Pruning techniques based on partial order reduction and symmetry elimination have recently found increasing attention for optimal planning. Although these techniques appear to be rather different, they base their pruning decisions on similar ideas from a high level perspective. In this paper, we propose safe integrations of partial order reduction and symmetry elimination for cost-optimal classical planning. We show that previously proposed symmetry-based search algorithms can safely be applied with strong stubborn sets. In addition, we derive the notion of symmetrical strong stubborn sets as a more tightly integrated concept. Our experiments show the potential of our approaches.

In optimal planning as heuristic search, admissible pruning techniques are paramount. One idea is dominance pruning, identifying states "better than" other states. Prior approaches are limited to simple dominance notions, like "more STRIPS facts true" or "higher resource supply". We apply simulation, well-known in model checking, to compute much more general dominance relations based on comparing transition behavior across states. We do so effectively by expressing state-space simulations through the composition of simulations on orthogonal projections. We show how simulation can be made more powerful by intertwining it with a notion of label dominance. Our experiments show substantial improvements across several IPC benchmark domains.

Real-time strategy (RTS) games are hard from an AI point of view because they have enormous state spaces, combinatorial branching factors, allow simultaneous and durative actions, and players have very little time to choose actions. For these reasons, standard game tree search methods such as alpha- beta search or Monte Carlo Tree Search (MCTS) are not sufficient by themselves to handle these games. This paper presents an alternative approach called Adversarial Hierarchical Task Network (AHTN) planning that combines ideas from game tree search with HTN planning. We present the basic algorithm, relate it to existing adversarial hierarchical planning methods, and present new extensions for simultaneous and durative actions to handle RTS games. We also present empirical results for the μRTS game, comparing it to other state of the art search algorithms for RTS games.

We describe Exploratory Digraph Navigation as a fundamental problem of graph theory concerned with using a graph with incomplete edge and vertex information for navigation in a partially unknown environment. We then introduce EDNA*, a simple A* extension which provably solves the problem and give worst-case bounds on the number of edges explored by said algorithm. We compare the performance of this algorithm to a non-exploratory strategy using A* and discuss its relation to existing algorithms such as D* Lite, PHA* with early stopping, EWP or exploration algorithms.

The Atari 2600 games supported in the Arcade Learning Environment [Bellemare et al., 2013] all feature a known initial (RAM) state and actions that have deterministic effects. Classical planners, however, cannot be used off-the-shelf as there is no compact PDDL-model of the games, and action effects and goals are not known a priori. Indeed, there are no explicit goals, and the planner must select actions on line while interacting with a simulator that returns successor states and rewards. None of this precludes the use of blind lookahead algorithms for action selection like breadth-first search or Dijkstra’s yet such methods are not effective over large state spaces. We thus turn to a different class of planning methods introduced recently that have been shown to be effective for solving large planning problems but which do not require prior knowledge of state transitions, costs (rewards) or goals. The empirical results over 54 Atari games show that the simplest such algorithm performs at the level of UCT, the state-of-the-art planning method in this domain, and suggest the potential of width-based methods for planning with simulators when factored, compact action models are not available.

Most work in planning focuses on tasks with state-independent or even uniform action costs. However, supporting state-dependent action costs admits a more compact representation of many tasks. We investigate how to solve such tasks using heuristic search, with a focus on delete-relaxation heuristics. We first define a generalization of the additive heuristic to such tasks and then discuss different ways of computing it via compilations to tasks with state-independent action costs and more directly by modifying the relaxed planning graph. We evaluate these approaches theoretically and present an implementation of the additive heuristic for planning with state-dependent action costs. To our knowledge, this gives rise to the first approach able to handle even the hardest instances of the combinatorial Academic Advising domain from the International Probabilistic Planning Competition (IPPC) 2014.

Nowadays, robots are programmed with a mix of discrete and continuous low level behaviors by experts in a very time consuming and expensive process. Existing automated planning approaches are either based on hybrid model predictive control techniques, which do not scale well due to time discretization, or temporal planners, which sacrifice plan expressivity by only supporting discretized fixed rates of change in continuous effects. We introduce Scotty, a mixed discrete-continuous generative planner that finds the middle ground between these two. Scotty can reason with linear time evolving effects whose behaviors can be modified by bounded control variables, with no discretization involved. Our planner exploits the expressivity of flow tubes, which compactly encapsulate continuous effects, and the performance of heuristic forward search. The generated solution plans are better suited for robust execution, as executives can use the flexibility in both time and continuous control variables to react to disturbances.

To engage diverse agents in cooperative behavior, it is important, even necessary, to provide algorithms that do not reveal information that is private or proprietary.A number of recent planning algorithms enable agents to plan together for shared goals without disclosing information about their private state and actions. But these algorithms lack clear and formal privacy guarantees: the fact that they do not require agents to explicitly reveal private information, does not imply that such information cannot be deduced. The main contribution of this paper is an enhanced version of the distributed forward-search planning framework of Nissim and Brafman that reveals less information than the original algorithm, and the first, to our knowledge, discussion and formal proof of privacy guarantees for distributed planning and search algorithms.

This paper addresses two classes of different, yet interrelated optimization problems. The first class of problems involves a robot that must locate a hidden target in an environment that consists of a set of concurrent rays. The second class pertains to the design of interruptible algorithms by means of a schedule of contract algorithms. We study several variants of these families of problems, such as searching and scheduling with probabilistic considerations, redundancy and fault-tolerance issues, randomized strategies, and trade-offs between performance and preemptions. For many of these problems we present the first known results that apply to multi-ray and multi-problem domains. Our objective is to demonstrate that several well-motivated settings can be addressed using a common approach.

Geometry reasoning and proof form a major and challenging component in the K-121 mathematics curriculum. Although several computerized systems exist that help students learn and practice general geometry concepts, they do not target geometry proof problems, which are more advanced and difficult. Powerful geometry theorem provers also exist, however they typically employ advanced algebraic methods and generate complex, difficult to understand proofs, and thus do not meet general K-12 students’ educational needs. This paper tackles these weaknesses of prior systems by introducing a geometry proof system, iGeoTutor, capable of generating human-readable elementary proofs, i.e. proofs using standard Euclidean axioms. We have gathered 77 problems in total from various sources, including ones unsolvable by other systems and from Math competitions. iGeoTutor solves all but two problems in under two minutes each, and more importantly, demonstrates a much more effective and intelligent proof search than prior systems. We have also conducted a pilot study with 12 high school students, and the results show that iGeoTutor provides a clear benefit in helping students learn geometry proofs. We are in active discussions with Khan Academy and local high schools for possible adoption of iGeo-Tutor in real learning environments.