We present a declarative language, PP, for the high-level specification of preferences between possible solutions (or trajectories) of a planning problem. This novel language allows users to elegantly express non-trivial, multi-dimensional preferences and priorities over such preferences. The semantics of PP allows the identification of most preferred trajectories for a given goal. We also provide an answer set programming implementation of planning problems with PP preferences.
introduced a framework for planning with action costs using logic programming @cite_3 . The focus of their proposal is to express certain classes of quantitative preferences. Each action is assigned an integer cost, and plans with the minimal cost are considered to be optimal. Costs can be either static or relative to the time step in which the action is executed. @cite_3 also presents the encoding of different preferences, such as shortest plan and the cheapest plan. Our approach also emphasizes the use of logic programming, but differs in several aspects. Here, we develop a for preference representation. Our language can express the preferences discussed in @cite_3 , but it is more high-level and flexible than the action costs approach. The approach in @cite_3 also does not allow the use of fully general dynamic preferences. On the other hand, while we only consider planning with complete information, @cite_3 deal with planning in the presence of incomplete information and non-deterministic actions.
@cite_3
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Recently, planning based on answer set programming has been proposed as an approach towards realizing declarative planning systems. In this paper, we present the language κc, which extends the declarative planning language κ by action costs. κc provides the notion of admissible and optimal plans, which are plans whose overall action costs are within a given limit resp. minimum over all plans (i.e., cheapest plans). As we demonstrate, this novel language allows for expressing some nontrivial planning tasks in a declarative way. Furthermore, it can be utilized for representing planning problems under other optimality criteria, such as computing "shortest" plans (with the least number of steps), and refinement combinations of cheapest and fastest plans. We study complexity aspects of the language κc and provide a transformation to logic programs, such that planning problems are solved via answer set programming. Furthermore, we report experimental results on selected problems. Our experience is encouraging that answer set planning may be a valuable approach to expressive planning systems in which intricate planning problems can be naturally specified and solved. Learning, planning, and representing knowledge at multiple levels of temporal ab- straction are key, longstanding challenges for AI. In this paper we consider how these challenges can be addressed within the mathematical framework of reinforce- ment learning and Markov decision processes (MDPs). We extend the usual notion of action in this framework to include options—closed-loop policies for taking ac- tion over a period of time. Examples of options include picking up an object, going to lunch, and traveling to a distant city, as well as primitive actions such as mus- cle twitches and joint torques. Overall, we show that options enable temporally abstract knowledge and action to be included in the reinforcement learning frame- work in a natural and general way. In particular, we show that options may be used interchangeably with primitive actions in planning methods such as dynamic pro- gramming and in learning methods such as Q-learning. Formally, a set of options defined over an MDP constitutes a semi-Markov decision process (SMDP), and the theory of SMDPs provides the foundation for the theory of options. However, the most interesting issues concern the interplay between the underlying MDP and the SMDP and are thus beyond SMDP theory. We present results for three such cases: 1) we show that the results of planning with options can be used during execution to interrupt options and thereby perform even better than planned, 2) we introduce new intra-option methods that are able to learn about an option from fragments of its execution, and 3) we propose a notion of subgoal that can be used to improve the options themselves. All of these results have precursors in the existing literature; the contribution of this paper is to establish them in a simpler and more general setting with fewer changes to the existing reinforcement learning framework. In particular, we show that these results can be obtained without committing to (or ruling out) any particular approach to state abstraction, hierarchy, function approximation, or the macro-utility problem. In this semi-tutorial paper, we first review the information-theoretic approach to account for the computational costs incurred during the search for optimal actions in a sequential decision-making problem. The traditional (MDP) framework ignores computational limitations while searching for optimal policies, essentially assuming that the acting agent is perfectly rational and aims for exact optimality. Using the free-energy, a variational principle is introduced that accounts not only for the value of a policy alone, but also considers the cost of finding this optimal policy. The solution of the variational equations arising from this formulation can be obtained using familiar Bellman-like value iterations from dynamic programming (DP) and the Blahut-Arimoto (BA) algorithm from rate distortion theory. Finally, we demonstrate the utility of the approach for generating hierarchies of state abstractions that can be used to best exploit the available computational resources. A numerical example showcases these concepts for a path-planning problem in a grid world environment. Traditional query optimizers assume accurate knowledge of run-time parameters such as selectivities and resource availability during plan optimization, i.e., at compile time. In reality, however, this assumption is often not justified. Therefore, the “static” plans produced by traditional optimizers may not be optimal for many of their actual run-time invocations. Instead, we propose a novel optimization model that assigns the bulk of the optimization effort to compile-time and delays carefully selected optimization decisions until run-time. Our previous work defined the run-time primitives, “dynamic plans” using “choose-plan” operators, for executing such delayed decisions, but did not solve the problem of constructing dynamic plans at compile-time. The present paper introduces techniques that solve this problem. Experience with a working prototype optimizer demonstrates (i) that the additional optimization and start-up overhead of dynamic plans compared to static plans is dominated by their advantage at run-time, (ii) that dynamic plans are as robust as the “brute-force” remedy of run-time optimization, i.e., dynamic plans maintain their optimality even if parameters change between compile-time and run-time, and (iii) that the start-up overhead of dynamic plans is significantly less than the time required for complete optimization at run-time. In other words, our proposed techniques are superior to both techniques considered to-date, namely compile-time optimization into a single static plan as well as run-time optimization. Finally, we believe that the concepts and technology described can be transferred to commercial query optimizers in order to improve the performance of embedded queries with host variables in the query predicate and to adapt to run-time system loads unpredictable at compile time.