Efficient Policy-Space Search for Fully-Observable Non-Deterministic Planning with Equivalence Pruning and Compression

Core Concepts

The core message of this work is to introduce techniques that substantially improve the performance of the policy-space search algorithm AND* for FOND planning. The key ideas are: (1) policy equivalence pruning, which avoids expanding multiple equivalent policies, (2) leveraging state symmetries to strengthen policy equivalence detection, (3) early deadlock pruning and satisficing search techniques, and (4) a solution compressor that finds a compact representation of the solution policy.

Abstract

This work focuses on improving the performance of the AND* algorithm, which performs an explicit heuristic search on the policy space of a FOND planning task. The authors present several key contributions:

Policy Equivalence Pruning:

The authors introduce three concepts of policy equivalence with different guarantees and effectiveness.
The "lanes" equivalence prunes policies that have the same domain but lead to different sets of unmapped states from each state.
The "domain-frontier" equivalence uses a polynomial-time "concretizer" procedure to construct a solution policy from just the domain and frontier states, allowing stronger pruning.

Leveraging State Symmetries:

The authors detect state equivalences through the computation of structural symmetries in the state space.
They apply a recent technique from group theory literature to improve the computation of these symmetries.
The detected state symmetries are used to strengthen the policy equivalence detection.

Early Deadlock Pruning and Satisficing Search:

The authors study the impact of early deadlock pruning on AND* with equivalence pruning.
They also investigate the use of satisficing search techniques, such as Weighted A* and Greedy Best-First Search, for FOND planning.

Solution Compression:

The authors introduce a "compressor" procedure that takes a solution policy defined over complete states and returns a policy defined over partial states that represents the same information using the minimum number of partial states.

The introduced techniques allow AND* to generate, on average, two orders of magnitude fewer policies to solve FOND tasks, making it competitive with other state-of-the-art FOND planners in terms of both coverage and solution compactness.

Stats

"The concretizer runs in O(|D| · |D ⊔ F| · |Π|) time."
"AND* with the introduced techniques generates, on average, two orders of magnitude fewer policies to solve FOND tasks."

Quotes

"The key ideas are: (1) policy equivalence pruning, which avoids expanding multiple equivalent policies, (2) leveraging state symmetries to strengthen policy equivalence detection, (3) early deadlock pruning and satisficing search techniques, and (4) a solution compressor that finds a compact representation of the solution policy."
"The introduced techniques allow AND* to generate, on average, two orders of magnitude fewer policies to solve FOND tasks, making it competitive with other state-of-the-art FOND planners in terms of both coverage and solution compactness."

Key Insights Distilled From

Policy-Space Search

by Fred... at arxiv.org 04-01-2024

https://arxiv.org/pdf/2403.19883.pdf

Deeper Inquiries

How could the policy equivalence concepts be extended or generalized to handle more complex planning domains or objectives beyond minimizing policy size

To extend the policy equivalence concepts for more complex planning domains or objectives, we can consider incorporating additional criteria or constraints into the equivalence definition. One approach could be to include probabilistic information or cost considerations in the equivalence definition. For example, policies could be considered equivalent if they achieve similar outcomes with respect to cost or probability distributions of outcomes. This would allow for a more nuanced comparison of policies beyond just their size.
Another extension could involve incorporating temporal aspects into the equivalence definition. Policies could be considered equivalent if they achieve the same goals within a similar timeframe or if they exhibit similar temporal patterns in their decision-making processes. This would be particularly relevant for planning domains where timing and sequencing of actions are crucial.
Furthermore, the concept of policy equivalence could be generalized to handle multi-agent planning scenarios. In such cases, policies could be considered equivalent if they lead to similar outcomes not only for a single agent but also for the overall system or group of agents. This would require defining equivalence criteria that take into account the interactions and dependencies between multiple agents' actions and goals.
Overall, by expanding the policy equivalence concepts to incorporate additional dimensions such as cost, probability, time, and multi-agent interactions, we can create a more comprehensive framework for comparing and evaluating policies in complex planning domains.

What other state-space analysis techniques, beyond symmetry detection, could be leveraged to further improve the performance of policy-space search algorithms for FOND planning

Beyond symmetry detection, several other state-space analysis techniques could be leveraged to further enhance the performance of policy-space search algorithms for FOND planning. Some of these techniques include:

Abstraction and Generalization: By abstracting the state space to a higher level of granularity, redundant or symmetrical states can be collapsed, reducing the search space. Generalization techniques can help identify common patterns or structures in the state space, leading to more efficient policy search.

Learning and Adaptation: Machine learning algorithms can be used to learn patterns from past policy search experiences and adapt the search strategy accordingly. Reinforcement learning techniques can guide the search process towards more promising regions of the policy space.

Constraint Satisfaction: Incorporating constraints derived from the problem domain can help prune the search space and focus on policies that satisfy specific requirements or objectives. Constraint satisfaction techniques can ensure that only feasible and valid policies are considered during the search.

Monte Carlo Tree Search: MCTS algorithms can be applied to explore the policy space in a more systematic and efficient manner. By sampling policies and evaluating their performance through simulation, MCTS can guide the search towards promising regions of the policy space.

By integrating these state-space analysis techniques with policy-space search algorithms, we can improve the efficiency, effectiveness, and scalability of FOND planning in complex domains.

What are the potential applications of the solution compression technique beyond FOND planning, and how could it be adapted to work with other planning formalisms or objectives

The solution compression technique introduced for FOND planning, which finds a policy that represents the same information using the minimum number of partial states, has potential applications beyond FOND planning. Some possible applications and adaptations include:

General Planning: The solution compressor could be adapted for use in classical planning domains to compress solution plans and reduce the complexity of the search space. By representing plans in a more compact form, the efficiency of classical planning algorithms could be improved.

Reinforcement Learning: In the context of reinforcement learning, the solution compressor could be used to compress and generalize policies learned by agents. This could lead to more efficient policy representation and transfer learning between different tasks.

Resource-Constrained Environments: In resource-constrained environments where memory or computational resources are limited, the solution compressor could help in generating more concise and efficient policies that require less memory and computational overhead.

Multi-Agent Systems: The compression technique could be extended to handle policies for multi-agent systems, where the goal is to find compact and effective coordination strategies among multiple agents. By compressing joint policies, the complexity of multi-agent planning could be reduced.

Overall, the solution compression technique has broad applicability across various planning formalisms and objectives, offering a way to streamline policy representation and improve the efficiency of planning algorithms in diverse domains.