Reward machines allow the definition of rewards for temporally extended tasks and behaviors. Specifying "informative" reward machines can be challenging. One way to address this is to generate reward machines from a high-level abstract description of the learning environment, using techniques such as AI planning. However, previous planning-based approaches generate a reward machine based on a single (sequential or partial-order) plan, and do not allow maximum flexibility to the learning agent. In this paper we propose a new approach to synthesising reward machines which is based on the set of partial order plans for a goal. We prove that learning using such "maximally permissive" reward machines results in higher rewards than learning using RMs based on a single plan. We present experimental results which support our theoretical claims by showing that our approach obtains higher rewards than the single-plan approach in practice.

Partial-order plans in AI planning facilitate execution flexibility and several other tasks, such as plan reuse, modification, and decomposition, due to their less constrained nature. A Partial-Order Plan (POP) allows two actions with no ordering between them, thus providing the flexibility of executing actions in different sequences. This flexibility can be further extended by enabling parallel execution of actions in a POP to reduce its overall execution time. While extensive studies exist on improving the flexibility of a POP by optimizing its action orderings through plan deordering and reordering, there has been limited focus on the flexibility of executing actions concurrently in a plan. Execution concurrency in a POP can be achieved by incorporating action non-concurrency constraints, specifying which actions can not be executed in parallel. This work formalizes the conditions for non-concurrency constraints to transform a POP into a parallel plan. We also introduce an algorithm to enhance the plan's concurrency by optimizing resource utilization through substitutions of its subplans with respect to the corresponding planning task. Our algorithm employs block deordering that eliminates orderings in a POP by encapsulating coherent actions in blocks, and then exploits blocks as candidate subplans for substitutions. Experiments over the benchmark problems from International Planning Competitions (IPC) exhibit significant improvement in plan concurrency, specifically, with improvement in 25% of the plans, and an overall increase of 2.1% in concurrency.

Partial-order plans in AI planning facilitate execution flexibility due to their less-constrained nature. Maximizing plan flexibility has been studied through the notions of plan deordering, and plan reordering. Plan deordering removes unnecessary action orderings within a plan, while plan reordering modifies them arbitrarily to minimize action orderings. This study, in contrast with traditional plan deordering and reordering strategies, improves a plan's flexibility by substituting its subplans with actions outside the plan for a planning problem. We exploit block deordering, which eliminates orderings in a POP by encapsulating coherent actions in blocks, to construct action blocks as candidate subplans for substitutions. In addition, this paper introduces a pruning technique for eliminating redundant actions within a BDPO plan. We also evaluate our approach when combined with MaxSAT-based reorderings. Our experimental result demonstrates a significant improvement in plan execution flexibility on the benchmark problems from International Planning Competitions (IPC), maintaining good coverage and execution time.

In a dynamic environment, an intelligent agent must consider unexpected changes to the world and plan for them. We aim to address this key issue by building more robust artificial agents through the generalization of plan representations. Our research focuses on the process of generalizing various plan forms and the development of a compact representation which embodies a generalized plan as a policy. Our techniques allow an agent to execute efficiently in an online setting. We have, to date, demonstrated our approach for sequential and partial order plans and are pursuing similar techniques for representations such as Hierarchical Task Networks and GOLOG programs

Complexity analysis of planning is problematic. Even very simple planning languages are PSPACE-complete, yet cannot model many simple problems naturally. Many languages with much more powerful features are also PSPACE-complete. It is thus difficult to separate planning languages in a useful way and to get complexity figures that better reflect reality. This paper introduces new methods for complexity analysis of planning and similar combinatorial search problems, in order to achieve more precision and complexity separations than standard methods allow. Padding instances with the solution size yields a complexity measure that is immune to this factor and reveals other causes of hardness, that are otherwise hidden. Further combining this method with limited non-determinism improves the precision, making even finer separations possible. We demonstrate with examples how these methods can narrow the gap between theory and practice.