Partially-Observable Markov Decision Processes (POMDPs) are a well-known stochastic model for sequential decision making under limited information. We consider the EXPTIME-hard problem of synthesising policies that almost-surely reach some goal state without ever visiting a bad state. In particular, we are interested in computing the winning region, that is, the set of system configurations from which a policy exists that satisfies the reachability specification. A direct application of such a winning region is the safe exploration of POMDPs by, for instance, restricting the behavior of a reinforcement learning agent to the region. We present two algorithms: A novel SAT-based iterative approach and a decision-diagram based alternative. The empirical evaluation demonstrates the feasibility and efficacy of the approaches.
Planning robust executions under uncertainty is a fundamental challenge for building autonomous robots. Partially Observable Markov Decision Processes (POMDPs) provide a standard framework for modeling uncertainty in many applications. In this work, we study POMDPs with safe-reachability objectives, which require that with a probability above some threshold, a goal state is eventually reached while keeping the probability of visiting unsafe states below some threshold. This POMDP formulation is different from the traditional POMDP models with optimality objectives and we show that in some case…
IST Austria（奥地利科学技术研究所）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
Partially observable Markov decision processes (POMDPs) are widely used in probabilistic planning problems in which an agent interacts with an environment using noisy and imprecise sensors. We study a setting in which the sensors are only partially defined and the goal is to synthesize "weakest" additional sensors, such that in the resulting POMDP, there is a small-memory policy for the agent that almost-surely (with probability~1) satisfies a reachability objective. We show that the problem is NP-complete, and present a symbolic algorithm by encoding the problem into SAT instances. We illustr…
We consider partially observable Markov decision processes (POMDPs) with a set of target states and every transition is associated with an integer cost. The optimization objective we study asks to minimize the expected total cost till the target set is reached, while ensuring that the target set is reached almost-surely (with probability 1). We show that for integer costs approximating the optimal cost is undecidable. For positive costs, our results are as follows: (i) we establish matching lower and upper bounds for the optimal cost and the bound is double exponential; (ii) we show that the p…
Preferences play a key role in determining what goals/constraints to satisfy when not all constraints can be satisfied simultaneously. In this paper, we study how to synthesize preference satisfying plans in stochastic systems, modeled as an MDP, given a (possibly incomplete) combinative preference model over temporally extended goals. We start by introducing new semantics to interpret preferences over infinite plays of the stochastic system. Then, we introduce a new notion of improvement to enable comparison between two prefixes of an infinite play. Based on this, we define two solution conce…
University of Georgia（佐治亚大学）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）
Partially observable Markov decision processes (POMDPs) provide a principled framework for sequential planning in uncertain single agent settings. An extension of POMDPs to multiagent settings, called interactive POMDPs (I-POMDPs), replaces POMDP belief spaces with interactive hierarchical belief systems which represent an agent's belief about the physical world, about beliefs of other agents, and about their beliefs about others' beliefs. This modification makes the difficulties of obtaining solutions due to complexity of the belief and policy spaces even more acute. We describe a general met…
Carnegie Mellon University（卡内基梅隆大学）；National University of Singapore（新加坡国立大学）
This work addresses the challenge of a robot using real-time feedback from contact sensors to reliably manipulate a movable object on a cluttered tabletop. We formulate contact manipulation as a partially observable Markov decision process (POMDP) in the joint space of robot configurations and object poses. The POMDP formulation enables the robot to actively gather information and reduce the uncertainty on the object pose. Further, it incorporates all major constraints for robot manipulation: kinematic reachability, self-collision, and collision with obstacles. To solve the POMDP, we apply DES…
Multi-agent partially observable Markov decision processes (MPOMDPs) provide a framework to represent heterogeneous autonomous agents subject to uncertainty and partial observation. In this paper, given a nominal policy provided by a human operator or a conventional planning method, we propose a technique based on barrier functions to design a minimally interfering safety-shield ensuring satisfaction of high-level specifications in terms of linear distribution temporal logic (LDTL). To this end, we use sufficient and necessary conditions for the invariance of a given set based on discrete-time…
IST Austria (Institute of Science and Technology Austria)（奥地利科学技术研究所）；Indian Institute of Technology, Bombay（印度理工学院孟买分校）
We consider partially observable Markov decision processes (POMDPs), that are a standard framework for robotics applications to model uncertainties present in the real world, with temporal logic specifications. All temporal logic specifications in linear-time temporal logic (LTL) can be expressed as parity objectives. We study the qualitative analysis problem for POMDPs with parity objectives that asks whether there is a controller (policy) to ensure that the objective holds with probability 1 (almost-surely). While the qualitative analysis of POMDPs with parity objectives is undecidable, rece…
The University of Texas at Austin（得克萨斯大学奥斯汀分校）；Radboud University（拉德堡德大学）
Recurrent neural networks (RNNs) have emerged as an effective representation of control policies in sequential decision-making problems. However, a major drawback in the application of RNN-based policies is the difficulty in providing formal guarantees on the satisfaction of behavioral specifications, e.g. safety and/or reachability. By integrating techniques from formal methods and machine learning, we propose an approach to automatically extract a finite-state controller (FSC) from an RNN, which, when composed with a finite-state system model, is amenable to existing formal verification tool…
We consider partially observable Markov decision processes (POMDPs) with limit-average payoff, where a reward value in the interval [0,1] is associated to every transition, and the payoff of an infinite path is the long-run average of the rewards. We consider two types of path constraints: (i) quantitative constraint defines the set of paths where the payoff is at least a given threshold λ in (0, 1]; and (ii) qualitative constraint which is a special case of quantitative constraint with λ = 1. We consider the computation of the almost-sure winning set, where the controller needs to ensure that…
We consider partially observable Markov decision processes (POMDPs) with limit-average payoff, where a reward value in the interval [0,1] is associated to every transition, and the payoff of an infinite path is the long-run average of the rewards. We consider two types of path constraints: (i) quantitative constraint defines the set of paths where the payoff is at least a given threshold lambda_1 in (0,1]; and (ii) qualitative constraint which is a special case of quantitative constraint with lambda_1=1. We consider the computation of the almost-sure winning set, where the controller needs to …
Aalto University（阿尔托大学）；Delft University of Technology（代尔夫特理工大学）；University of Manchester（曼彻斯特大学）
Centaurs are half-human, half-AI decision-makers where the AI's goal is to complement the human. To do so, the AI must be able to recognize the goals and constraints of the human and have the means to help them. We present a novel formulation of the interaction between the human and the AI as a sequential game where the agents are modelled using Bayesian best-response models. We show that in this case the AI's problem of helping bounded-rational humans make better decisions reduces to a Bayes-adaptive POMDP. In our simulated experiments, we consider an instantiation of our framework for humans…
POMDPs are standard models for probabilistic planning problems, where an agent interacts with an uncertain environment. We study the problem of almost-sure reachability, where given a set of target states, the question is to decide whether there is a policy to ensure that the target set is reached with probability 1 (almost-surely). While in general the problem is EXPTIME-complete, in many practical cases policies with a small amount of memory suffice. Moreover, the existing solution to the problem is explicit, which first requires to construct explicitly an exponential reduction to a belief-s…
In this work, we propose a trajectory generation method for robotic systems with contact force constraint based on optimal control and reachability analysis. Normally, the dynamics and constraints of the contact-constrained robot are nonlinear and coupled to each other. Instead of linearizing the model and constraints, we directly solve the optimal control problem to obtain the feasible state trajectory and the control input of the system. A tractable optimal control problem is formulated which is addressed by dual approaches, which are sampling-based dynamic programming and rigorous reachabil…
University of Texas at Austin（德克萨斯大学奥斯汀分校）；Sony AI（索尼人工智能研究院）
Agents that operate in an unknown environment are bound to make mistakes while learning, including, at least occasionally, some that lead to catastrophic consequences. When humans make catastrophic mistakes, they are expected to learn never to repeat them, such as a toddler who touches a hot stove and immediately learns never to do so again. In this work we consider a novel class of POMDPs, called POMDP with Catastrophic Actions (POMDP-CA) in which pairs of states and actions are labeled as catastrophic. Agents that act in a POMDP-CA do not have a priori knowledge about which (state, action) p…
