We partially reverse-engineer a convolutional recurrent neural network (RNN) trained to play the puzzle game Sokoban with model-free reinforcement learning. Prior work found that this network solves more levels with more test-time compute. Our analysis reveals several mechanisms analogous to components of classic bidirectional search. For each square, the RNN represents its plan in the activations of channels associated with specific directions. These state-action activations are analogous to a value function - their magnitudes determine when to backtrack and which plan branch survives pruning. Specialized kernels extend these activations (containing plan and value) forward and backward to create paths, forming a transition model. The algorithm is also unlike classical search in some ways. State representation is not unified; instead, the network considers each box separately. Each layer has its own plan representation and value function, increasing search depth. Far from being inscrutable, the mechanisms leveraging test-time compute learned in this network by model-free training can be understood in familiar terms.
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.
We present the first mechanistic evidence that model-free reinforcement learning agents can learn to plan. This is achieved by applying a methodology based on concept-based interpretability to a model-free agent in Sokoban -- a commonly used benchmark for studying planning. Specifically, we demonstrate that DRC, a generic model-free agent introduced by Guez et al. (2019), uses learned concept representations to internally formulate plans that both predict the long-term effects of actions on the environment and influence action selection. Our methodology involves: (1) probing for planning-relevant concepts, (2) investigating plan formation within the agent's representations, and (3) verifying that discovered plans (in the agent's representations) have a causal effect on the agent's behavior through interventions. We also show that the emergence of these plans coincides with the emergence of a planning-like property: the ability to benefit from additional test-time compute. Finally, we perform a qualitative analysis of the planning algorithm learned by the agent and discover a strong resemblance to parallelized bidirectional search. Our findings advance understanding of the internal mechanisms underlying planning behavior in agents, which is important given the recent trend of emergent planning and reasoning capabilities in LLMs through RL
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.
Goal recognition (GR) involves inferring an agent's unobserved goal from a sequence of observations. This is a critical problem in AI with diverse applications. Traditionally, GR has been addressed using 'inference to the best explanation' or abduction, where hypotheses about the agent's goals are generated as the most plausible explanations for observed behavior. Alternatively, some approaches enhance interpretability by ensuring that an agent's behavior aligns with an observer's expectations or by making the reasoning behind decisions more transparent. In this work, we tackle a different challenge: explaining the GR process in a way that is comprehensible to humans. We introduce and evaluate an explainable model for goal recognition (GR) agents, grounded in the theoretical framework and cognitive processes underlying human behavior explanation. Drawing on insights from two human-agent studies, we propose a conceptual framework for human-centered explanations of GR. Using this framework, we develop the eXplainable Goal Recognition (XGR) model, which generates explanations for both why and why not questions. We evaluate the model computationally across eight GR benchmarks and through three user studies. The first study assesses the efficiency of generating human-like explanations within the Sokoban game domain, the second examines perceived explainability in the same domain, and the third evaluates the model's effectiveness in aiding decision-making in illegal fishing detection. Results demonstrate that the XGR model significantly enhances user understanding, trust, and decision-making compared to baseline models, underscoring its potential to improve human-agent collaboration.
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.
We introduce Autoverse, an evolvable, domain-specific language for single-player 2D grid-based games, and demonstrate its use as a scalable training ground for Open-Ended Learning (OEL) algorithms. Autoverse uses cellular-automaton-like rewrite rules to describe game mechanics, allowing it to express various game environments (e.g. mazes, dungeons, sokoban puzzles) that are popular testbeds for Reinforcement Learning (RL) agents. Each rewrite rule can be expressed as a series of simple convolutions, allowing for environments to be parallelized on the GPU, thereby drastically accelerating RL training. Using Autoverse, we propose jump-starting open-ended learning by imitation learning from search. In such an approach, we first evolve Autoverse environments (their rules and initial map topology) to maximize the number of iterations required by greedy tree search to discover a new best solution, producing a curriculum of increasingly complex environments and playtraces. We then distill these expert playtraces into a neural-network-based policy using imitation learning. Finally, we use the learned policy as a starting point for open-ended RL, where new training environments are continually evolved to maximize the RL player agent's value function error (a proxy for its regret, or the learnability of generated environments), finding that this approach improves the performance and generality of resultant player agents.
This paper presents an interactive platform to interpret multi-objective evolutionary algorithms. Sokoban level generation is selected as a showcase for its widespread use in procedural content generation. By balancing the emptiness and spatial diversity of Sokoban levels, we illustrate the improved two-archive algorithm, Two_Arch2, a well-known multi-objective evolutionary algorithm. Our web-based platform integrates Two_Arch2 into an interface that visually and interactively demonstrates the evolutionary process in real-time. Designed to bridge theoretical optimisation strategies with practical game generation applications, the interface is also accessible to both researchers and beginners to multi-objective evolutionary algorithms or procedural content generation on a website. Through dynamic visualisations and interactive gameplay demonstrations, this web-based platform also has potential as an educational tool.
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.
Planning at execution time has been shown to dramatically improve performance for agents in both single-agent and multi-agent settings. A well-known family of approaches to planning at execution time are AlphaZero and its variants, which use Monte Carlo Tree Search together with a neural network that guides the search by predicting state values and action probabilities. AlphaZero trains these networks by minimizing a planning loss that makes the value prediction match the episode return, and the policy prediction at the root of the search tree match the output of the full tree expansion. AlphaZero has been applied to both single-agent environments (such as Sokoban) and multi-agent environments (such as chess and Go) with great success. In this paper, we explore an intriguing question: In single-agent environments, can we outperform AlphaZero by directly maximizing the episode score instead of minimizing this planning loss, while leaving the MCTS algorithm and neural architecture unchanged? To directly maximize the episode score, we use evolution strategies, a family of algorithms for zeroth-order blackbox optimization. Our experiments indicate that, across multiple environments, directly maximizing the episode score outperforms minimizing the planning loss.
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.
Goal recognition is a fundamental cognitive process that enables individuals to infer intentions based on available cues. Current goal recognition algorithms often take only observed actions as input, but here we use a Bayesian framework to explore the role of actions, timing, and goal solvability in goal recognition. We analyze human responses to goal-recognition problems in the Sokoban domain, and find that actions are assigned most importance, but that timing and solvability also influence goal recognition in some cases, especially when actions are uninformative. We leverage these findings to develop a goal recognition model that matches human inferences more closely than do existing algorithms. Our work provides new insight into human goal recognition and takes a step towards more human-like AI models.
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.
The paper presents the PCGPT framework, an innovative approach to procedural content generation (PCG) using offline reinforcement learning and transformer networks. PCGPT utilizes an autoregressive model based on transformers to generate game levels iteratively, addressing the challenges of traditional PCG methods such as repetitive, predictable, or inconsistent content. The framework models trajectories of actions, states, and rewards, leveraging the transformer's self-attention mechanism to capture temporal dependencies and causal relationships. The approach is evaluated in the Sokoban puzzle game, where the model predicts items that are needed with their corresponding locations. Experimental results on the game Sokoban demonstrate that PCGPT generates more complex and diverse game content. Interestingly, it achieves these results in significantly fewer steps compared to existing methods, showcasing its potential for enhancing game design and online content generation. Our model represents a new PCG paradigm which outperforms previous methods.
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.
Search and planning algorithms have been a cornerstone of artificial intelligence since the field's inception. Giving reinforcement learning agents the ability to plan during execution time has resulted in significant performance improvements in various domains. However, in real-world environments, the model with respect to which the agent plans has been constrained to be grounded in the real environment itself, as opposed to a more abstract model which allows for planning over compound actions and behaviors. We propose a new method, called PiZero, that gives an agent the ability to plan in an abstract search space that the agent learns during training, which is completely decoupled from the real environment. Unlike prior approaches, this enables the agent to perform high-level planning at arbitrary timescales and reason in terms of compound or temporally-extended actions, which can be useful in environments where large numbers of base-level micro-actions are needed to perform relevant macro-actions. In addition, our method is more general than comparable prior methods because it seamlessly handles settings with continuous action spaces, combinatorial action spaces, and partial observability. We evaluate our method on multiple domains, including the traveling salesman problem, Sokoban, 2048, the facility location problem, and Pacman. Experimentally, it outperforms comparable prior methods without assuming access to an environment simulator at execution time.
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.
We introduce and evaluate an eXplainable Goal Recognition (XGR) model that uses the Weight of Evidence (WoE) framework to explain goal recognition problems. Our model provides human-centered explanations that answer why? and why not? questions. We computationally evaluate the performance of our system over eight different domains. Using a human behavioral study to obtain the ground truth from human annotators, we further show that the XGR model can successfully generate human-like explanations. We then report on a study with 60 participants who observe agents playing Sokoban game and then receive explanations of the goal recognition output. We investigate participants' understanding obtained by explanations through task prediction, explanation satisfaction, and trust.
Large Language Models (LLMs) are powerful tools, capable of leveraging their training on natural language to write stories, generate code, and answer questions. But can they generate functional video game levels? Game levels, with their complex functional constraints and spatial relationships in more than one dimension, are very different from the kinds of data an LLM typically sees during training. Datasets of game levels are also hard to come by, potentially taxing the abilities of these data-hungry models. We investigate the use of LLMs to generate levels for the game Sokoban, finding that LLMs are indeed capable of doing so, and that their performance scales dramatically with dataset size. We also perform preliminary experiments on controlling LLM level generators and discuss promising areas for future work.