We describe a new sound and complete method forcompiling contingent planning problems with sensingactions into classical planning. Our method encodesconditional plans within a linear, classicalplan. This allows our planner, MPSR, to reasonabout multiple future outcomes of sensing actions,and makes it less susceptible to dead-ends. MPRS,however, generates very large classical planningproblems. To overcome this, we use an incompletevariant of the method, based on state sampling,within an online replanner. On most currentdomains, MPSR finds plans faster, although itsplans are often longer. But on a new challengingvariant of Wumpus with dead-ends, it finds smallerplans, faster, and scales much better.

Recent work in the field of probabilistic inference demonstrated the efficiency of weighted model counting (WMC) enginesfor exact inference in propositional and, very recently, first order models. To date, these methods have not been applied to decision making models, propositional or first order, such as influence diagrams, and Markov decision networks (MDN). In this paper we show how this technique can be applied to such models. First, we show how WMC can be used to solve (propositional) MDNs. Then, we show how this can be extended to handle a first-order model — the Markov Logic Decision Network (MLDN). WMC offers two central benefits: it is a very simple and very efficient technique. This is particularly true for the first-order case, where the WMC approach is simpler conceptually, and, in many cases, more effective computationally than the existing methods for solving MLDNs via first-order variable elimination, or via propositionalization. We demonstrate the above empirically.

Many real-world decision-theoretic planning problemsare naturally modeled using both continuous state andaction (CSA) spaces, yet little work has provided ex-act solutions for the case of continuous actions. Inthis work, we propose a symbolic dynamic program-ming (SDP) solution to obtain the optimal closed-formvalue function and policy for CSA-MDPs with mul-tivariate continuous state and actions, discrete noise,piecewise linear dynamics, and piecewise linear (or re-stricted piecewise quadratic) reward. Our key contribu-tion over previous SDP work is to show how the contin-uous action maximization step in the dynamic program-ming backup can be evaluated optimally and symboli-cally — a task which amounts to symbolic constrainedoptimization subject to unknown state parameters; wefurther integrate this technique to work with an efficientand compact data structure for SDP — the extendedalgebraic decision diagram (XADD). We demonstrateempirical results on a didactic nonlinear planning exam-ple and two domains from operations research to showthe first automated exact solution to these problems.

We introduce a highly efficient method for solving continuous partially-observable Markov decision processes (POMDPs) in which beliefs can be modeled using Gaussian distributions over the state space. Our method enables fast solutions to sequential decision making under uncertainty for a variety of problems involving noisy or incomplete observations and stochastic actions. We present an efficient approach to compute locally-valid approximations to the value function over continuous spaces in time polynomial (O[n^4]) in the dimension n of the state space. To directly tackle the intractability of solving general POMDPs, we leverage the assumption that beliefs are Gaussian distributions over the state space, approximate the belief update using an extended Kalman filter (EKF), and represent the value function by a function that is quadratic in the mean and linear in the variance of the belief. Our approach iterates towards a linear control policy over the state space that is locally-optimal with respect to a user defined cost function, and is approximately valid in the vicinity of a nominal trajectory through belief space. We demonstrate the scalability and potential of our approach on problems inspired by robot navigation under uncertainty for state spaces of up to 128 dimensions.

Optimal solutions to Stochastic Shortest Path Problems (SSPs) usually require that there exists at least one policy that reaches the goal with probability 1 from the initial state. This condition is very strong and prevents from solving many interesting problems, for instance where all possible policies reach some dead-end states with a positive probability. We introduce a more general and richer dual optimization criterion, which minimizes the average (undiscounted) cost of only paths leading to the goal among all policies that maximize the probability to reach the goal. We present policy update equations in the form of dynamic programming for this new dual criterion, which are different from the standard Bellman equations, but produce the same solution if there exists one policy leading to the goal with probability 1 from the initial state. We demonstrate that our equations converge in infinite horizon without any condition on the structure of the problem or on its policies, which actually extends the class of SSPs that can be solved. We experimentally show that our dual criterion provides well-founded solutions to SSPs that can not be solved by the standard criterion, and that using a discount factor with the latter certainly provides solution policies but which are not optimal considering our well-founded criterion.

Penetration Testing is a methodology for assessing network security, by generating and executing possible hacking attacks. Doing so automatically allows for regular and systematic testing. A key question is how to generate the attacks. This is naturally formulated as planning under uncertainty, i.e., under incomplete knowledge about the network configuration. Previous work uses classical planning, and requires costly pre-processes reducing this uncertainty by extensive application of scanning methods. By contrast, we herein model the attack planning problem in terms of partially observable Markov decision processes (POMDP). This allows to reason about the knowledge available, and to intelligently employ scanning actions as part of the attack. As one would expect, this accurate solution does not scale. We devise a method that relies on POMDPs to find good attacks on individual machines, which are then composed into an attack on the network as a whole. This decomposition exploits network structure to the extent possible, making targeted approximations (only) where needed. Evaluating this method on a suitably adapted industrial test suite, we demonstrate its effectiveness in both runtime and solution quality.

In this paper, we consider the problem of feasibly integrating new pick-up and delivery requests into existing vehicle itineraries in a dynamic, dial-a-ride problem (DARP) setting. Generalizing from previous work in oversubscribed task scheduling, we define a controlled iterative repair search procedure for finding an alternative set of vehicle itineraries in which the overall solution has been feasibly extended to include newly received requests. We first evaluate the performance of this technique on a set of DARP feasibility benchmark problems from the literature. We then consider its use on a real-world DARP problem, where it is necessary to accommodate all requests and constraints must be relaxed when a request cannot be feasibly integrated. For this latter analysis, we introduce a constraint relaxation post processing step and consider the performance impact of using our controlled iterative search over the current greedy search approach.

We consider symbolic dynamic programming (SDP) for solving Markov Decision Processes (MDP) with factored state and action spaces, where both states and actions are described by sets of discrete variables. Prior work on SDP has considered only the case of factored states and ignored structure in the action space, causing them to scale poorly in terms of the number of action variables. Our main contribution is to present the first SDP-based planning algorithm for leveraging both state and action space structure in order to compute compactly represented value functions and policies. Since our new algorithm can potentially require more space than when action structure is ignored, our second contribution is to describe an approach for smoothly trading-off space versus time via recursive conditioning. Finally, our third contribution is to introduce a novel SDP approximation that often significantly reduces planning time with little loss in quality by exploiting action structure in weakly coupled MDPs. We present empirical results in three domains with factored action spaces that show that our algorithms scale much better with the number of action variables as compared to state-of-the-art SDP algorithms.

Recent work on planning in incomplete domains focuses on constructing plans that succeed despite incomplete knowledge of action preconditions and effects. As planning models become more expressive, such as in temporal planning, the types of incompleteness may not only change, but plans become more challenging to evaluate. The primary difficulty to temporal plan evaluation is accounting for temporal constraints that may not be satisfied under all interpretations of the incomplete domain. In this work, we formulate incomplete temporal plan evaluation as a generalization of the temporal consistency problem, called partial temporal consistency. We present a knowledge compilation approach that is combined with symbolic constraint propagation and model counting algorithms for counting the number of incomplete domain model interpretations under which a plan is consistent. We present an evaluation that identifies the aspects of incomplete temporal plans most impact performance.

UCT, the premier method for solving games such as Go, is also becoming the dominant algorithm for probabilistic planning. Out of the five solvers at the International Probabilistic Planning Competition (IPPC) 2011, four were based on the UCT algorithm. However, while a UCT-based planner, PROST, won the contest, an LRTDP-based system, Glutton, came in a close second, outperforming other systems derived from UCT. These results raise a question: what are the strengths and weaknesses of LRTDP and UCT in practice? This paper starts answering this question by contrasting the two approaches in the context of finite-horizon MDPs. We demonstrate that in such scenarios, UCT's lack of a sound termination condition is a serious practical disadvantage. In order to handle an MDP with a large finite horizon under a time constraint, UCT forces an expert to guess a non-myopic lookahead value for which it should be able to converge on the encountered states. Mistakes in setting this parameter can greatly hurt UCT's performance. In contrast, LRTDP's convergence criterion allows for an iterative deepening strategy. Using this strategy, LRTDP automatically finds the largest lookahead value feasible under the given time constraint. As a result, LRTDP has better performance and stronger theoretical properties. We present an online version of Glutton, named Gourmand, that illustrates this analysis and outperforms PROST on the set of IPPC-2011 problems.