We present the domain-independent HRFF algorithm, which solves goal-oriented HMDPs by incrementally aggregating plans generated by the METRIC-FF planner into a policy defined over discrete and continuous state variables. HRFF takes into account non-monotonic state variables, and complex combinations of many discrete and continuous probability distributions. We introduce new data structures and algorithmic paradigms to deal with continuous state spaces: hybrid hierarchical hash tables, domain determinization based on dynamic domain sampling or on static computation of probability distributions' modes, optimization settings under METRIC-FF based on plan probability and length. We deeply analyze the behavior of HRFF on a probabilistically-interesting structured navigation problem with continuous dead-ends and non-monotonic continuous state variables. We compare with HAO* on the Rover domain and show that HRFF outperforms HAO* by many order of magnitudes in terms of computation time and memory usage. We also experiment challenging and combinatorial HMDP versions of benchmarks from numeric classical planning.

Moving-target search, where a hunter has to catch a moving target, is an important problem for video game developers. In our case, the hunter repeatedly moves towards the target and thus has to solve similar search problems repeatedly. We develop Incremental ARA* (I-ARA*) for this purpose, the first incremental anytime search algorithm for moving-target search in known terrain. We provide an error bound on the lengths of the paths found by I-ARA* and show experimentally in known four-neighbor gridworlds that I-ARA* can be used with smaller time limits between moves of the hunter than competing state-of-the-art moving-target search algorithms, namely repeated A*, G-FRA*, FRA*, and sometimes repeated ARA*. The hunter tends to make more moves with I-ARA* than repeated A*, G-FRA* or FRA*, which find shortest paths for the hunter, but fewer moves with I-ARA* than repeated ARA*, which finds suboptimal paths for the hunter like I-ARA*. Also, the error bounds on the lengths of the paths of the hunter tend to be smaller with I-ARA* than repeated ARA*.

Optimal planning and heuristic search systems solve state-space searchproblems by finding a least-cost path from start to goal. As a byproduct of having an optimal path they also determine the optimal solution cost. In this paper we focus on the problem of determining the optimal solution cost for a state-space search problem directly, i.e. without actually finding a solution path of that cost. We present an efficient algorithm, BiSS, based on ideas of bidirectional search and stratified sampling that produces accurate estimates of the optimal solution cost. Our method is guaranteed to return the optimal solution cost in the limit as the sample size goes to infinity.We show empirically that our method makes accurate predictions in several domains. In addition, we show that our method scales to state spaces much larger than can be solved optimally. In particular, we estimate the average solution cost for the 6x6, 7x7, and 8x8 Sliding-Tile Puzzle and provide indirect evidence that these estimates are accurate.

There has been much interest recently in problems that com-bine high-level task planning with low-level motion planning.In this paper, we present a problem of this kind that arises inmulti-vehicle mission planning. It tightly integrates task al-location and scheduling, who will do what when, with pathplanning, how each task will actually be performed. It ex-tends classical vehicle routing in that the cost of executing aset of high-level tasks can vary significantly in time and costaccording to the low-level paths selected. It extends classi-cal motion planning in that each path must minimize costwhile also respecting temporal constraints, including thoseimposed by the agent’s other tasks and the tasks assigned toother agents. Furthermore, the problem is a subtask withinan interactive system and therefore must operate within se-vere time constraints. We present an approach to the problembased on a combination of tabu search, linear programming,and heuristic search. We evaluate our planner on represen-tative problem instances and find that its performance meetsthe demanding requirements of our application. These resultsdemonstrate how integrating multiple diverse techniques cansuccessfully solve challenging real-world planning problemsthat are beyond the reach of any single method.

Heuristics based on the delete relaxation are at the forefront of modern domain-independent planning techniques. Here we introduce a principled and flexible technique for augmenting delete-relaxed tasks with a limited amount of delete information, by introducing special fluents that explicitly represent conjunctions of fluents in the original planning task. Differently from previous work in this direction, conditional effects are used to limit the growth of the task to be linear, rather than exponential, in the number of conjunctions that are introduced, making its use for obtaining heuristic functions feasible. We discuss how to obtain an informative set of conjunctions to be represented explicitly, and analyze and extend existing methods for relaxed planning in the presence of conditional effects. The resulting heuristics are empirically evaluated, and shown to be sometimes much more informative than standard delete-relaxation heuristics.

We present PROST, a probabilistic planning system that is based on the UCT algorithm by Kocsis and Szepesvari (2006), which has been applied successfully to many areas of planning and acting under uncertainty. The objective of this paper is to show the application of UCT to domain- independent probabilistic planning, an area it had not been applied to before. We furthermore present several enhance- ments to the algorithm, including a method that is able to drastically reduce the branching factor by identifying super- fluous actions. We show how search depth limitation leads to a more thoroughly investigated search space in parts that are influential on the quality of a policy, and present a sound and polynomially computable detection of reward locks, states that correspond to, e.g., dead ends or goals. We describe a general Q-value initialization for unvisited nodes in the search tree that circumvents the initial random walks inher- ent to UCT, and leads to a faster convergence on average. We demonstrate the significant influence of the enhancements by providing a comparison on the IPPC benchmark domains.

Considering cost-optimal heuristic search, we introduce the notion of global admissibility of a heuristic, a property weaker than standard admissibility, yet sufficient for guaranteeing solution optimality within forward search. We describe a concrete approach for creating globally admissible heuristics for domain independent planning; it is based on exploiting information gradually gathered by the search via a new form of reasoning about what we call existential optimal-plan landmarks. We evaluate our approach on some state-of-the-art heuristic search tools for cost-optimal planning, and discuss the results of this evaluation.

Delete-free planning underlies many popular relaxation (h+) based heuristics used in state-of-the-art planners; it provides a simpler setting for exploring new pruning methods and other ideas; and a number of interesting recent planning domains are naturally delete-free. In this paper we explore new pruning methods for planning in delete-free planning domains. First, we observe that optimal delete-free plans can be composed from contiguous sub-plans that focus on one fact landmark at a time. Thus, instead of attempting to achieve the goal, the planner can focus on more easily achievable landmarks at each stage. Then, we suggest a number of complementary pruning techniques that are made more powerful with this observation. To carry out these pruning techniques efficiently, we make heavy use of an And/Or graph depicting the planning problem. We empirically evaluate these ideas using the FD framework, and show that they lead to clear improvements.

This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is a "forward-backward" greedy procedure that -- uniquely -- operates on two distinct classes of objects. In particular, we organize our target sparse vectors as a matrix; our algorithm involves iterative addition and removal of both (a) individual elements, and (b) entire rows (corresponding to shared features), of the matrix. Analytically, we establish that our algorithm manages to recover the supports (exactly) and values (approximately) of the sparse vectors, under assumptions similar to existing approaches based on convex optimization. However, our algorithm has a much smaller computational complexity. Perhaps most interestingly, it is seen empirically to require visibly fewer samples. Ours represents the first attempt to extend greedy algorithms to the class of models that can only/best be represented by a combination of component structural assumptions (sparse and group-sparse, in our case).

In this paper we describe an improvement to the popular IDA* search algorithm that emphasizes a different space-for-time trade-off than previously suggested. In particular, our algorithm, called Iterative-Expansion A* (IEA*), focuses on reducing redundant node expansions within individual depth-first search DFS iterations of IDA* by employing a relatively small amount of available memory--bounded by the error in the heuristic--to store selected nodes. The additional memory required is exponential not in the solution depth, but only in the difference between the solution depth and the estimated solution depth. A constant-time hash set lookup can then be used to prune entire subtrees as DFS proceeds. Overall, we show 2- to 26-fold time speedups vs. an optimized version of IDA* across several domains, and compare IEA* with several other competing approaches. We also sketch proofs of optimality and completeness for IEA*, and note that IEA* is particularly efficient for solving implicitly-defined general graph search problems.