Multi-task IRL allows for the possibility that the expert could be switching between multiple ways of solving the same problem, or interleaving demonstrations of multiple tasks. The learner aims to learn the multiple reward functions that guide these ways of solving the problem. We present a new method for multi-task IRL that generalizes the well-known maximum entropy approach to IRL by combining it with the Dirichlet process based clustering of the observed input. This yields a single nonlinear optimization problem, called MaxEnt Multi-task IRL, which can be solved using the Lagrangian relaxation and gradient descent methods. We evaluate MaxEnt Multi-task IRL in simulation on the robotic task of sorting onions on a processing line where the expert utilizes multiple ways of detecting and removing blemished onions. The method is able to learn the underlying reward functions to a high level of accuracy and it improves on the previous approaches to multi-task IRL.
Two hitherto disconnected threads of research, diverse exploration (DE) and maximum entropy RL have addressed a wide range of problems facing reinforcement learning algorithms via ostensibly distinct mechanisms. In this work, we identify a connection between these two approaches. First, a discriminator-based diversity objective is put forward and connected to commonly used divergence measures. We then extend this objective to the maximum entropy framework and propose an algorithm Maximum Entropy Diverse Exploration (MEDE) which provides a principled method to learn diverse behaviors. A theoret…
Inverse Reinforcement Learning (IRL) algorithms infer a reward function that explains demonstrations provided by an expert acting in the environment. Maximum Causal Entropy (MCE) IRL is currently the most popular formulation of IRL, with numerous extensions. In this tutorial, we present a compressed derivation of MCE IRL and the key results from contemporary implementations of MCE IRL algorithms. We hope this will serve both as an introductory resource for those new to the field, and as a concise reference for those already familiar with these topics.
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 a 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 need hundreds of demonstrations to solve. We outline preliminary work using meta-learning to…
Singapore Management University（新加坡管理大学）；Nanyang Technological University（南洋理工大学）；Massachusetts Institute of Technology（麻省理工学院）
We consider the problem of learning from demonstrated trajectories with inverse reinforcement learning (IRL). Motivated by a limitation of the classical maximum entropy model in capturing the structure of the network of states, we propose an IRL model based on a generalized version of the causal entropy maximization problem, which allows us to generate a class of maximum entropy IRL models. Our generalized model has an advantage of being able to recover, in addition to a reward function, another expert's function that would (partially) capture the impact of the connecting structure of the stat…
Mixture models are an expressive hypothesis class that can approximate a rich set of policies. However, using mixture policies in the Maximum Entropy (MaxEnt) framework is not straightforward. The entropy of a mixture model is not equal to the sum of its components, nor does it have a closed-form expression in most cases. Using such policies in MaxEnt algorithms, therefore, requires constructing a tractable approximation of the mixture entropy. In this paper, we derive a simple, low-variance mixture-entropy estimator. We show that it is closely related to the sum of marginal entropies. Equippe…
Inverse Reinforcement Learning (IRL) is a powerful way of learning from demonstrations. In this paper, we address IRL problems with the availability of prior knowledge that optimal policies will never violate certain constraints. Conventional approaches ignoring these constraints need many demonstrations to converge. We propose XOR-Maximum Entropy Constrained Inverse Reinforcement Learning (X-MEN), which is guaranteed to converge to the optimal policy in linear rate w.r.t. the number of learning iterations. X-MEN embeds XOR-sampling -- a provable sampling approach that transforms the #P comple…
In recent years, there have been many deep structures for Reinforcement Learning, mainly for value function estimation and representations. These methods achieved great success in Atari 2600 domain. In this paper, we propose an improved architecture based upon Dueling Networks, in this architecture, there are two separate estimators, one approximate the state value function and the other, state advantage function. This improvement based on Maximum Entropy, shows better policy evaluation compared to the original network and other value-based architectures in Atari domain.
Singapore Management University（新加坡管理大学）；Massachusetts Institute of Technology（麻省理工学院）
We study inverse reinforcement learning (IRL) and imitation learning (IM), the problems of recovering a reward or policy function from expert's demonstrated trajectories. We propose a new way to improve the learning process by adding a weight function to the maximum entropy framework, with the motivation of having the ability to learn and recover the stochasticity (or the bounded rationality) of the expert policy. Our framework and algorithms allow to learn both a reward (or policy) function and the structure of the entropy terms added to the Markov Decision Processes, thus enhancing the learn…
University of Virginia（弗吉尼亚大学）；University of Illinois at Urbana Champaign（伊利诺伊大学厄巴纳-香槟分校）；Rice University（莱斯大学）
Inspired by human visual attention, we propose a novel inverse reinforcement learning formulation using Maximum Entropy Deep Inverse Reinforcement Learning (MEDIRL) for predicting the visual attention of drivers in accident-prone situations. MEDIRL predicts fixation locations that lead to maximal rewards by learning a task-sensitive reward function from eye fixation patterns recorded from attentive drivers. Additionally, we introduce EyeCar, a new driver attention dataset in accident-prone situations. We conduct comprehensive experiments to evaluate our proposed model on three common benchmark…
University of North Carolina Asheville（北卡罗来纳大学阿什维尔分校）；University of Georgia（佐治亚大学）
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible while constrained to match empirically estimated feature expectations. However, in many real-world applications that use noisy sensors computing the feature expectations may be challenging due to partial observation of the relevant model variables. For example, a robot performing apprenticeship learning may lose sight of the agent it is learning from due to environmental occlusion. We show that in generalizing the principle of maximum entropy to these ty…
This paper presents a general framework for exploiting the representational capacity of neural networks to approximate complex, nonlinear reward functions in the context of solving the inverse reinforcement learning (IRL) problem. We show in this context that the Maximum Entropy paradigm for IRL lends itself naturally to the efficient training of deep architectures. At test time, the approach leads to a computational complexity independent of the number of demonstrations, which makes it especially well-suited for applications in life-long learning scenarios. Our approach achieves performance c…
BCAM-Basque Center for Applied Mathematics（巴斯克应用数学中心）；IKERBASQUE-Basque Foundation for Science（巴斯克科学基金会）；Department of Electronic Engineering, Tsinghua University（清华大学电子工程系）
The maximum entropy principle advocates to evaluate events' probabilities using a distribution that maximizes entropy among those that satisfy certain expectations' constraints. Such principle can be generalized for arbitrary decision problems where it corresponds to minimax approaches. This paper establishes a framework for supervised classification based on the generalized maximum entropy principle that leads to minimax risk classifiers (MRCs). We develop learning techniques that determine MRCs for general entropy functions and provide performance guarantees by means of convex optimization. …
University of Toronto（多伦多大学）；University of Waterloo（滑铁卢大学）；University of Missouri（密苏里大学）
We present a new statistical learning paradigm for Boltzmann machines based on a new inference principle we have proposed: the latent maximum entropy principle (LME). LME is different both from Jaynes maximum entropy principle and from standard maximum likelihood estimation.We demonstrate the LME principle BY deriving new algorithms for Boltzmann machine parameter estimation, and show how robust and fast new variant of the EM algorithm can be developed.Our experiments show that estimation based on LME generally yields better results than maximum likelihood estimation, particularly when inferri…
The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family, has been very popular in machine learning due to its "Occam's razor" interpretation. Unfortunately, calculating the potentials in the maximum-entropy distribution is intractable \cite{bresler2014hardness}. We provide computationally efficient versions of this principle when the mean parameters are pairwise moments: we design distributions that approximately match given pairwise moments, while having entropy which is compara…
University of Science and Technology of China（中国科学技术大学）；Beijing Jiaotong University（北京交通大学）
Deep learning achieves remarkable generalization capability with overwhelming number of model parameters. Theoretical understanding of deep learning generalization receives recent attention yet remains not fully explored. This paper attempts to provide an alternative understanding from the perspective of maximum entropy. We first derive two feature conditions that softmax regression strictly apply maximum entropy principle. DNN is then regarded as approximating the feature conditions with multilayer feature learning, and proved to be a recursive solution towards maximum entropy principle. The …
University of North Carolina Asheville（北卡罗来纳大学阿什维尔分校）
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize this principle to scenarios where the empirical feature expectations cannot be computed because the model variables are only partially observed, which introduces a dependency on the learned model. Generalizing the principle of latent maximum entropy, we introduce uncertain maximum entropy and describe an expectation-maximization based solution to approximately …
Universidad Central de Venezuela（委内瑞拉中央大学）；Instituto de Estudios Superiores de Administración IESA（IESA高级管理研究院）
The purpose of this note is to show how the method of maximum entropy in the mean (MEM) may be used to improve parametric estimation when the measurements are corrupted by large level of noise. The method is developed in the context on a concrete example: that of estimation of the parameter in an exponential distribution. We compare the performance of our method with the bayesian and maximum likelihood approaches.
In this paper, it is shown that an auto-encoder using optimal reconstruction significantly outperforms a conventional auto-encoder. Optimal reconstruction uses the conditional mean of the input given the features, under a maximum entropy prior distribution. The optimal reconstruction network, which is called deterministic projected belied network (D-PBN), resembles a standard reconstruction network, but with special non-linearities that mist be iteratively solved. The method, which can be seen as a generalization of maximum entropy image reconstruction, extends to multiple layers. In experimen…
