We consider the problem of designing policies for Markov decision processes (MDPs) with dynamic coherent risk objectives and constraints. We begin by formulating the problem in a Lagrangian framework. Under the assumption that the risk objectives and constraints can be represented by a Markov risk transition mapping, we propose an optimization-based method to synthesize Markovian policies that lower-bound the constrained risk-averse problem. We demonstrate that the formulated optimization problems are in the form of difference convex programs (DCPs) and can be solved by the disciplined convex-concave programming (DCCP) framework. We show that these results generalize linear programs for constrained MDPs with total discounted expected costs and constraints. Finally, we illustrate the effectiveness of the proposed method with numerical experiments on a rover navigation problem involving conditional-value-at-risk (CVaR) and entropic-value-at-risk (EVaR) coherent risk measures.
California Institute of Technology（加州理工学院）；NASA Jet Propulsion Laboratory（美国国家航空航天局喷气推进实验室）
We consider the problem of designing policies for partially observable Markov decision processes (POMDPs) with dynamic coherent risk objectives. Synthesizing risk-averse optimal policies for POMDPs requires infinite memory and thus undecidable. To overcome this difficulty, we propose a method based on bounded policy iteration for designing stochastic but finite state (memory) controllers, which takes advantage of standard convex optimization methods. Given a memory budget and optimality criterion, the proposed method modifies the stochastic finite state controller leading to sub-optimal soluti…
We consider the stochastic shortest path planning problem in MDPs, i.e., the problem of designing policies that ensure reaching a goal state from a given initial state with minimum accrued cost. In order to account for rare but important realizations of the system, we consider a nested dynamic coherent risk total cost functional rather than the conventional risk-neutral total expected cost. Under some assumptions, we show that optimal, stationary, Markovian policies exist and can be found via a special Bellman's equation. We propose a computational technique based on difference convex programs…
In this paper, we consider a finite-horizon Markov decision process (MDP) for which the objective at each stage is to minimize a quantile-based risk measure (QBRM) of the sequence of future costs; we call the overall objective a dynamic quantile-based risk measure (DQBRM). In particular, we consider optimizing dynamic risk measures where the one-step risk measures are QBRMs, a class of risk measures that includes the popular value at risk (VaR) and the conditional value at risk (CVaR). Although there is considerable theoretical development of risk-averse MDPs in the literature, the computation…
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…
Stochastic domains often involve risk-averse decision makers. While recent work has focused on how to model risk in Markov decision processes using risk measures, it has not addressed the problem of solving large risk-averse formulations. In this paper, we propose and analyze a new method for solving large risk-averse MDPs with hybrid continuous-discrete state spaces and continuous action spaces. The proposed method iteratively improves a bound on the value function using a linearity structure of the MDP. We demonstrate the utility and properties of the method on a portfolio optimization probl…
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…
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…
We introduce a distributional method for learning the optimal policy in risk averse Markov decision process with finite state action spaces, latent costs, and stationary dynamics. We assume sequential observations of states, actions, and costs and assess the performance of a policy using dynamic risk measures constructed from nested Kusuoka-type conditional risk mappings. For such performance criteria, randomized policies may outperform deterministic policies, therefore, the candidate policies lie in the d-dimensional simplex where d is the cardinality of the action space. Existing risk averse…
We present an historical overview about the connections between the analysis of risk and the control of autonomous systems. We offer two main contributions. Our first contribution is to propose three overlapping paradigms to classify the vast body of literature: the worst-case, risk-neutral, and risk-averse paradigms. We consider an appropriate assessment for the risk of an autonomous system to depend on the application at hand. In contrast, it is typical to assess risk using an expectation, variance, or probability alone. Our second contribution is to unify the concepts of risk and autonomous…
Northumbria University（诺森比亚大学）；University of Macedonia（马其顿大学）；University of Oxford（牛津大学）
Designing tax policies that are effective in curbing tax evasion and maximize state revenues requires a rigorous understanding of taxpayer behavior. This work explores the problem of determining the strategy a self-interested, risk-averse tax entity is expected to follow, as it "navigates" - in the context of a Markov Decision Process - a government-controlled tax environment that includes random audits, penalties and occasional tax amnesties. Although simplified versions of this problem have been previously explored, the mere assumption of risk-aversion (as opposed to risk-neutrality) raises …
Measures of Variability for Risk-averse Policy Gradient
School of Computer Science, University of Waterloo（滑铁卢大学计算机科学学院）；Vector Institute（矢量研究所）；Department of Engineering Science, University of Oxford（牛津大学工程科学系）；School of Computing Science, Simon Fraser University（西蒙菲莎大学计算科学学院）
In this paper, we tackle the problem of risk-averse route planning in a transportation network with time-dependent and stochastic costs. To solve this problem, we propose an adaptation of the A* algorithm that accommodates any risk measure or decision criterion that is monotonic with first-order stochastic dominance. We also present a case study of our algorithm on the Manhattan, NYC, transportation network.
Qualcomm AI Research（高通人工智能研究院）；Qualcomm Automotive Research（高通汽车研究院）
Autonomous vehicles have to navigate the surrounding environment with partial observability of other objects sharing the road. Sources of uncertainty in autonomous vehicle measurements include sensor fusion errors, limited sensor range due to weather or object detection latency, occlusion, and hidden parameters such as other human driver intentions. Behavior planning must consider all sources of uncertainty in deciding future vehicle maneuvers. This paper presents a scalable framework for risk-averse behavior planning under uncertainty by incorporating QMDP, unscented transform, and Monte Carl…
Imitation learning algorithms learn viable policies by imitating an expert's behavior when reward signals are not available. Generative Adversarial Imitation Learning (GAIL) is a state-of-the-art algorithm for learning policies when the expert's behavior is available as a fixed set of trajectories. We evaluate in terms of the expert's cost function and observe that the distribution of trajectory-costs is often more heavy-tailed for GAIL-agents than the expert at a number of benchmark continuous-control tasks. Thus, high-cost trajectories, corresponding to tail-end events of catastrophic failur…
