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.
Nara Institute of Science and Technology（奈良先端科学技术大学院大学）；Osaka University（大阪大学）；Advanced Telecommunication Research（国际电气通信基础技术研究所）
Maximum Tsallis entropy (MTE) framework in reinforcement learning has gained popularity recently by virtue of its flexible modeling choices including the widely used Shannon entropy and sparse entropy. However, non-Shannon entropies suffer from approximation error and subsequent underperformance either due to its sensitivity or the lack of closed-form policy expression. To improve the tradeoff between flexibility and empirical performance, we propose to strengthen their error-robustness by enforcing implicit Kullback-Leibler (KL) regularization in MTE motivated by Munchausen DQN (MDQN). We do …
Recently deep reinforcement learning (DRL) has achieved outstanding success on solving many difficult and large-scale RL problems. However the high sample cost required for effective learning often makes DRL unaffordable in resource-limited applications. With the aim of improving sample efficiency and learning performance, we will develop a new DRL algorithm in this paper that seamless integrates entropy-induced and bootstrap-induced techniques for efficient and deep exploration of the learning environment. Specifically, a general form of Tsallis entropy regularizer will be utilized to drive e…
Nara Institute of Science and Technology（奈良先端科学技术大学院大学）；Osaka University（大阪大学）；Advanced Telecommunication Research（先进电信研究所）
The recently successful Munchausen Reinforcement Learning (M-RL) features implicit Kullback-Leibler (KL) regularization by augmenting the reward function with logarithm of the current stochastic policy. Though significant improvement has been shown with the Boltzmann softmax policy, when the Tsallis sparsemax policy is considered, the augmentation leads to a flat learning curve for almost every problem considered. We show that it is due to the mismatch between the conventional logarithm and the non-logarithmic (generalized) nature of Tsallis entropy. Drawing inspiration from the Tsallis statis…
Seoul National University（首尔国立大学）；KAIST（韩国科学技术院）；Kakao Brain
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 o…
We derive an algorithm that achieves the optimal (within constants) pseudo-regret in both adversarial and stochastic multi-armed bandits without prior knowledge of the regime and time horizon. The algorithm is based on online mirror descent (OMD) with Tsallis entropy regularization with power $α=1/2$ and reduced-variance loss estimators. More generally, we define an adversarial regime with a self-bounding constraint, which includes stochastic regime, stochastically constrained adversarial regime (Wei and Luo), and stochastic regime with adversarial corruptions (Lykouris et al.) as special case…
Continuous-time q-Learning for Jump-Diffusion Models under Tsallis Entropy
School of Mathematics and Statistics, Xidian University（西安电子科技大学数学与统计学院）；Department of Applied Mathematics, The Hong Kong Polytechnic University（香港理工大学应用数学系）；Center for Financial Engineering, Soochow University（苏州大学金融工程中心）
Korea Advanced Institute of Science and Technology（韩国科学技术院）；Microsoft Research Asia（微软亚洲研究院）
Behavioral cloning has proven to be effective for learning sequential decision-making policies from expert demonstrations. However, behavioral cloning often suffers from the causal confusion problem where a policy relies on the noticeable effect of expert actions due to the strong correlation but not the cause we desire. This paper presents Object-aware REgularizatiOn (OREO), a simple technique that regularizes an imitation policy in an object-aware manner. Our main idea is to encourage a policy to uniformly attend to all semantic objects, in order to prevent the policy from exploiting nuisanc…
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 estim…
Technische Universität Darmstadt（达姆施塔特工业大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Monte-Carlo planning and Reinforcement Learning (RL) are essential to sequential decision making. The recent AlphaGo and AlphaZero algorithms have shown how to successfully combine these two paradigms in order to solve large scale sequential decision problems. These methodologies exploit a variant of the well-known UCT algorithm to trade off exploitation of good actions and exploration of unvisited states, but their empirical success comes at the cost of poor sample-efficiency and high computation time. In this paper, we overcome these limitations by considering convex regularization in Monte-…
This work elaborates on the important problem of (1) designing optimal randomized routing policies for reaching a target node t from a source note s on a weighted directed graph G and (2) defining distance measures between nodes interpolating between the least cost (based on optimal movements) and the commute-cost (based on a random walk on G), depending on a temperature parameter T. To this end, the randomized shortest path formalism (RSP, [2,99,124]) is rephrased in terms of Tsallis divergence regularization, instead of Kullback-Leibler divergence. The main consequence of this change is that…
University of California, Los Angeles（加州大学洛杉矶分校）；University of Cambridge（剑桥大学）；The Alan Turing Institute（艾伦图灵研究所）
Regularization improves generalization of supervised models to out-of-sample data. Prior works have shown that prediction in the causal direction (effect from cause) results in lower testing error than the anti-causal direction. However, existing regularization methods are agnostic of causality. We introduce Causal Structure Learning (CASTLE) regularization and propose to regularize a neural network by jointly learning the causal relationships between variables. CASTLE learns the causal directed acyclical graph (DAG) as an adjacency matrix embedded in the neural network's input layers, thereby…
University of Tübingen（蒂宾根大学）；Technical University of Munich（慕尼黑工业大学）；Munich Data Science Institute（慕尼黑数据科学研究所）
We study the problem of learning causal models from observational data through the lens of interpolation and its counterpart -- regularization. A large volume of recent theoretical, as well as empirical work, suggests that, in highly complex model classes, interpolating estimators can have good statistical generalization properties and can even be optimal for statistical learning. Motivated by an analogy between statistical and causal learning recently highlighted by Janzing (2019), we investigate whether interpolating estimators can also learn good causal models. To this end, we consider a si…
University of Chicago（芝加哥大学）；Illinois Institute of Technology（伊利诺伊理工学院）；Tulane University（杜兰大学）
Recent work has raised concerns on the risk of spurious correlations and unintended biases in statistical machine learning models that threaten model robustness and fairness. In this paper, we propose a simple and intuitive regularization approach to integrate causal knowledge during model training and build a robust and fair model by emphasizing causal features and de-emphasizing spurious features. Specifically, we first manually identify causal and spurious features with principles inspired from the counterfactual framework of causal inference. Then, we propose a regularization approach to p…
Georgia Institute of Technology（佐治亚理工学院）；California Institute of Technology（加州理工学院）；Sutter Health（萨特健康）
In application domains such as healthcare, we want accurate predictive models that are also causally interpretable. In pursuit of such models, we propose a causal regularizer to steer predictive models towards causally-interpretable solutions and theoretically study its properties. In a large-scale analysis of Electronic Health Records (EHR), our causally-regularized model outperforms its L1-regularized counterpart in causal accuracy and is competitive in predictive performance. We perform non-linear causality analysis by causally regularizing a special neural network architecture. We also sho…
The University of Chicago（芝加哥大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
Motivated by the rising abundance of observational data with continuous treatments, we investigate the problem of estimating the average dose-response curve (ADRF). Available parametric methods are limited in their model space, and previous attempts in leveraging neural network to enhance model expressiveness relied on partitioning continuous treatment into blocks and using separate heads for each block; this however produces in practice discontinuous ADRFs. Therefore, the question of how to adapt the structure and training of neural network to estimate ADRFs remains open. This paper makes two…
I argue that regularizing terms in standard regression methods not only help against overfitting finite data, but sometimes also yield better causal models in the infinite sample regime. I first consider a multi-dimensional variable linearly influencing a target variable with some multi-dimensional unobserved common cause, where the confounding effect can be decreased by keeping the penalizing term in Ridge and Lasso regression even in the population limit. Choosing the size of the penalizing term, is however challenging, because cross validation is pointless. Here it is done by first estimati…
University College London（伦敦大学学院）；The Alan Turing Institute（艾伦·图灵研究所）
In this extended abstract paper, we address the problem of interpretability and targeted regularization in causal machine learning models. In particular, we focus on the problem of estimating individual causal/treatment effects under observed confounders, which can be controlled for and moderate the effect of the treatment on the outcome of interest. Black-box ML models adjusted for the causal setting perform generally well in this task, but they lack interpretable output identifying the main drivers of treatment heterogeneity and their functional relationship. We propose a novel deep counterf…
University of Cambridge（剑桥大学）；Mila, Université de Montréal（蒙特利尔大学米拉（Mila）实验室）；Alan Turing Institute（艾伦·图灵研究所）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
This paper considers the problem of unsupervised 3D object reconstruction from in-the-wild single-view images. Due to ambiguity and intrinsic ill-posedness, this problem is inherently difficult to solve and therefore requires strong regularization to achieve disentanglement of different latent factors. Unlike existing works that introduce explicit regularizations into objective functions, we look into a different space for implicit regularization -- the structure of latent space. Specifically, we restrict the structure of latent space to capture a topological causal ordering of latent factors …
Graph attention networks estimate the relational importance of node neighbors to aggregate relevant information over local neighborhoods for a prediction task. However, the inferred attentions are vulnerable to spurious correlations and connectivity in the training data, hampering the generalizability of the model. We introduce CAR, a general-purpose regularization framework for graph attention networks. Embodying a causal inference approach, CAR aligns the attention mechanism with the causal effects of active interventions on graph connectivity in a scalable manner. CAR is compatible with a v…
Adaptive-CaRe: Adaptive Causal Regularization for Robust Outcome Prediction
Department of Translational Surgical Oncology, National Center for Tumor Diseases (NCT), NCT/UCC Dresden, a partnership between DKFZ, Faculty of Medicine and University Hospital Carl Gustav Carus, TUD Dresden University of Technology, and Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Germany（translational Surgical Oncology部门，国家肿瘤疾病中心（NCT），NCT/UCC德累斯顿，由DKFZ、医学院和德累斯顿卡尔·戈斯塔夫·卡尔医院、德累斯顿技术大学以及德累斯顿-罗斯托克霍尔茨研究中心（HZDR）组成，德国）；Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, USA（生物医学工程学院，普渡大学，西拉法基，美国）；Department of Visceral, Thoracic and Vascular Surgery, University Hospital and Faculty of Medicine Carl Gustav Carus, TUD Dresden University of Technology, Germany（visceral, Thoracic and Vascular Surgery部门，德累斯顿卡尔·戈斯塔夫·卡尔医院和德累斯顿技术大学医学院，德国）；Ludwig-Maximilians-Universität München, Munich, Germany（慕尼黑大学，慕尼黑，德国）；Munich Center for Machine Learning (MCML), Munich, Germany（慕尼黑机器学习中心（MCML），慕尼黑，德国）；University of Tromsø, Tromsø, Norway（特罗姆斯大学，特罗姆斯，挪威）；DLR-German Aerospace Center, Germany（德国航空航天中心（DLR））
A Gradient-based Causal Discovery Framework with Applications to Complex Industrial Processes
School of Artificial Intelligence, Beijing Normal University（北京师范大学人工智能学院）；Advanced Institute of Natural Sciences, Beijing Normal University（北京师范大学自然科学院）
In the field of machine learning there is a growing interest towards more robust and generalizable algorithms. This is for example important to bridge the gap between the environment in which the training data was collected and the environment where the algorithm is deployed. Machine learning algorithms have increasingly been shown to excel in finding patterns and correlations from data. Determining the consistency of these patterns and for example the distinction between causal correlations and nonsensical spurious relations has proven to be much more difficult. In this paper a regularization…
This paper considers joint learning of multiple sparse Granger graphical models to discover underlying common and differential Granger causality (GC) structures across multiple time series. This can be applied to drawing group-level brain connectivity inferences from a homogeneous group of subjects or discovering network differences among groups of signals collected under heterogeneous conditions. By recognizing that the GC of a single multivariate time series can be characterized by common zeros of vector autoregressive (VAR) lag coefficients, a group sparse prior is included in joint regular…
We propose a novel method for modeling data by using structural models based on economic theory as regularizers for statistical models. We show that even if a structural model is misspecified, as long as it is informative about the data-generating mechanism, our method can outperform both the (misspecified) structural model and un-structural-regularized statistical models. Our method permits a Bayesian interpretation of theory as prior knowledge and can be used both for statistical prediction and causal inference. It contributes to transfer learning by showing how incorporating theory into sta…
On the Identification of Temporally Causal Representation with Instantaneous Dependence
Carnegie Mellon University（卡内基梅隆大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Guangdong University of Technology（广东技术大学）；The University of Melbourne（墨尔本大学）
University of Copenhagen（哥本哈根大学）；Technical University of Denmark（丹麦技术大学）；University of Amsterdam（阿姆斯特丹大学）
This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of stochastic systems affected by external manipulation (interventions). This thesis contributes to the research areas concerning the estimation of causal effects, causal structure learning, and distributionally robust (out-of-distribution generalizing) prediction methods. We present novel and consistent linear and non-linear causal effects estimators in instrum…
