs), which combine an RNN with domain-specific knowledge encoded as software and system action templates. Compared to existing end-to-end approaches, HCNs considerably reduce the amount of training data required, while retaining the key benefit of inferring a latent representation of dialog state. In addition, HCNs can be optimized with supervised learning, reinforcement learning, or a mixture of both. HCNs attain state-of-the-art performance on the bAbI dialog dataset, and outperform two commercially deployed customer-facing dialog systems.
In 55th Annual Meeting of the Association for Computational Linguistics (ACL),
A softmax operator applied to a set of values acts somewhat like the maximization function and somewhat like an average. In sequential decision making, softmax is often used in settings where it is necessary to maximize utility but also to hedge against problems that arise from putting all of one’s weight behind a single maximum utility decision. The Boltzmann softmax operator is the most commonly used softmax operator in this setting, but we show that this operator is prone to misbehavior. In this work, we study a differentiable softmax operator that, among other properties, is a non-expansion ensuring a convergent behavior in learning and planning. We introduce a variant of SARSA algorithm that, by utilizing the new operator, computes a Boltzmann policy with a state-dependent temperature parameter. We show that the algorithm is convergent and that it performs favorably in practice.
In 34th International Conference on Machine Learning (ICML),