The primary revolution in automated planning in the last decade has been the very impressive scaleup in planner performance. A large part of the credit for this can be attributed squarely to the invention and deployment of powerful reachability heuristics. Most, if not all, modern reachability heuristics are based on a remarkably extensible data structure called the planning graph, which made its debut as a bit player in the success of GraphPlan, but quickly grew in prominence to occupy the center stage. Planning graphs are a cheap means to obtain informative look-ahead heuristics for search and have become ubiquitous in state of the art heuristic search planners. We present the foundations of planning graph heuristics in classical planning and explain how their flexibility lets them adapt to more expressive scenarios that consider action costs, goal utility, numeric resources, time, and uncertainty.

Probabilistic planning problems are typically modeled as a Markov Decision Process (MDP). MDPs, while an otherwise expressive model, allow only for sequential, non-durative actions. This poses severe restrictions in modeling and solving a real world planning problem. We extend the MDP model to incorporate — 1) simultaneous action execution, 2) durative actions, and 3) stochatic durations. We develop several algorithms to combat the computational explosion introduced by these features. The key theoretical ideas used in building these algorithms are — modeling a complex problem as an MDP in extended state/action space, pruning of irrelevant actions, sampling of relevant actions, using informed heuristics to guide the search, hybridizing different planners to achieve benefits of both, approximating the problem and replanning. Our empirical evaluation illuminates the different merits in using various algorithms, viz., optimality, empirical closeness to optimality, theoretical error bounds, and speed. 1.

Probabilistic temporal planning attempts to find good policies for acting in domains with concurrent durative tasks, multiple uncertain outcomes, and limited resources. These domains are typically modelled as Markov decision problems and solved using dynamic programming methods. This paper demonstrates the application of reinforcement learning — in the form of a policy-gradient method — to these domains. Our emphasis is large domains that are infeasible for dynamic programming. Our approach is to construct simple policies, or agents, for each planning task. The result is a general probabilistic temporal planner, named the Factored Policy-Gradient Planner (FPG-Planner), which can handle hundreds of tasks, optimising for probability of success, duration, and resource use. 1

We present a new algorithm for probabilistic planning with no observability. Our algorithm, called Probabilistic-FF, extends the heuristic forward-search machinery of Conformant-FF to problems with probabilistic uncertainty about both the initial state and action effects. Specifically, Probabilistic-FF combines Conformant-FF’s techniques with a powerful machinery for weighted model counting in (weighted) CNFs, serving to elegantly define both the search space and the heuristic function. Our evaluation of Probabilistic-FF shows its fine scalability in a range of probabilistic domains, constituting a several orders of magnitude improvement over previous results in this area. We use a problematic case to point out the main open issue to be addressed by further research. 1.

heuristic "distance" estimates between states and goals. A few authors have also attempted to use plan graphs in probabilistic planning to compute estimates of the probability that propositions can be achieved and actions can be performed.

Some of the current best conformant probabilistic planners focus on finding a fixed length plan with maximal probability. While these approaches can find optimal solutions, they often do not scale for large problems or plan lengths. As has been shown in classical planning, heuristic search outperforms bounded length search (especially when an appropriate plan length is not given a priori). The problem with applying heuristic search in probabilistic planning is that effective heuristics are as yet lacking. In this work, we apply heuristic search to conformant probabilistic planning by adapting planning graph heuristics developed for non-deterministic planning. We evaluate a straightforward application of these planning graph techniques, which amounts to exactly computing a distribution over many relaxed planning graphs (one planning graph for each joint outcome of uncertain actions at each time step). Computing this distribution is costly, so we apply Sequential Monte Carlo (SMC) to approximate it. One important issue that we explore in this work is how to automatically determine the number of samples required for effective heuristic computation. We empirically demonstrate on several domains how our efficient, but sometimes suboptimal, approach enables our planner to solve much larger problems than an existing optimal bounded length probabilistic planner and still find reasonable quality solutions.

We present an any-time concurrent probabilistic temporal planner that includes continuous and discrete uncertainties and metric functions. Our approach is a direct policy search that attempts to optimise a parameterised policy using gradient ascent. Low memory use, plus the use of function approximation methods, plus factorisation of the policy, allow us to scale to challenging domains. This Factored Policy Gradient (FPG) Planner also attempts to optimise both steps to goal and the probability of success. We compare the FPG planner to other planners on CPTP domains, and on simpler but better studied probabilistic non-temporal domains.

We present a hill-climbing algorithm to solve planning problems with temporal uncertainty. First an optimistic plan that is valid when all actions complete quickly is found. Then temporal reasoning techniques are used to determine when the plan may fail. At time points that cause an unsafe situation, contingency branches are inserted. We describe our planner PHOCUS-HC, give preliminary results, and discuss future work.

Probabilistic planning is an inherently multi-objective problem where plans must trade-off probability of goal satisfaction with expected plan cost. To date, probabilistic plan synthesis algorithms have focussed on single objective formulations that bound one of the objectives by making some unnatural assumptions. We show that a multi-objective formulation is not only needed, but also enables us to (i) generate Pareto sets of plans, (ii) use recent advances in probabilistic planning reachability heuristics, and (iii) elegantly solve limited contingency planning problems. We extend LAO ∗ to its multi-objective counterpart MOLAO ∗ , and discuss a number of speed-up techniques that form the basis for a state of the art conditional probabilistic planner. 1

The primary revolution in automated planning in the last decade has been the very impressive scaleup in planner performance. A large part of the credit for this can be attributed squarely to the invention and deployment of powerful reachability heuristics. Most, if not all, modern reachability heuristics are based on a remarkably extensible data structure called the planning graph, which made its debut as a bit player in the success of GraphPlan, but quickly grew in prominence to occupy the center stage. Planning graphs are a cheap means to obtain informative look-ahead heuristics for search and have become ubiquitous in state-of-the-art heuristic search planners. We present the foundations of planning graph heuristics in classical planning and explain how their flexibility lets them adapt to more expressive scenarios that consider action costs, goal utility, numeric resources, time, and uncertainty.