We introduce a novel hierarchical reinforcement learning (HRL) framework that performs top-down recursive planning via learned subgoals, successfully applied to the complex combinatorial puzzle game Sokoban. Our approach constructs a six-level policy hierarchy, where each higher-level policy generates subgoals for the level below. All subgoals and policies are learned end-to-end from scratch, without any domain knowledge. Our results show that the agent can generate long action sequences from a single high-level call. While prior work has explored 2-3 level hierarchies and subgoal-based planning heuristics, we demonstrate that deep recursive goal decomposition can emerge purely from learning, and that such hierarchies can scale effectively to hard puzzle domains.
LMMs have shown impressive visual understanding capabilities, with the potential to be applied in agents, which demand strong reasoning and planning abilities. Nevertheless, existing benchmarks mostly assess their reasoning abilities in language part, where the chain-of-thought is entirely composed of text.We consider the scenario where visual signals are continuously updated and required along the decision making process. Such vision-in-the-chain reasoning paradigm is more aligned with the needs of multimodal agents, while being rarely evaluated. In this paper, we introduce MageBench, a reasoning capability oriented multimodal agent benchmark that, while having light-weight environments, poses significant reasoning challenges and holds substantial practical value. This benchmark currently includes three types of environments: WebUI, Sokoban, and Football, comprising a total of 483 different scenarios. It thoroughly validates the agent's knowledge and engineering capabilities, visual intelligence, and interaction skills. The results show that only a few product-level models are better than random acting, and all of them are far inferior to human-level. More specifically, we found current models severely lack the ability to modify their planning based on visual feedback, as well as visual imagination, interleaved image-text long context handling, and other abilities. We hope that our work will provide optimization directions for LMM from the perspective of being an agent. We release our code and data at https://github.com/microsoft/MageBench.
How a neural network (NN) generalizes to novel situations depends on whether it has learned to select actions heuristically or via a planning process. "An investigation of model-free planning" (Guez et al. 2019) found that a recurrent NN (RNN) trained to play Sokoban appears to plan, with extra computation steps improving the RNN's success rate. We replicate and expand on their behavioral analysis, finding the RNN learns to give itself extra computation steps in complex situations by "pacing" in cycles. Moreover, we train linear probes that predict the future actions taken by the network and find that intervening on the hidden state using these probes controls the agent's subsequent actions. Leveraging these insights, we perform model surgery, enabling the convolutional NN to generalize beyond its 10x10 architectural limit to arbitrarily sized inputs. The resulting model solves challenging, highly off-distribution levels. We open-source our model and code, and believe the neural network's small size (1.29M parameters) makes it an excellent model organism to deepen our understanding of learned planning.
Combining Large Language Models (LLMs) with heuristic search algorithms like A* holds the promise of enhanced LLM reasoning and scalable inference. To accelerate training and reduce computational demands, we investigate the coreset selection problem for the training data of LLM heuristic learning. Few methods to learn the heuristic functions consider the interaction between the search algorithm and the machine learning model. In this work, we empirically disentangle the requirements of A* search algorithm from the requirements of the LLM to generalise on this task. Surprisingly, we find an overlap between their requirements; A* requires more accurate predictions on search nodes near the goal, and LLMs need the same set of nodes for effective generalisation. With these insights, we derive a data-selection distribution for learning LLM-based heuristics. On three classical planning domains, maze navigation, Sokoban and sliding tile puzzles, our technique reduces the number of iterations required to find the solutions by up to 15x, with a wall-clock speed-up of search up to 5x. The codebase is at https://github.com/devaansh100/a_star.
Recently, procedural content generation has exhibited considerable advancements in the domain of 2D game level generation such as Super Mario Bros. and Sokoban through large language models (LLMs). To further validate the capabilities of LLMs, this paper explores how LLMs contribute to the generation of 3D buildings in a sandbox game, Minecraft. We propose a Text to Building in Minecraft (T2BM) model, which involves refining prompts, decoding interlayer representation and repairing. Facade, indoor scene and functional blocks like doors are supported in the generation. Experiments are conducted to evaluate the completeness and satisfaction of buildings generated via LLMs. It shows that LLMs hold significant potential for 3D building generation. Given appropriate prompts, LLMs can generate correct buildings in Minecraft with complete structures and incorporate specific building blocks such as windows and beds, meeting the specified requirements of human users.
While Transformers have enabled tremendous progress in various application settings, such architectures still trail behind traditional symbolic planners for solving complex decision making tasks. In this work, we demonstrate how to train Transformers to solve complex planning tasks. This is accomplished by training an encoder-decoder Transformer model to predict the search dynamics of the $A^*$ search algorithm. We fine tune this model to obtain a Searchformer, a Transformer model that optimally solves previously unseen Sokoban puzzles 93.7% of the time, while using up to 26.8% fewer search steps than the $A^*$ implementation that was used for training initially. In our training method, $A^*$'s search dynamics are expressed as a token sequence outlining when task states are added and removed into the search tree during symbolic planning. Searchformer significantly outperforms baselines that predict the optimal plan directly with a 5-10$\times$ smaller model size and a 10$\times$ smaller training dataset. Lastly, we demonstrate how Searchformer scales to larger and more complex decision making tasks with improved percentage of solved tasks and shortened search dynamics.
We propose the Thinker algorithm, a novel approach that enables reinforcement learning agents to autonomously interact with and utilize a learned world model. The Thinker algorithm wraps the environment with a world model and introduces new actions designed for interacting with the world model. These model-interaction actions enable agents to perform planning by proposing alternative plans to the world model before selecting a final action to execute in the environment. This approach eliminates the need for handcrafted planning algorithms by enabling the agent to learn how to plan autonomously and allows for easy interpretation of the agent's plan with visualization. We demonstrate the algorithm's effectiveness through experimental results in the game of Sokoban and the Atari 2600 benchmark, where the Thinker algorithm achieves state-of-the-art performance and competitive results, respectively. Visualizations of agents trained with the Thinker algorithm demonstrate that they have learned to plan effectively with the world model to select better actions. Thinker is the first work showing that an RL agent can learn to plan with a learned world model in complex environments.
Many puzzle video games, like Sokoban, involve moving some agent in a maze. The reachable locations are usually apparent for a human player, and the difficulty of the game is mainly related to performing actions on objects, such as pushing (reachable) boxes. For this reason, the difficulty of a particular level is often measured as the number of actions on objects, other than agent walking, needed to find a solution. In this paper we study CP and SAT approaches for solving these kind of problems. We review some reachability encodings and propose a new one. We empirically show that the new encoding is well-suited for solving puzzle problems in the planning as SAT paradigm, especially when considering the execution of several actions in parallel.
Levin Tree Search (LTS) is a search algorithm that makes use of a policy (a probability distribution over actions) and comes with a theoretical guarantee on the number of expansions before reaching a goal node, depending on the quality of the policy. This guarantee can be used as a loss function, which we call the LTS loss, to optimize neural networks representing the policy (LTS+NN). In this work we show that the neural network can be substituted with parameterized context models originating from the online compression literature (LTS+CM). We show that the LTS loss is convex under this new model, which allows for using standard convex optimization tools, and obtain convergence guarantees to the optimal parameters in an online setting for a given set of solution trajectories -- guarantees that cannot be provided for neural networks. The new LTS+CM algorithm compares favorably against LTS+NN on several benchmarks: Sokoban (Boxoban), The Witness, and the 24-Sliding Tile puzzle (STP). The difference is particularly large on STP, where LTS+NN fails to solve most of the test instances while LTS+CM solves each test instance in a fraction of a second. Furthermore, we show that LTS+CM is able to learn a policy that solves the Rubik's cube in only a few hundred expansions, which considerably improves upon previous machine learning techniques.
A level generator is a tool that generates game levels from noise. Training a generator without a dataset suffers from feedback sparsity, since it is unlikely to generate a playable level via random exploration. A common solution is shaped rewards, which guides the generator to achieve subgoals towards level playability, but they consume effort to design and require game-specific domain knowledge. This paper proposes a novel approach to train generators without datasets or shaped rewards by learning at multiple level sizes starting from small sizes and up to the desired sizes. The denser feedback at small sizes negates the need for shaped rewards. Additionally, the generators learn to build levels at various sizes, including sizes they were not trained for. We apply our approach to train recurrent auto-regressive generative flow networks (GFlowNets) for controllable level generation. We also adapt diversity sampling to be compatible with GFlowNets. The results show that our generators create diverse playable levels at various sizes for Sokoban, Zelda, and Danger Dave. When compared with controllable reinforcement learning level generators for Sokoban, the results show that our generators achieve better controllability and competitive diversity, while being 9x faster at training and level generation.
Complex reasoning problems contain states that vary in the computational cost required to determine a good action plan. Taking advantage of this property, we propose Adaptive Subgoal Search (AdaSubS), a search method that adaptively adjusts the planning horizon. To this end, AdaSubS generates diverse sets of subgoals at different distances. A verification mechanism is employed to filter out unreachable subgoals swiftly, allowing to focus on feasible further subgoals. In this way, AdaSubS benefits from the efficiency of planning with longer subgoals and the fine control with the shorter ones, and thus scales well to difficult planning problems. We show that AdaSubS significantly surpasses hierarchical planning algorithms on three complex reasoning tasks: Sokoban, the Rubik's Cube, and inequality proving benchmark INT.
Online tree-based search algorithms iteratively simulate trajectories and update action-values for a set of states stored in a tree structure. It works reasonably well in practice but fails to effectively utilise the information gathered from similar states. Depending upon the smoothness of the action-value function, one approach to overcoming this issue is through online learning, where information is interpolated among similar states; Policy Gradient Search provides a practical algorithm to achieve this. However, Policy Gradient Search lacks an explicit exploration mechanism, which is a key feature of tree-based online search algorithms. In this paper, we propose an efficient and effective online search algorithm called Exploratory Policy Gradient Search (ExPoSe), which leverages information sharing among states by updating the search policy parameters directly, while incorporating a well-defined exploration mechanism during the online search process. We evaluate ExPoSe on a range of decision-making problems, including Atari games, Sokoban, and Hamiltonian cycle search in sparse graphs. The results demonstrate that ExPoSe consistently outperforms other popular online search algorithms across all domains. The ExPoSe source code is available at \textit{\url{https://github.com/dixantmittal/ExPoSe}}.
We present a method of generating diverse collections of neural cellular automata (NCA) to design video game levels. While NCAs have so far only been trained via supervised learning, we present a quality diversity (QD) approach to generating a collection of NCA level generators. By framing the problem as a QD problem, our approach can train diverse level generators, whose output levels vary based on aesthetic or functional criteria. To efficiently generate NCAs, we train generators via Covariance Matrix Adaptation MAP-Elites (CMA-ME), a quality diversity algorithm which specializes in continuous search spaces. We apply our new method to generate level generators for several 2D tile-based games: a maze game, Sokoban, and Zelda. Our results show that CMA-ME can generate small NCAs that are diverse yet capable, often satisfying complex solvability criteria for deterministic agents. We compare against a Compositional Pattern-Producing Network (CPPN) baseline trained to produce diverse collections of generators and show that the NCA representation yields a better exploration of level-space.
Humans excel in solving complex reasoning tasks through a mental process of moving from one idea to a related one. Inspired by this, we propose Subgoal Search (kSubS) method. Its key component is a learned subgoal generator that produces a diversity of subgoals that are both achievable and closer to the solution. Using subgoals reduces the search space and induces a high-level search graph suitable for efficient planning. In this paper, we implement kSubS using a transformer-based subgoal module coupled with the classical best-first search framework. We show that a simple approach of generating $k$-th step ahead subgoals is surprisingly efficient on three challenging domains: two popular puzzle games, Sokoban and the Rubik's Cube, and an inequality proving benchmark INT. kSubS achieves strong results including state-of-the-art on INT within a modest computational budget.
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.
The use of a policy and a heuristic function for guiding search can be quite effective in adversarial problems, as demonstrated by AlphaGo and its successors, which are based on the PUCT search algorithm. While PUCT can also be used to solve single-agent deterministic problems, it lacks guarantees on its search effort and it can be computationally inefficient in practice. Combining the A* algorithm with a learned heuristic function tends to work better in these domains, but A* and its variants do not use a policy. Moreover, the purpose of using A* is to find solutions of minimum cost, while we seek instead to minimize the search loss (e.g., the number of search steps). LevinTS is guided by a policy and provides guarantees on the number of search steps that relate to the quality of the policy, but it does not make use of a heuristic function. In this work we introduce Policy-guided Heuristic Search (PHS), a novel search algorithm that uses both a heuristic function and a policy and has theoretical guarantees on the search loss that relates to both the quality of the heuristic and of the policy. We show empirically on the sliding-tile puzzle, Sokoban, and a puzzle from the commercial game `The Witness' that PHS enables the rapid learning of both a policy and a heuristic function and compares favorably with A*, Weighted A*, Greedy Best-First Search, LevinTS, and PUCT in terms of number of problems solved and search time in all three domains tested.
Player modeling attempts to create a computational model which accurately approximates a player's behavior in a game. Most player modeling techniques rely on domain knowledge and are not transferable across games. Additionally, player models do not currently yield any explanatory insight about a player's cognitive processes, such as the creation and refinement of mental models. In this paper, we present our findings with using action model learning (AML), in which an action model is learned given data in the form of a play trace, to learn a player model in a domain-agnostic manner. We demonstrate the utility of this model by introducing a technique to quantitatively estimate how well a player understands the mechanics of a game. We evaluate an existing AML algorithm (FAMA) for player modeling and develop a novel algorithm called Blackout that is inspired by player cognition. We compare Blackout with FAMA using the puzzle game Sokoban and show that Blackout generates better player models.
Recent work in deep reinforcement learning (RL) has produced algorithms capable of mastering challenging games such as Go, chess, or shogi. In these works the RL agent directly observes the natural state of the game and controls that state directly with its actions. However, when humans play such games, they do not just reason about the moves but also interact with their physical environment. They understand the state of the game by looking at the physical board in front of them and modify it by manipulating pieces using touch and fine-grained motor control. Mastering complicated physical systems with abstract goals is a central challenge for artificial intelligence, but it remains out of reach for existing RL algorithms. To encourage progress towards this goal we introduce a set of physically embedded planning problems and make them publicly available. We embed challenging symbolic tasks (Sokoban, tic-tac-toe, and Go) in a physics engine to produce a set of tasks that require perception, reasoning, and motor control over long time horizons. Although existing RL algorithms can tackle the symbolic versions of these tasks, we find that they struggle to master even the simplest of their physically embedded counterparts. As a first step towards characterizing the space of solution to these tasks, we introduce a strong baseline that uses a pre-trained expert game player to provide hints in the abstract space to an RL agent's policy while training it on the full sensorimotor control task. The resulting agent solves many of the tasks, underlining the need for methods that bridge the gap between abstract planning and embodied control. See illustrating video at https://youtu.be/RwHiHlym_1k.
This paper introduces RL Brush, a level-editing tool for tile-based games designed for mixed-initiative co-creation. The tool uses reinforcement-learning-based models to augment manual human level-design through the addition of AI-generated suggestions. Here, we apply RL Brush to designing levels for the classic puzzle game Sokoban. We put the tool online and tested it in 39 different sessions. The results show that users using the AI suggestions stay around longer and their created levels on average are more playable and more complex than without.
This paper introduces a new system to design constructive level generators by searching the space of constructive level generators defined by Marahel language. We use NSGA-II, a multi-objective optimization algorithm, to search for generators for three different problems (Binary, Zelda, and Sokoban). We restrict the representation to a subset of Marahel language to push the evolution to find more efficient generators. The results show that the generated generators were able to achieve good performance on most of the fitness functions over these three problems. However, on Zelda and Sokoban, they tend to depend on the initial state than modifying the map.