A privacy-preserving model for multi-agent propositional planning

Abstract

Over the last years, the planning community has formalised several models and approaches to multi-agent (MA) propositional planning. One of the main motivations in MA planning is that some or all agents have private knowledge that cannot be communicated to other agents during the planning process and the plan execution. We argue that the existing models of the multi-agent planning task do not maintain the agents’ privacy when a (strict) subset of the involved agents share confidential knowledge, or when the identity/existence of at least one agent is confidential. In this paper, first we propose a model of the MA-planning tasks that preserves the privacy of the involved agents when this happens. Then we investigate an algorithm based on best first search for our model that uses some new heuristics providing a trade-off between accuracy and agents’ privacy. Finally, an experimental study compares the effectiveness of using the proposed heuristics.     

MERGING SEPARATELY GENERATED PLANS WITH RESTRICTED INTERACTIONS

Generating action sequences to achieve a set of goals is a computationally difficult task. When multiple goals are present, the problem is even worse. Although many solutions to this problem have been discussed in the literature, practical solutions focus on the use of restricted mechanisms for planning or the application of domain dependent heuristics for providing rapid solutions (i.e., domain-dependent planning). One previously proposed technique for handling multiple goals efficiently is to design a planner or even a set of planners (usually domain-dependent) that can be used to generate separate plans for each goal. The outputs are typically either restricted to be independent and then concatenated into a single global plan, or else they are merged together using complex heuristic techniques. In this paper we explore a set of limitations, less restrictive than the assumption of independence, that still allow for the efficient merging of separate plans using straightforward algorithmic techniques.
In particular, we demonstrate that for cases where separate plans can be individually generated, we can define a set of limitations on the allowable interactions between goals that allow efficient plan merging to occur. We propose a set of restrictions that are satisfied across a significant class of planning domains. We present algorithms that are efficient for special cases of multiple plan merging, propose a heuristic search algorithm that performs well in a more general case (where alternative partially ordered plans have been generated for each goal), and describe an empirical study that demonstrates the efficiency of this search algorithm.     

Sequential Monte Carlo in reachability heuristics for probabilistic planning

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 straight-forward 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.     

Heavy-Tailed Phenomena in Satisfiability and Constraint Satisfaction Problems

We study the runtime distributions of backtrack procedures for propositional satisfiability and constraint satisfaction. Such procedures often exhibit a large variability in performance. Our study reveals some intriguing properties of such distributions: They are often characterized by very long tails or heavy tails. We will show that these distributions are best characterized by a general class of distributions that can have infinite moments (i.e., an infinite mean, variance, etc.). Such nonstandard distributions have recently been observed in areas as diverse as economics, statistical physics, and geophysics. They are closely related to fractal phenomena, whose study was introduced by Mandelbrot. We also show how random restarts can effectively eliminate heavy-tailed behavior. Furthermore, for harder problem instances, we observe long tails on the left-hand side of the distribution, which is indicative of a non-negligible fraction of relatively short, successful runs. A rapid restart strategy eliminates heavy-tailed behavior and takes advantage of short runs, significantly reducing expected solution time. We demonstrate speedups of up to two orders of magnitude on SAT and CSP encodings of hard problems in planning, scheduling, and circuit synthesis.     

A bidirectional shortest-path algorithm with good average-case behavior

The two-terminal shortest-path problem asks for the shortest directed path from a specified nodes to a specified noded in a complete directed graphG onn nodes, where each edge has a nonnegative length. We show that if the length of each edge is chosen independently from the exponential distribution, and adjacency lists at each node are sorted by length, then a priority-queue implementation of Dijkstra's unidirectional search algorithm has the expected running time (n logn). We present a bidirectional search algorithm that has expected running time (n logn). These results are generalized to apply to a wide class of edge-length distributions, and to sparse graphs. If adjacency lists are not sorted, bidirectional search has the expected running time (an) on graphs of average degreea, as compared with (an) for unidirectional search.     

Planning in domains with derived predicates through rule-action graphs and local search

The ability to express derived predicates in the formalization of a planning domain is both practically and theoretically important. In this paper, we propose an approach to planning with derived predicates where the search space consists of ??Rule-Action Graphs??, particular graphs of actions and rules representing derived predicates. We propose some techniques for representing such rules and reasoning with them, which are integrated into a framework for planning through local search and rule-action graphs. We also present some heuristics for guiding the search of a rule-action graph representing a valid plan. Finally, we analyze our approach through an extensive experimental study aimed at evaluating the importance of some specific techniques for the performance of the approach. The results of our experiments also show that our planner performs quite well compared to other state-of-the-art planners handling derived predicates.     

Anytime search in dynamic graphs

Agents operating in the real world often have limited time available for planning their next actions. Producing optimal plans is infeasible in these scenarios. Instead, agents must be satisfied with the best plans they can generate within the time available. One class of planners well-suited to this task are anytime planners, which quickly find an initial, highly suboptimal plan, and then improve this plan until time runs out.A second challenge associated with planning in the real world is that models are usually imperfect and environments are often dynamic. Thus, agents need to update their models and consequently plans over time. Incremental planners, which make use of the results of previous planning efforts to generate a new plan, can substantially speed up each planning episode in such cases.In this paper, we present an A^∗-based anytime search algorithm that produces significantly better solutions than current approaches, while also providing suboptimality bounds on the quality of the solution at any point in time. We also present an extension of this algorithm that is both anytime and incremental. This extension improves its current solution while deliberation time allows and is able to incrementally repair its solution when changes to the world model occur. We provide a number of theoretical and experimental results and demonstrate the effectiveness of the approaches in a robot navigation domain involving two physical systems. We believe that the simplicity, theoretical properties, and generality of the presented methods make them well suited to a range of search problems involving dynamic graphs.     

Directed explicit-state model checking in the validation of communication protocols

The success of model checking is largely based on its ability to efficiently locate errors in software designs. If an error is found, a model checker produces a trail that shows how the error state can be reached, which greatly facilitates debugging. However, while current model checkers find error states efficiently, the counterexamples are often unnecessarily lengthy, which hampers error explanation. This is due to the use of naive search algorithms in the state space exploration.In this paper we present approaches to the use of heuristic search algorithms in explicit-state model checking. We present the class of A^* directed search algorithms and propose heuristics together with bitstate compression techniques for the search of safety property violations. We achieve great reductions in the length of the error trails, and in some instances render problems analyzable by exploring a much smaller number of states than standard depth-first search. We then suggest an improvement of the nested depth-first search algorithm and show how it can be used together with A^* to improve the search for liveness property violations. Our approach to directed explicit-state model checking has been implemented in a tool set called HSF-SPIN. We provide experimental results from the protocol validation domain using HSF-SPIN.     

Case-Based Learning: Predictive Features in Indexing

Interest in psychological experimentation from the Artificial Intelligence community often takes the form of rigorous post-hoc evaluation of completed computer models. Through an example of our own collaborative research, we advocate a different view of how psychology and AI may be mutually relevant, and propose an integrated approach to the study of learning in humans and machines. We begin with the problem of learning appropriate indices for storing and retrieving information from memory. From a planning task perspective, the most useful indices may be those that predict potential problems and access relevant plans in memory, improving the planner's ability to predict and avoid planning failures. This predictive features hypothesis is then supported as a psychological claim, with results showing that such features offer an advantage in terms of the selectivity of reminding because they more distinctively characterize planning situations where differing plans are appropriate.We present a specific case-based model of plan execution, RUNNER, along with its indices for recognizing when to select particular plans—appropriateness conditions—and how these predictive indices serve to enhance learning. We then discuss how this predictive features claim as implemented in the RUNNER model is then tested in a second set of psychological studies. The results show that learning appropriateness conditions results in greater success in recognizing when a past plan is in fact relevant in current processing, and produces more reliable recall of the related information. This form of collaboration has resulted in a unique integration of computational and empirical efforts to create a model of case-based learning.     

Planning with Multistep Forward Search with Forced Goal‐Ordering Constraints

To solve a real‐world planning problem with interfering subgoals, it is essential to perform early detection of subgoal dependencies and achieve the subgoals in the correct order. This is also the case for planning problems with forced goal‐ordering (FGO) constraints. In automated planning, forward search with FGO constraints has been proposed many times over the years, but there are still major difficulties in realizing these FGOs in plan generation. Many existing methods such as goal agenda manager and ordered landmarks cannot detect the FGOs accurately, and thus, the undiscovered ordering relationship may cause the forward search to suffer from deadlocks. In this article, we put forward an approach via an effective search heuristic to constrain a planner to satisfy the FGOs. We make use of an atomic goal‐achievement graph in a look‐ahead search under the FGO constraints. This allows a forward search strategy to plan forward efficiently in multiple steps toward a goal state along a search path. Experimental results illustrate that, by avoiding deadlocks, we can solve more benchmark planning problems more efficiently than previous approaches. We also prove several formal properties for search that are related to FGO detection.     

A Mixed Closure-CSP Method for Solving Scheduling Problems

Scheduling problems can be viewed as a set of temporal metric and disjunctive constraints and so they can be formulated in terms of CSP techniques. In the literature, there are CSP-based methods which sequentially interleave search efforts with the application of consistency enforcing mechanisms and variable/ordering heuristics. Therefore, the number of backtrackings needed to obtain a solution is reduced. In this paper, we propose a new method that effectively integrates the CSP process into a limited closure process: not by interleaving them but rather as a part of the same process. Such an integration allows us to define more informed heuristics. These heuristics are used to limit the complete closure process to a maximum number of disjunctions, thereby reducing its complexity while at the same time reducing the search space. Some open disjunctive solutions can be maintained in the CSP process, limiting the number of backtrackings necessary, and avoiding having to know all the problem constraints in advance. Our experiments with flow-shop and job-shop instances show that this approach obtains a feasible solution/optimal solution without having to use backtracking in most cases. We also analyze the behaviour of our algorithm when some constraints are known dynamically and we demonstrate that it can provide better results than a pure CSP process.     

A graph coloring heuristic using partial solutions and a reactive tabu scheme

Most of the recent heuristics for the graph coloring problem start from an infeasible k-coloring (adjacent vertices may have the same color) and try to make the solution feasible through a sequence of color exchanges. In contrast, our approach (called FOO-PARTIALCOL), which is based on tabu search, considers feasible but partial solutions and tries to increase the size of the current partial solution. A solution consists of k disjoint stable sets (and, therefore, is a feasible, partial k-coloring) and a set of uncolored vertices. We introduce a reactive tabu tenure which substantially enhances the performance of both our heuristic as well as the classical tabu algorithm (called TABUCOL) proposed by Hertz and de Werra [Using tabu search techniques for graph coloring, Computing 1987;39:345–51]. We will report numerical results on different benchmark graphs and we will observe that FOO-PARTIALCOL, though very simple, outperforms TABUCOL on some instances, provides very competitive results on a set of benchmark graphs which are known to be difficult, and outperforms the best-known methods on the graph flat300_28_0. For this graph, FOO-PARTIALCOL finds an optimal coloring with 28 colors. The best coloring achieved to date uses 31 colors. Algorithms very close to TABUCOL are still used as intensification procedures in the best coloring methods, which are evolutionary heuristics. FOO-PARTIALCOL could then be a powerful alternative. In conclusion FOO-PARTIALCOL is one of the most efficient simple local search coloring methods yet available.     

A CSP Search Algorithm with Responsibility Sets and Kernels

A CSP search algorithm, like FC or MAC, explores a search tree during its run. Every node of the search tree can be associated with a CSP created by the refined domains of unassigned variables. If the algorithm detects that the CSP associated with a node is insoluble, the node becomes a dead-end. A strategy of pruning “by analogy” states that the current node of the search tree can be discarded if the CSP associated with it is “more constrained” than a CSP associated with some dead-end node. In this paper we present a method of pruning based on the above strategy. The information about the CSPs associated with dead-end nodes is kept in the structures called responsibility sets and kernels. We term the method that uses these structures for pruning RKP, which is abbreviation of Responsibility set, Kernel, Propagation. We combine the pruning method with algorithms FC and MAC. We call the resulting solvers FC-RKP and MAC-RKP, respectively. Experimental evaluation shows that MAC-RKP outperforms MAC-CBJ on random CSPs and on random graph coloring problems. The RKP-method also has theoretical interest. We show that under certain restrictions FC-RKP simulates FC-CBJ. It follows from the fact that intelligent backtracking implicitly uses the strategy of pruning “by analogy.”     

Hierarchical Path Search with Partial Materialization of Costs for a Smart Wheelchair

In this paper, the off-line path planner module of a smart wheelchair aided navigation system is described. Environmental information is structured into a hierarchical graph (H-graph) and used either by the user interface or the path planner module. This information structure facilitates efficient path search and easier information access and retrieval. Special path planning issues like planning between floors of a building (vertical path planning) are also viewed. The H-graph proposed is modelled by a tree. The hierarchy of abstractions contained in the tree has several levels of detail. Each abstraction level is a graph whose nodes can represent other graphs in a deeper level of the hierarchy. Path planning is performed using a path skeleton which is built from the deepest abstraction levels of the hierarchy to the most upper levels and completed in the last step of the algorithm. In order not to lose accuracy in the path skeleton generation and speed up the search, a set of optimal subpaths are previously stored in some nodes of the H-graph (path costs are partially materialized). Finally, some experimental results are showed and compared to traditional heuristic search algorithms used in robot path planning.     

规划问题编码为约束可满足问题的研究

基于约束可满足问题的规划求解是研究智能规划的重要技术方法。把规划问题编码为约束可满足（CSP）问题，是这种规划求解方法的关键技术之一。本文介绍把规划问题编码为约束可满足问题的方法，及一些已有的并且已经用于规划的可满足过程，并对这些编码方法做进一步的研究，主要讨论领域知识在编码方法中的应用，提出在编码求解中加入领域知识的观点。     

A Path-Consistent Singleton Modeling (CSM) Algorithm for Arc-Constrained Networks

There is very little of time in a temporal constraint propagation algorithm. Most of these algorithms could easily handle reasoning over any domain mapable onto rational numbers, e.g., weight, frequency, luminosity, etc. Actually some of these algorithms are capable of handling more sophisticated domains than those mapped onto rational numbers, e.g., intervals, or partially ordered objects (say, time). In this article we have generalized such an algorithm, which was originally developed for time-interval domain, to any generic domain, where binary constraints are expressed over arcs of the constraint network. Given the composition table for the primitive relations between a pair of the domain entities (e.g., intervals) as an additional input along with a constraint graph, the algorithm would generate all consistent singleton models for a given network. The algorithm is also extended here to handle uncertainty values.     

On the importance of breaking ties in the relaxed plan heuristic

The relaxed plan heuristic is a domain-independent heuristic for automated planning that computes an estimate of the cost for achieving the goals from a given state. This heuristic is based on the idea of solving a relaxed version of the planning task. Due to the great size of the state space, most heuristic search algorithms in planning suffer from scalability problems. These algorithms have to evaluate a great amount of states, and the time devoted to heuristic evaluations is one of the causes of the scalability problems. We argue that one way to lighten this problem is breaking ties in the heuristic value using additional information computed during the relaxed plan construction. We add a complementary value to the heuristic, allowing algorithms to discriminate between states with relaxed plans of the same length but with a different difficulty. The experimental evaluation in some planning benchmarks shows that the modification to the original heuristic can reduce the number of evaluated nodes for the most common algorithms used in heuristic planning.     

Tractable Decision for a Constraint Language Implies Tractable Search

A constraint satisfaction problem (CSP) instance has a set of variables, each of which can take values in some domain. It also has a set of constraints, each of which restricts the variables in its scope to take values limited by its constraint relation.The language of a constraint satisfaction problem instance is the set of different constraint relations used in its specification. For a given set of relations over some domain we define the problem CSP () to the set of CSP instances whose language is contained in .The decision problem for a set of CSP instances is, given an instance in the class, to decide whether a solution exists. The search problem is to find such a solution. Here we address the connection between the tractability of the decision and search problems. We prove that given a constraint language over a finite domain for which the decision problem for CSP () is tractable, the search problem is always tractable.We define a surjective language over a finite domain in a standard way. We also show that we can determine in polynomial time whether an instance over a surjective language with a tractable decision problem has fewer than k solutions, and that we can generate all of its solutions with polynomial delay.     

Structural plan similarity based on refinements in the space of partial plans

Plan similarity measures play a key role in many areas of artificial intelligence, such as case‐based planning, plan recognition, ambient intelligence, or digital storytelling. In this paper, we present 2 novel structural similarity measures to compare plans based on a search process in the space of partial plans. Partial plans are compact representations of sets of plans with some common structure and can be organized in a lattice so that the most general partial plans are above the most specific ones. To compute our similarity measures, we traverse this space of partial plans from the most general to the most specific using successive refinements. Our first similarity measure is designed for propositional plan formalisms, and the second is designed for classical planning formalisms (including variables and types). We also introduce 2 novel refinement operators used to traverse the space of plans: an ideal downward refinement operator for propositional partial plans and a finite and complete downward refinement operator for classical partial plans. Finally, we evaluate our similarity measures in the context of a nearest neighbor classifier using 2 datasets commonly used in the plan recognition literature (Linux and Monroe), showing good results in both synthetic and real data.