We study an efficient implementation of Multi-Armed Bandit (MAB)-based Monte-Carlo Tree Search (MCTS) for classical planning. One weakness of MCTS is that it spends a significant time in deciding which node to expand next. While selecting a node from an OPEN list with N nodes has O(1) runtime complexity with traditional array-based priority-queues for dense integer keys, the tree-based OPEN list used by MCTS requires O(log N), which roughly corresponds to the search depth d. In classical planning, d is arbitrarily large (e.g., 2^k-1 in k-disk Tower-of-Hanoi) and the runtime for node selection is significant, unlike in game tree search, where the cost is negligible compared to the node evaluation (rollouts) because d is inherently limited by the game (e.g. d≦361 in Go). To improve this bottleneck, we propose a bilevel modification to MCTS that runs a best-first search from each selected leaf nodes with an expansion budget proportional to d, which achieves amortized O(1) runtime for node selection, equivalent to traditional queue-based OPEN list. In addition, we introduce Tree Collapsing, an enhancement that reduces action selection steps and further improves the performance.

Despite being successful in board games and reinforcement learning (RL), Monte Carlo Tree Search (MCTS) combined with Multi Armed Bandit (MAB) has seen limited success in domain-independent classical planning until recently. Previous work (Wissow and Asai, 2024) showed that UCB1, designed for bounded rewards, does not perform well as applied to cost-to-go estimates in classical planning, because cost-to-go estimates are unbounded, and showed improved performance using a Gaussian reward MAB instead. This paper further sharpens our understanding of ideal bandits for planning tasks. Existing work has two issues: first, Gaussian MABs under-specify the support of cost-to-go estimates as (-∞, ∞), which we can narrow down. Second, Full Bellman backup (Schulte and Keller, 2014) that backpropagates sample max/min lacks theoretical justification. We use Peaks-Over-Threashold Extreme Value Theory to resolve both issues at once, propose a new bandit algorithm (UCB1-Uniform). We formally prove its regret bound and empirically demonstrate its performance in classical planning.

Balancing exploration and exploitation has been an important problem in both adversarial games and automated planning. While it has been extensively analyzed in the Multi-Armed Bandit (MAB) literature, and the game community has achieved great success with MAB-based Monte Carlo Tree Search (MCTS) methods, the planning community has struggled to advance in this area. We describe how Upper Confidence Bound 1’s (UCB1’s) assumption of reward distributions with known bounded support shared among siblings (arms) is violated when MCTS/Trial-based Heuristic Tree Search (THTS) in previous work uses heuristic values of search nodes in classical planning problems as rewards. To address this issue, we propose a new Gaussian bandit, UCB1-Normal2, and analyze its regret bound. It is variance-aware like UCB1-Normal and UCB-V, but has a distinct advantage: it neither shares UCB-V’s assumption of known bounded support nor relies on UCB1-Normal’s conjectures on Student’s t and χ2 distributions. Our theoretical analysis predicts that UCB1-Normal2 will perform well when the estimated variance is accurate, which can be expected in deterministic, discrete, finite state-space search, as in classical planning. Our empirical evaluation confirms that MCTS combined with UCB1-Normal2 outperforms Greedy Best First Search (traditional baseline) as well as MCTS with other bandits.

Monte-Carlo Tree Search (MCTS) combined with Multi-Armed Bandit (MAB) has had limited success in domain-independent classical planning until recently. Previous work (Wissow and Asai 2023) showed that UCB1, designed for bounded rewards, does not perform well when applied to the cost-to-go estimates of classical planning, which are unbounded in R, then improved the performance by using a Gaussian reward MAB instead. We further sharpen our understanding of ideal bandits for planning tasks by resolving three issues: First, Gaussian MABs under-specify the support of cost-to-go estimates as [−∞, ∞]. Second, Full-Bellman backup that backpropagates max/min of samples lacks theoretical justifications. Third, removing dead-ends lacks justifications in Monte-Carlo backup. We use Extreme Value Theory Type 2 to resolve them at once, propose two bandits (UCB1-Uniform/Power), and apply them to MCTS for classical planning. We formally prove their regret bounds and empirically demonstrate their performance in classical planning.

Current domain-independent, classical planners require symbolic models of the problem domain and instance as input, resulting in a knowledge acquisition bottleneck. Meanwhile, although deep learning has achieved significant success in many fields, the knowledge is encoded in a subsymbolic representation which is incompatible with symbolic systems such as planners. We propose Latplan, an unsupervised architecture combining deep learning and classical planning. Given only an unlabeled set of image pairs showing a subset of transitions allowed in the environment (training inputs), Latplan learns a complete propositional PDDL action model of the environment. Later, when a pair of images representing the initial and the goal states (planning inputs) is given, Latplan finds a plan to the goal state in a symbolic latent space and returns a visualized plan execution. We evaluate Latplan using image-based versions of 6 planning domains: 8-puzzle, 15-Puzzle, Blocksworld, Sokoban and Two variations of LightsOut.

We achieved a new milestone in the difficult task of enabling agents to learn about their environment autonomously. Our neuro-symbolic architecture is trained end-to-end to produce a succinct and effective discrete state transition model from images alone. Our target representation (the Planning Domain Definition Language) is already in a form that off-the-shelf solvers can consume, and opens the door to the rich array of modern heuristic search capabilities. We demonstrate how the sophisticated innate prior we place on the learning process significantly reduces the complexity of the learned representation, and reveals a connection to the graph-theoretic notion of ``cube-like graphs'', thus opening the door to a deeper understanding of the ideal properties for learned symbolic representations. We show that the powerful domain-independent heuristics allow our system to solve visual 15-Puzzle instances which are beyond the reach of blind search, without resorting to the Reinforcement Learning approach that requires a huge amount of training on the domain-dependent reward information.

Current domain-independent, classical planners require symbolic models of the problem domain and instance as input, resulting in a knowledge acquisition bottleneck. Meanwhile, although deep learning has achieved significant success in many fields, the knowledge is encoded in a subsymbolic representation which is incompatible with symbolic systems such as planners. We propose LatPlan, an unsupervised architecture combining deep learning and classical planning. Given only an unlabeled set of image pairs showing a subset of transitions allowed in the environment (training inputs), and a pair of images representing the initial and the goal states (planning inputs), LatPlan finds a plan to the goal state in a symbolic latent space and returns a visualized plan execution. The contribution of this paper is twofold: (1) State Autoencoder, which finds a propositional state representation of the environment using a Variational Autoencoder. It generates a discrete latent vector from the images, based on which a PDDL model can be constructed and then solved by an off-the-shelf planner. (2) Action Autoencoder / Discriminator, a neural architecture which jointly finds the action symbols and the implicit action models (preconditions/effects), and provides a successor function for the implicit graph search. We evaluate LatPlan using image-based versions of 3 planning domains: 8-puzzle, Towers of Hanoi and LightsOut.

Optimal heuristic search has been successful in many domains, including journey planning, route planning and puzzle solving. Existing work typically assumes that the cost of each action can easily be obtained. However, in many problems, the exact edge cost is expensive to compute. Existing search algorithms face a significant performance bottleneck, due to an excessive overhead associated with dynamically calculating exact edge costs. We present DEA*, an algorithm for problems with expensive edge cost computations. DEA* combines heuristic edge cost evaluations with delayed node expansions, reducing the number of exact edge computations. We formally prove that DEA* is optimal and it is efficient with respect to the number of exact edge cost computations. We empirically evaluate DEA* on multiple-worker routing problems where the exact edge cost is calculated by invoking an external multi-modal journey planning engine. The results demonstrate the effectiveness of our ideas in reducing the computational time and improving the solving ability. In addition, we show the advantages of DEA* in domain-independent planning, where we simulate that accurate edge costs are expensive to compute.

Best-first search algorithms such as A* need to apply tie-breaking strategies in order to decide which node to expand when multiple search nodes have the same evaluation score. We investigate and improve tie-breaking strategies for cost-optimal search using A*. We first experimentally analyze the performance of common tie-breaking strategies that break ties according to the heuristic value of the nodes. We find that the tie-breaking strategy has a significant impact on search algorithm performance when there are 0-cost operators that induce large plateau regions in the search space. Based on this, we develop two new classes of tie-breaking strategies. We first propose a depth diversification strategy which breaks ties according to the distance from the entrance to the plateau, and then show that this new strategy significantly outperforms standard strategies on domains with 0-cost actions. Next, we propose a new framework for interpreting A* search as a series of satisficing searches within plateaus consisting of nodes with the same f-cost. Based on this framework, we investigate a second, new class of tie-breaking strategy, a multi-heuristic tie-breaking strategy which embeds inadmissible, distance-to-go variations of various heuristics within an admissible search. This is shown to further improve the performance in combination with the depth metric.

Despite recent improvements in search techniques for cost-optimal classical planning, the exponential growth of the size of the search frontier in A* is unavoidable. We investigate tiebreaking strategies for A*, experimentally analyzing the performance of standard tiebreaking strategies that break ties according to the heuristic value of the nodes. We find that tiebreaking has a significant impact on search algorithm performance when there are zero-cost operators that induce large plateau regions in the search space. We develop a new framework for tiebreaking based on a depth metric which measures distance from the entrance to the plateau, and propose a new, randomized strategy which significantly outperforms standard strategies on domains with zero-cost actions.