In this paper, we present a new class of Markov decision processes (MDPs), called Tsallis MDPs, with Tsallis entropy maximization, which generalizes existing maximum entropy reinforcement learning (RL). A Tsallis MDP provides a unified framework for the original RL problem and RL with various types of entropy, including the well-known standard Shannon-Gibbs (SG) entropy, using an additional real-valued parameter, called an entropic index. By controlling the entropic index, we can generate various types of entropy, including the SG entropy, and a different entropy results in a different class of the optimal policy in Tsallis MDPs. We also provide a full mathematical analysis of Tsallis MDPs, including the optimality condition, performance error bounds, and convergence. Our theoretical result enables us to use any positive entropic index in RL. To handle complex and large-scale problems, we propose a model-free actor-critic RL method using Tsallis entropy maximization. We evaluate the regularization effect of the Tsallis entropy with various values of entropic indices and show that the entropic index controls the exploration tendency of the proposed method. For a different type of RL problems, we find that a different value of the entropic index is desirable. The proposed method is evaluated using the MuJoCo simulator and achieves the state-of-the-art performance.

Incremental learning suffers from two challenging problems; forgetting of old knowledge and intransigence on learning new knowledge. Prediction by the model incrementally learned with a subset of the dataset are thus uncertain and the uncertainty accumulates through the tasks by knowledge transfer. To prevent overfitting to the uncertain knowledge, we propose to penalize confident fitting to the uncertain knowledge by the Maximum Entropy Regularizer (MER). Additionally, to reduce class imbalance and induce a self-paced curriculum on new classes, we exclude a few samples from the new classes in every mini-batch, which we call DropOut Sampling (DOS). We further rethink evaluation metrics for forgetting and intransigence in incremental learning by tracking each sample's confusion at the transition of a task since the existing metrics that compute the difference in accuracy are often misleading. We show that the proposed method, named 'MEDIC', outperforms the state-of-the-art incremental learning algorithms in accuracy, forgetting, and intransigence measured by both the existing and the proposed metrics by a large margin in extensive empirical validations on CIFAR100 and a popular subset of ImageNet dataset (TinyImageNet).

Wang, D., and Liu, Q. Learning to draw samples: With application to amortized MLE for generative adversarial learning.

Fine-Grained Visual Classification (FGVC) is an important computer vision problem that involves small diversity within the different classes, and often requires expert annotators to collect data. Utilizing this notion of small visual diversity, we revisit Maximum-Entropy learning in the context of fine-grained classification, and provide a training routine that maximizes the entropy of the output probability distribution for training convolutional neural networks on FGVC tasks. We provide a theoretical as well as empirical justification of our approach, and achieve state-of-the-art performance across a variety of classification tasks in FGVC, that can potentially be extended to any fine-tuning task. Our method is robust to different hyperparameter values, amount of training data and amount of training label noise and can hence be a valuable tool in many similar problems.

Connectionist Temporal Classification (CTC) is an objective function for end-to-end sequence learning, which adopts dynamic programming algorithms to directly learn the mapping between sequences. CTC has shown promising results in many sequence learning applications including speech recognition and scene text recognition. However, CTC tends to produce highly peaky and overconfident distributions, which is a symptom of overfitting. To remedy this, we propose a regularization method based on maximum conditional entropy which penalizes peaky distributions and encourages exploration. We also introduce an entropy-based pruning method to dramatically reduce the number of CTC feasible paths by ruling out unreasonable alignments. Experiments on scene text recognition show that our proposed methods consistently improve over the CTC baseline without the need to adjust training settings. Code has been made publicly available at: https://github.com/liuhu-bigeye/enctc.crnn.

Connectionist Temporal Classification (CTC) is an objective function for end-to-end sequence learning, which adopts dynamic programming algorithms to directly learn the mapping between sequences. CTC has shown promising results in many sequence learning applications including speech recognition and scene text recognition. However, CTC tends to produce highly peaky and overconfident distributions, which is a symptom of overfitting. To remedy this, we propose a regularization method based on maximum conditional entropy which penalizes peaky distributions and encourages exploration. We also introduce an entropy-based pruning method to dramatically reduce the number of CTC feasible paths by ruling out unreasonable alignments. Experiments on scene text recognition show that our proposed methods consistently improve over the CTC baseline without the need to adjust training settings. Code has been made publicly available at: https://github.com/liuhu-bigeye/enctc.crnn.

Fine-Grained Visual Classification (FGVC) is an important computer vision problem that involves small diversity within the different classes, and often requires expert annotators to collect data. Utilizing this notion of small visual diversity, we revisit Maximum-Entropy learning in the context of fine-grained classification, and provide a training routine that maximizes the entropy of the output probability distribution for training convolutional neural networks on FGVC tasks. We provide a theoretical as well as empirical justification of our approach, and achieve state-of-the-art performance across a variety of classification tasks in FGVC, that can potentially be extended to any fine-tuning task. Our method is robust to different hyperparameter values, amount of training data and amount of training label noise and can hence be a valuable tool in many similar problems.

Suppose an agent is in a (possibly unknown) Markov decision process (MDP) in the absence of a reward signal, what might we hope that an agent can efficiently learn to do? One natural, intrinsically defined, objective problem is for the agent to learn a policy which induces a distribution over state space that is as uniform as possible, which can be measured in an entropic sense. Despite the corresponding mathematical program being non-convex, our main result provides a provably efficient method (both in terms of sample size and computational complexity) to construct such a maximum-entropy exploratory policy. Key to our algorithmic methodology is utilizing the conditional gradient method (a.k.a. the Frank-Wolfe algorithm) which utilizes an approximate MDP solver.

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.

Model-free deep reinforcement learning (RL) algorithms have been demonstrated on a range of challenging decision making and control tasks. However, these methods typically suffer from two major challenges: very high sample complexity and brittle convergence properties, which necessitate meticulous hyperparameter tuning. Both of these challenges severely limit the applicability of such methods to complex, real-world domains. In this paper, we propose soft actor-critic, an off-policy actor-critic deep RL algorithm based on the maximum entropy reinforcement learning framework. In this framework, the actor aims to maximize expected reward while also maximizing entropy - that is, succeed at the task while acting as randomly as possible. Prior deep RL methods based on this framework have been formulated as Q-learning methods. By combining off-policy updates with a stable stochastic actor-critic formulation, our method achieves state-of-the-art performance on a range of continuous control benchmark tasks, outperforming prior on-policy and off-policy methods. Furthermore, we demonstrate that, in contrast to other off-policy algorithms, our approach is very stable, achieving very similar performance across different random seeds.