We model human decision-making behaviors in a risk-taking task using inverse reinforcement learning (IRL) for the purposes of understanding real human decision making under risk. To the best of our knowledge, this is the first work applying IRL to reveal the implicit reward function in human risk-taking decision making and to interpret risk-prone and risk-averse decision-making policies. We hypothesize that the state history (e.g. rewards and decisions in previous trials) are related to the human reward function, which leads to risk-averse and risk-prone decisions. We design features that reflect these factors in the reward function of IRL and learn the corresponding weight that is interpretable as the importance of features. The results confirm the sub-optimal risk-related decisions of human-driven by the personalized reward function. In particular, the risk-prone person tends to decide based on the current pump number, while the risk-averse person relies on burst information from the previous trial and the average end status. Our results demonstrate that IRL is an effective tool to model human decision-making behavior, as well as to help interpret the human psychological process in risk decision-making.
Scientific Computing and Imaging Institute, University of Utah（犹他大学科学计算与成像研究所）
Applying machine learning techniques to graph drawing has become an emergent area of research in visualization. In this paper, we interpret graph drawing as a multi-agent reinforcement learning (MARL) problem. We first demonstrate that a large number of classic graph drawing algorithms, including force-directed layouts and stress majorization, can be interpreted within the framework of MARL. Using this interpretation, a node in the graph is assigned to an agent with a reward function. Via multi-agent reward maximization, we obtain an aesthetically pleasing graph layout that is comparable to th…
Bosch Center for Artificial Intelligence（博世人工智能中心）；Technion – Israel Institute of Technology（以色列理工学院）
Practical application of Reinforcement Learning (RL) often involves risk considerations. We study a generalized approximation scheme for risk measures, based on Monte-Carlo simulations, where the risk measures need not necessarily be \emph{coherent}. We demonstrate that, even in simple problems, measures such as the variance of the reward-to-go do not capture the risk in a satisfactory manner. In addition, we show how a risk measure can be derived from model's realizations. We propose a neural architecture for estimating the risk and suggest the risk critic architecture that can be use to opti…
One major obstacle that precludes the success of reinforcement learning in real-world applications is the lack of robustness, either to model uncertainties or external disturbances, of the trained policies. Robustness is critical when the policies are trained in simulations instead of real world environment. In this work, we propose a risk-aware algorithm to learn robust policies in order to bridge the gap between simulation training and real-world implementation. Our algorithm is based on recently discovered distributional RL framework. We incorporate CVaR risk measure in sample based distrib…
Active learning from demonstration allows a robot to query a human for specific types of input to achieve efficient learning. Existing work has explored a variety of active query strategies; however, to our knowledge, none of these strategies directly minimize the performance risk of the policy the robot is learning. Utilizing recent advances in performance bounds for inverse reinforcement learning, we propose a risk-aware active inverse reinforcement learning algorithm that focuses active queries on areas of the state space with the potential for large generalization error. We show that risk-…
Chalmers University of Technology（查尔姆斯理工大学）；Zenuity AB（Zenuity公司）
We develop a framework for interacting with uncertain environments in reinforcement learning (RL) by leveraging preferences in the form of utility functions. We claim that there is value in considering different risk measures during learning. In this framework, the preference for risk can be tuned by variation of the parameter $β$ and the resulting behavior can be risk-averse, risk-neutral or risk-taking depending on the parameter choice. We evaluate our framework for learning problems with model uncertainty. We measure and control for \emph{epistemic} risk using dynamic programming (DP) and p…
University of Oxford（牛津大学）；Auburn University（奥本大学）
We present a mean-variance policy iteration (MVPI) framework for risk-averse control in a discounted infinite horizon MDP optimizing the variance of a per-step reward random variable. MVPI enjoys great flexibility in that any policy evaluation method and risk-neutral control method can be dropped in for risk-averse control off the shelf, in both on- and off-policy settings. This flexibility reduces the gap between risk-neutral control and risk-averse control and is achieved by working on a novel augmented MDP directly. We propose risk-averse TD3 as an example instantiating MVPI, which outperfo…
Ecole polytechnique（巴黎综合理工学院）；INRIA（法国国家信息与自动化研究所）；INSERM（法国国家健康与医学研究院）；Sorbonne Université（索邦大学）；Université Paris Cité（巴黎西岱大学）
Robust Reinforcement Learning tries to make predictions more robust to changes in the dynamics or rewards of the system. This problem is particularly important when the dynamics and rewards of the environment are estimated from the data. In this paper, we approximate the Robust Reinforcement Learning constrained with a $Φ$-divergence using an approximate Risk-Averse formulation. We show that the classical Reinforcement Learning formulation can be robustified using standard deviation penalization of the objective. Two algorithms based on Distributional Reinforcement Learning, one for discrete a…
University of Pennsylvania（宾夕法尼亚大学）；Stanford University（斯坦福大学）
In safety-critical applications of reinforcement learning such as healthcare and robotics, it is often desirable to optimize risk-sensitive objectives that account for tail outcomes rather than expected reward. We prove the first regret bounds for reinforcement learning under a general class of risk-sensitive objectives including the popular CVaR objective. Our theory is based on a novel characterization of the CVaR objective as well as a novel optimistic MDP construction.
University of Washington（华盛顿大学）；University of California, Berkeley（加州大学伯克利分校）
We address the problem of inverse reinforcement learning in Markov decision processes where the agent is risk-sensitive. In particular, we model risk-sensitivity in a reinforcement learning framework by making use of models of human decision-making having their origins in behavioral psychology, behavioral economics, and neuroscience. We propose a gradient-based inverse reinforcement learning algorithm that minimizes a loss function defined on the observed behavior. We demonstrate the performance of the proposed technique on two examples, the first of which is the canonical Grid World example a…
We study risk-sensitive reinforcement learning in episodic Markov decision processes with unknown transition kernels, where the goal is to optimize the total reward under the risk measure of exponential utility. We propose two provably efficient model-free algorithms, Risk-Sensitive Value Iteration (RSVI) and Risk-Sensitive Q-learning (RSQ). These algorithms implement a form of risk-sensitive optimism in the face of uncertainty, which adapts to both risk-seeking and risk-averse modes of exploration. We prove that RSVI attains an $\tilde{O}\big(λ(|β| H^2) \cdot \sqrt{H^{3} S^{2}AT} \big)$ regre…
In this paper, we study gap-dependent regret guarantees for risk-sensitive reinforcement learning based on the entropic risk measure. We propose a novel definition of sub-optimality gaps, which we call cascaded gaps, and we discuss their key components that adapt to the underlying structures of the problem. Based on the cascaded gaps, we derive non-asymptotic and logarithmic regret bounds for two model-free algorithms under episodic Markov decision processes. We show that, in appropriate settings, these bounds feature exponential improvement over existing ones that are independent of gaps. We …
Northwestern University（西北大学）；Princeton University（普林斯顿大学）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）
We study risk-sensitive reinforcement learning (RL) based on the entropic risk measure. Although existing works have established non-asymptotic regret guarantees for this problem, they leave open an exponential gap between the upper and lower bounds. We identify the deficiencies in existing algorithms and their analysis that result in such a gap. To remedy these deficiencies, we investigate a simple transformation of the risk-sensitive Bellman equations, which we call the exponential Bellman equation. The exponential Bellman equation inspires us to develop a novel analysis of Bellman backup pr…
KAIST（韩国科学技术院）；Kim Jaechul Graduate School of Artificial Intelligence（金在澈人工智能研究生院）
Distributional reinforcement learning demonstrates state-of-the-art performance in continuous and discrete control settings with the features of variance and risk, which can be used to explore. However, the exploration method employing the risk property is hard to find, although numerous exploration methods in Distributional RL employ the variance of return distribution per action. In this paper, we present risk scheduling approaches that explore risk levels and optimistic behaviors from a risk perspective. We demonstrate the performance enhancement of the DMIX algorithm using risk scheduling …
Reinforcement learning agents are faced with two types of uncertainty. Epistemic uncertainty stems from limited data and is useful for exploration, whereas aleatoric uncertainty arises from stochastic environments and must be accounted for in risk-sensitive applications. We highlight the challenges involved in simultaneously estimating both of them, and propose a framework for disentangling and estimating these uncertainties on learned Q-values. We derive unbiased estimators of these uncertainties and introduce an uncertainty-aware DQN algorithm, which we show exhibits safe learning behavior a…
In risk-averse reinforcement learning (RL), the goal is to optimize some risk measure of the returns. A risk measure often focuses on the worst returns out of the agent's experience. As a result, standard methods for risk-averse RL often ignore high-return strategies. We prove that under certain conditions this inevitably leads to a local-optimum barrier, and propose a soft risk mechanism to bypass it. We also devise a novel Cross Entropy module for risk sampling, which (1) preserves risk aversion despite the soft risk; (2) independently improves sample efficiency. By separating the risk avers…
Intesa Sanpaolo（联合圣保罗银行）；Politecnico di Milano（米兰理工大学）
In this paper we show how risk-averse reinforcement learning can be used to hedge options. We apply a state-of-the-art risk-averse algorithm: Trust Region Volatility Optimization (TRVO) to a vanilla option hedging environment, considering realistic factors such as discrete time and transaction costs. Realism makes the problem twofold: the agent must both minimize volatility and contain transaction costs, these tasks usually being in competition. We use the algorithm to train a sheaf of agents each characterized by a different risk aversion, so to be able to span an efficient frontier on the vo…
Training Reinforcement Learning (RL) agents in high-stakes applications might be too prohibitive due to the risk associated to exploration. Thus, the agent can only use data previously collected by safe policies. While previous work considers optimizing the average performance using offline data, we focus on optimizing a risk-averse criteria, namely the CVaR. In particular, we present the Offline Risk-Averse Actor-Critic (O-RAAC), a model-free RL algorithm that is able to learn risk-averse policies in a fully offline setting. We show that O-RAAC learns policies with higher CVaR than risk-neutr…
Northeastern University（东北大学）；University of Waterloo（滑铁卢大学）
Biopharmaceutical manufacturing faces critical challenges, including complexity, high variability, lengthy lead time, and limited historical data and knowledge of the underlying system stochastic process. To address these challenges, we propose a green simulation assisted model-based reinforcement learning to support process online learning and guide dynamic decision making. Basically, the process model risk is quantified by the posterior distribution. At any given policy, we predict the expected system response with prediction risk accounting for both inherent stochastic uncertainty and model…
Carnegie Mellon University（卡内基梅隆大学）；University of Michigan（密歇根大学）；Xi’an Jiaotong University（西安交通大学）
One typical assumption in inverse reinforcement learning (IRL) is that human experts act to optimize the expected utility of a stochastic cost with a fixed distribution. This assumption deviates from actual human behaviors under ambiguity. Risk-sensitive inverse reinforcement learning (RS-IRL) bridges such gap by assuming that humans act according to a random cost with respect to a set of subjectively distorted distributions instead of a fixed one. Such assumption provides the additional flexibility to model human's risk preferences, represented by a risk envelope, in safe-critical tasks. Howe…
This paper considers batch Reinforcement Learning (RL) with general value function approximation. Our study investigates the minimal assumptions to reliably estimate/minimize Bellman error, and characterizes the generalization performance by (local) Rademacher complexities of general function classes, which makes initial steps in bridging the gap between statistical learning theory and batch RL. Concretely, we view the Bellman error as a surrogate loss for the optimality gap, and prove the followings: (1) In double sampling regime, the excess risk of Empirical Risk Minimizer (ERM) is bounded b…
As safety violations can lead to severe consequences in real-world robotic applications, the increasing deployment of Reinforcement Learning (RL) in robotic domains has propelled the study of safe exploration for reinforcement learning (safe RL). In this work, we propose a risk preventive training method for safe RL, which learns a statistical contrastive classifier to predict the probability of a state-action pair leading to unsafe states. Based on the predicted risk probabilities, we can collect risk preventive trajectories and reshape the reward function with risk penalties to induce safe R…
The use of Reinforcement Learning (RL) agents in practical applications requires the consideration of suboptimal outcomes, depending on the familiarity of the agent with its environment. This is especially important in safety-critical environments, where errors can lead to high costs or damage. In distributional RL, the risk-sensitivity can be controlled via different distortion measures of the estimated return distribution. However, these distortion functions require an estimate of the risk level, which is difficult to obtain and depends on the current state. In this work, we demonstrate the …
Identifying uncertainty and taking mitigating actions is crucial for safe and trustworthy reinforcement learning agents, especially when deployed in high-risk environments. In this paper, risk sensitivity is promoted in a model-based reinforcement learning algorithm by exploiting the ability of a bootstrap ensemble of dynamics models to estimate environment epistemic uncertainty. We propose uncertainty guided cross-entropy method planning, which penalises action sequences that result in high variance state predictions during model rollouts, guiding the agent to known areas of the state space w…
We introduce a novel framework to account for sensitivity to rewards uncertainty in sequential decision-making problems. While risk-sensitive formulations for Markov decision processes studied so far focus on the distribution of the cumulative reward as a whole, we aim at learning policies sensitive to the uncertain/stochastic nature of the rewards, which has the advantage of being conceptually more meaningful in some cases. To this end, we present a new decomposition of the randomness contained in the cumulative reward based on the Doob decomposition of a stochastic process, and introduce a n…
In this work, we address risk-averse Bayes-adaptive reinforcement learning. We pose the problem of optimising the conditional value at risk (CVaR) of the total return in Bayes-adaptive Markov decision processes (MDPs). We show that a policy optimising CVaR in this setting is risk-averse to both the parametric uncertainty due to the prior distribution over MDPs, and the internal uncertainty due to the inherent stochasticity of MDPs. We reformulate the problem as a two-player stochastic game and propose an approximate algorithm based on Monte Carlo tree search and Bayesian optimisation. Our expe…
We extend temporal-difference (TD) learning in order to obtain risk-sensitive, model-free reinforcement learning algorithms. This extension can be regarded as modification of the Rescorla-Wagner rule, where the (sigmoidal) stimulus is taken to be either the event of over- or underestimating the TD target. As a result, one obtains a stochastic approximation rule for estimating the free energy from i.i.d. samples generated by a Gaussian distribution with unknown mean and variance. Since the Gaussian free energy is known to be a certainty-equivalent sensitive to the mean and the variance, the lea…
Indian Institute of Technology Madras（印度理工学院马德拉斯分校）；University of Maryland, College Park（马里兰大学帕克分校）
The objective in a traditional reinforcement learning (RL) problem is to find a policy that optimizes the expected value of a performance metric such as the infinite-horizon cumulative discounted or long-run average cost/reward. In practice, optimizing the expected value alone may not be satisfactory, in that it may be desirable to incorporate the notion of risk into the optimization problem formulation, either in the objective or as a constraint. Various risk measures have been proposed in the literature, e.g., exponential utility, variance, percentile performance, chance constraints, value a…
The Ohio State University（俄亥俄州立大学）；University of Michigan（密歇根大学）
Traditional reinforcement learning (RL) aims to maximize the expected total reward, while the risk of uncertain outcomes needs to be controlled to ensure reliable performance in a risk-averse setting. In this paper, we consider the problem of maximizing dynamic risk of a sequence of rewards in infinite-horizon Markov Decision Processes (MDPs). We adapt the Expected Conditional Risk Measures (ECRMs) to the infinite-horizon risk-averse MDP and prove its time consistency. Using a convex combination of expectation and conditional value-at-risk (CVaR) as a special one-step conditional risk measure,…
Deep reinforcement learning has recently made significant progress in solving computer games and robotic control tasks. A known problem, though, is that policies overfit to the training environment and may not avoid rare, catastrophic events such as automotive accidents. A classical technique for improving the robustness of reinforcement learning algorithms is to train on a set of randomized environments, but this approach only guards against common situations. Recently, robust adversarial reinforcement learning (RARL) was developed, which allows efficient applications of random and systematic…
Fraunhofer Institute for Integrated Circuits IIS（弗劳恩霍夫集成电路研究所IIS）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希-亚历山大大学）
Autonomous driving has the potential to revolutionize mobility and is hence an active area of research. In practice, the behavior of autonomous vehicles must be acceptable, i.e., efficient, safe, and interpretable. While vanilla reinforcement learning (RL) finds performant behavioral strategies, they are often unsafe and uninterpretable. Safety is introduced through Safe RL approaches, but they still mostly remain uninterpretable as the learned behaviour is jointly optimized for safety and performance without modeling them separately. Interpretable machine learning is rarely applied to RL. Thi…
Zenseact AB（Zenseact公司）；Chalmers University of Technology（查尔姆斯理工大学）；Scool INRIA Lille-Nord Europe（法国国家信息与自动化研究所里尔-北欧洲Scool团队）；CRIStAL, CNRS（法国国家科学研究中心CRIStAL实验室）；University of Neuchatel（纳沙泰尔大学）；University of Oslo（奥斯陆大学）
In this paper, we consider risk-sensitive sequential decision-making in Reinforcement Learning (RL). Our contributions are two-fold. First, we introduce a novel and coherent quantification of risk, namely composite risk, which quantifies the joint effect of aleatory and epistemic risk during the learning process. Existing works considered either aleatory or epistemic risk individually, or as an additive combination. We prove that the additive formulation is a particular case of the composite risk when the epistemic risk measure is replaced with expectation. Thus, the composite risk is more sen…
In many sequential decision-making problems one is interested in minimizing an expected cumulative cost while taking into account \emph{risk}, i.e., increased awareness of events of small probability and high consequences. Accordingly, the objective of this paper is to present efficient reinforcement learning algorithms for risk-constrained Markov decision processes (MDPs), where risk is represented via a chance constraint or a constraint on the conditional value-at-risk (CVaR) of the cumulative cost. We collectively refer to such problems as percentile risk-constrained MDPs. Specifically, we …
We develop an approach for solving time-consistent risk-sensitive stochastic optimization problems using model-free reinforcement learning (RL). Specifically, we assume agents assess the risk of a sequence of random variables using dynamic convex risk measures. We employ a time-consistent dynamic programming principle to determine the value of a particular policy, and develop policy gradient update rules that aid in obtaining optimal policies. We further develop an actor-critic style algorithm using neural networks to optimize over policies. Finally, we demonstrate the performance and flexibil…
University of Minnesota（明尼苏达大学）；US Army Research Laboratory（美国陆军研究实验室）；Princeton University（普林斯顿大学）
We study the estimation of risk-sensitive policies in reinforcement learning problems defined by a Markov Decision Process (MDPs) whose state and action spaces are countably finite. Prior efforts are predominately afflicted by computational challenges associated with the fact that risk-sensitive MDPs are time-inconsistent. To ameliorate this issue, we propose a new definition of risk, which we call caution, as a penalty function added to the dual objective of the linear programming (LP) formulation of reinforcement learning. The caution measures the distributional risk of a policy, which is a …
