Markov decision processes (MDPs) are widely used in modeling decision making problems in stochastic environments. However, precise specification of the reward functions in MDPs is often very difficult. Recent approaches have focused on computing an optimal policy based on the minimax regret criterion for obtaining a robust policy under uncertainty in the reward function. One of the core tasks in computing the minimax regret policy is to obtain the set of all policies that can be optimal for some candidate reward function. In this paper, we propose an efficient algorithm that exploits the geometric properties of the reward function associated with the policies. We also present an approximate version of the method for further speed up. We experimentally demonstrate that our algorithm improves the performance by orders of magnitude.
Robust Markov decision processes (MDPs) aim to handle changing or partially known system dynamics. To solve them, one typically resorts to robust optimization methods. However, this significantly increases computational complexity and limits scalability in both learning and planning. On the other hand, regularized MDPs show more stability in policy learning without impairing time complexity. Yet, they generally do not encompass uncertainty in the model dynamics. In this work, we aim to learn robust MDPs using regularization. We first show that regularized MDPs are a particular instance of robu…
Radboud University Nijmegen（拉德堡德大学奈梅亨分校）；Eindhoven University of Technology（埃因霍温理工大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）；Ruhr-University Bochum（波鸿鲁尔大学）
University at Buffalo, The State University of New York（纽约州立大学布法罗分校）；University of Colorado Boulder（科罗拉多大学博尔德分校）；University of Central Florida（中佛罗里达大学）；Air Force Research Laboratory（空军研究实验室）
In robust Markov decision processes (MDPs), the uncertainty in the transition kernel is addressed by finding a policy that optimizes the worst-case performance over an uncertainty set of MDPs. While much of the literature has focused on discounted MDPs, robust average-reward MDPs remain largely unexplored. In this paper, we focus on robust average-reward MDPs, where the goal is to find a policy that optimizes the worst-case average reward over an uncertainty set. We first take an approach that approximates average-reward MDPs using discounted MDPs. We prove that the robust discounted value fun…
Markov decision processes (MDPs) are a popular model for performance analysis and optimization of stochastic systems. The parameters of stochastic behavior of MDPs are estimates from empirical observations of a system; their values are not known precisely. Different types of MDPs with uncertain, imprecise or bounded transition rates or probabilities and rewards exist in the literature. Commonly, analysis of models with uncertainties amounts to searching for the most robust policy which means that the goal is to generate a policy with the greatest lower bound on performance (or, symmetrically, …
SCOUT: Semantic scene COverage via Uncertainty-guided Traversal
Nokia Bell Labs, France（诺基亚贝尔实验室，法国）；Nokia Bell Labs, Murray Hill, NJ, USA（诺基亚贝尔实验室，美国，新泽西州 Murray Hill）；Imperial College London（帝国理工学院伦敦分校）；Locus Robotics（Locus机器人技术公司）
This paper addresses the problem of planning under uncertainty in large Markov Decision Processes (MDPs). Factored MDPs represent a complex state space using state variables and the transition model using a dynamic Bayesian network. This representation often allows an exponential reduction in the representation size of structured MDPs, but the complexity of exact solution algorithms for such MDPs can grow exponentially in the representation size. In this paper, we present two approximate solution algorithms that exploit structure in factored MDPs. Both use an approximate value function represe…
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…
Markov decision processes capture sequential decision making under uncertainty, where an agent must choose actions so as to optimize long term reward. The paper studies efficient reasoning mechanisms for Relational Markov Decision Processes (RMDP) where world states have an internal relational structure that can be naturally described in terms of objects and relations among them. Two contributions are presented. First, the paper develops First Order Decision Diagrams (FODD), a new compact representation for functions over relational structures, together with a set of operators to combine FODDs…
In order to make good decision under uncertainty an agent must learn from observations. To do so, two of the most common frameworks are Contextual Bandits and Markov Decision Processes (MDPs). In this paper, we study whether there exist algorithms for the more general framework (MDP) which automatically provide the best performance bounds for the specific problem at hand without user intervention and without modifying the algorithm. In particular, it is found that a very minor variant of a recently proposed reinforcement learning algorithm for MDPs already matches the best possible regret boun…
California Institute of Technology（加州理工学院）；NASA Jet Propulsion Laboratory（NASA喷气推进实验室）
A large class of decision making under uncertainty problems can be described via Markov decision processes (MDPs) or partially observable MDPs (POMDPs), with application to artificial intelligence and operations research, among others. Traditionally, policy synthesis techniques are proposed such that a total expected cost or reward is minimized or maximized. However, optimality in the total expected cost sense is only reasonable if system behavior in the large number of runs is of interest, which has limited the use of such policies in practical mission-critical scenarios, wherein large deviat…
University of Washington（华盛顿大学）；Microsoft Research（微软研究院）
The conventional model for online planning under uncertainty assumes that an agent can stop and plan without incurring costs for the time spent planning. However, planning time is not free in most real-world settings. For example, an autonomous drone is subject to nature's forces, like gravity, even while it thinks, and must either pay a price for counteracting these forces to stay in place, or grapple with the state change caused by acquiescing to them. Policy optimization in these settings requires metareasoning---a process that trades off the cost of planning and the potential policy improv…
University of New Hampshire（新罕布什尔大学）；City University of Hong Kong（香港城市大学）
We address the problem of computing reliable policies in reinforcement learning problems with limited data. In particular, we compute policies that achieve good returns with high confidence when deployed. This objective, known as the \emph{percentile criterion}, can be optimized using Robust MDPs~(RMDPs). RMDPs generalize MDPs to allow for uncertain transition probabilities chosen adversarially from given ambiguity sets. We show that the RMDP solution's sub-optimality depends on the spans of the ambiguity sets along the value function. We then propose new algorithms that minimize the span of a…
Markov Decision Processes (MDPs) are a mathematical framework for modeling sequential decision making under uncertainty. The classical approaches for solving MDPs are well known and have been widely studied, some of which rely on approximation techniques to solve MDPs with large state space and/or action space. However, most of these classical solution approaches and their approximation techniques still take much computation time to converge and usually must be re-computed if the reward function is changed. This paper introduces a novel alternative approach for exactly and efficiently solving …
General-purpose, intelligent, learning agents cycle through sequences of observations, actions, and rewards that are complex, uncertain, unknown, and non-Markovian. On the other hand, reinforcement learning is well-developed for small finite state Markov decision processes (MDPs). Up to now, extracting the right state representations out of bare observations, that is, reducing the general agent setup to the MDP framework, is an art that involves significant effort by designers. The primary goal of this work is to automate the reduction process and thereby significantly expand the scope of many…
Optimal policies in Markov decision processes (MDPs) are very sensitive to model misspecification. This raises serious concerns about deploying them in high-stake domains. Robust MDPs (RMDP) provide a promising framework to mitigate vulnerabilities by computing policies with worst-case guarantees in reinforcement learning. The solution quality of an RMDP depends on the ambiguity set, which is a quantification of model uncertainties. In this paper, we propose a new approach for optimizing the shape of the ambiguity sets for RMDPs. Our method departs from the conventional idea of constructing a …
Markov decision processes (MDPs) are a well studied framework for solving sequential decision making problems under uncertainty. Exact methods for solving MDPs based on dynamic programming such as policy iteration and value iteration are effective on small problems. In problems with a large discrete state space or with continuous state spaces, a compact representation is essential for providing an efficient approximation solutions to MDPs. Commonly used approximation algorithms involving constructing basis functions for projecting the value function onto a low dimensional subspace, and buildin…
Delft University of Technology（代尔夫特理工大学）；University of Amsterdam（阿姆斯特丹大学）；University of Liverpool（利物浦大学）
In cooperative multi-agent sequential decision making under uncertainty, agents must coordinate to find an optimal joint policy that maximises joint value. Typical algorithms exploit additive structure in the value function, but in the fully-observable multi-agent MDP setting (MMDP) such structure is not present. We propose a new optimal solver for transition-independent MMDPs, in which agents can only affect their own state but their reward depends on joint transitions. We represent these dependencies compactly in conditional return graphs (CRGs). Using CRGs the value of a joint policy and th…
Oxford Robotics Institute, University of Oxford（牛津大学牛津机器人研究所）
The parameters for a Markov Decision Process (MDP) often cannot be specified exactly. Uncertain MDPs (UMDPs) capture this model ambiguity by defining sets which the parameters belong to. Minimax regret has been proposed as an objective for planning in UMDPs to find robust policies which are not overly conservative. In this work, we focus on planning for Stochastic Shortest Path (SSP) UMDPs with uncertain cost and transition functions. We introduce a Bellman equation to compute the regret for a policy. We propose a dynamic programming algorithm that utilises the regret Bellman equation, and sho…
Bidding Games on Markov Decision Processes with Quantitative Reachability Objectives
University of Haifa（海法大学）；Masaryk University（马萨里克大学）；Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所）；IMDEA Software Institute（IMDEA软件研究所）
Radboud University（拉德堡德大学）；Nijmegen Institute for Computing and Information Sciences（奈梅亨计算与信息科学研究所）
We study Markov decision processes (MDPs), where agents have direct control over when and how they gather information, as formalized by action-contingent noiselessly observable MDPs (ACNO-MPDs). In these models, actions consist of two components: a control action that affects the environment, and a measurement action that affects what the agent can observe. To solve ACNO-MDPs, we introduce the act-then-measure (ATM) heuristic, which assumes that we can ignore future state uncertainty when choosing control actions. We show how following this heuristic may lead to shorter policy computation time…
University of Ottawa（渥太华大学）；National Research Council of Canada（加拿大国家研究委员会）；University of Waterloo（滑铁卢大学）；Vector Institute for Artificial Intelligence（向量人工智能研究所）
Using a novel toy nautical navigation environment, we show that dynamic programming can be used when only incomplete information about a partially observed Markov decision process (POMDP) is known. By incorporating uncertainty into our model, we show that navigation policies can be constructed that maintain safety, outperforming the baseline performance of traditional dynamic programming for Markov decision processes (MDPs). Adding in controlled sensing methods, we show that these policies can also lower measurement costs at the same time.
UC Berkeley（加州大学伯克利分校）；EPFL（洛桑联邦理工学院）；UC San Diego（加州大学圣迭戈分校）；UC Los Angeles（加州大学洛杉矶分校）
Planning in adversarial and uncertain environments can be modeled as the problem of devising strategies in stochastic perfect information games. These games are generalizations of Markov decision processes (MDPs): there are two (adversarial) players, and a source of randomness. The main practical obstacle to computing winning strategies in such games is the size of the state space. In practice therefore, one typically works with abstractions of the model. The diffculty is to come up with an abstraction that is neither too coarse to remove all winning strategies (plans), nor too fine to be intr…
We integrate information-theoretic concepts into the design and analysis of optimistic algorithms and Thompson sampling. By making a connection between information-theoretic quantities and confidence bounds, we obtain results that relate the per-period performance of the agent with its information gain about the environment, thus explicitly characterizing the exploration-exploitation tradeoff. The resulting cumulative regret bound depends on the agent's uncertainty over the environment and quantifies the value of prior information. We show applicability of this approach to several environments…
Oxford Robotics Institute, University of Oxford（牛津大学牛津机器人研究所）
Previous work on planning as active inference addresses finite horizon problems and solutions valid for online planning. We propose solving the general Stochastic Shortest-Path Markov Decision Process (SSP MDP) as probabilistic inference. Furthermore, we discuss online and offline methods for planning under uncertainty. In an SSP MDP, the horizon is indefinite and unknown a priori. SSP MDPs generalize finite and infinite horizon MDPs and are widely used in the artificial intelligence community. Additionally, we highlight some of the differences between solving an MDP using dynamic programming …
Masaryk University（马萨里克大学）；Institute of Science and Technology Austria（奥地利科学技术研究所）
Markov decision processes (MDPs) are the defacto frame-work for sequential decision making in the presence ofstochastic uncertainty. A classical optimization criterion forMDPs is to maximize the expected discounted-sum pay-off, which ignores low probability catastrophic events withhighly negative impact on the system. On the other hand,risk-averse policies require the probability of undesirableevents to be below a given threshold, but they do not accountfor optimization of the expected payoff. We consider MDPswith discounted-sum payoff with failure states which repre-sent catastrophic outcomes…
This paper targets the efficient construction of a safety shield for decision making in scenarios that incorporate uncertainty. Markov decision processes (MDPs) are prominent models to capture such planning problems. Reinforcement learning (RL) is a machine learning technique to determine near-optimal policies in MDPs that may be unknown prior to exploring the model. However, during exploration, RL is prone to induce behavior that is undesirable or not allowed in safety- or mission-critical contexts. We introduce the concept of a probabilistic shield that enables decision-making to adhere to s…
Certified Policy Verification and Synthesis for MDPs under Distributional Reach-avoidance Properties
Indian Institute of Technology Bombay（印度理工学院孟买分校）；Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所）；Lancaster University Leipzig（莱斯特兰卡斯特大学）；Singapore Management University（新加坡管理大学）
Bosch Center for Artificial Intelligence（博世人工智能中心）；TU Darmstadt（达姆施塔特工业大学）；German Research Center for AI (DFKI)（德国人工智能研究中心）
We consider the problem of quantifying uncertainty over expected cumulative rewards in model-based reinforcement learning. In particular, we focus on characterizing the variance over values induced by a distribution over MDPs. Previous work upper bounds the posterior variance over values by solving a so-called uncertainty Bellman equation, but the over-approximation may result in inefficient exploration. We propose a new uncertainty Bellman equation whose solution converges to the true posterior variance over values and explicitly characterizes the gap in previous work. Moreover, our uncertain…
LTCI, Télécom Paris, Institut Polytechnique de Paris（巴黎理工学院巴黎电信学院 LTCI）；Microsoft Research Montréal（蒙特利尔微软研究院）
Batch Reinforcement Learning (Batch RL) consists in training a policy using trajectories collected with another policy, called the behavioural policy. Safe policy improvement (SPI) provides guarantees with high probability that the trained policy performs better than the behavioural policy, also called baseline in this setting. Previous work shows that the SPI objective improves mean performance as compared to using the basic RL objective, which boils down to solving the MDP with maximum likelihood. Here, we build on that work and improve more precisely the SPI with Baseline Bootstrapping algo…
Sequential decision problems in applications such as manipulation in warehouses, multi-step meal preparation, and routing in autonomous vehicle networks often involve reasoning about uncertainty, planning over discrete modes as well as continuous states, and reacting to dynamic updates. To formalize such problems generally, we introduce a class of Markov Decision Processes (MDPs) called Dynamic Multimodal Stochastic Shortest Paths (DMSSPs). Much of the work in these domains solves deterministic variants, which can yield poor results when the uncertainty has downstream effects. We develop a Hyb…
University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of Virginia（弗吉尼亚大学）；University of Birmingham（伯明翰大学）
Complex real-world applications of cyber-physical systems give rise to the need for multi-objective controller synthesis, which concerns the problem of computing an optimal controller subject to multiple (possibly conflicting) criteria. The relative importance of objectives is often specified by human decision-makers. However, there is inherent uncertainty in human preferences (e.g., due to artifacts resulting from different preference elicitation methods). In this paper, we formalize the notion of uncertain human preferences and present a novel approach that accounts for this uncertainty in t…
This position paper reflects on the state-of-the-art in decision-making under uncertainty. A classical assumption is that probabilities can sufficiently capture all uncertainty in a system. In this paper, the focus is on the uncertainty that goes beyond this classical interpretation, particularly by employing a clear distinction between aleatoric and epistemic uncertainty. The paper features an overview of Markov decision processes (MDPs) and extensions to account for partial observability and adversarial behavior. These models sufficiently capture aleatoric uncertainty but fail to account for…
Well-executed emergency evacuations can save lives and reduce suffering. However, decision makers struggle to determine optimal evacuation policies given the chaos, uncertainty, and value judgments inherent in emergency evacuations. We propose and analyze a decision support tool for pre-crisis training exercises for teams preparing for civilian evacuations and explore the tool in the case of the 2021 U.S.-led evacuation from Afghanistan. We use different classes of Markov decision processes (MDPs) to capture compounding levels of uncertainty in (1) the priority category of who appears next at …
