AIApr 21, 2022Code
PG3: Policy-Guided Planning for Generalized Policy GenerationRyan Yang, Tom Silver, Aidan Curtis et al. · mit
A longstanding objective in classical planning is to synthesize policies that generalize across multiple problems from the same domain. In this work, we study generalized policy search-based methods with a focus on the score function used to guide the search over policies. We demonstrate limitations of two score functions and propose a new approach that overcomes these limitations. The main idea behind our approach, Policy-Guided Planning for Generalized Policy Generation (PG3), is that a candidate policy should be used to guide planning on training problems as a mechanism for evaluating that candidate. Theoretical results in a simplified setting give conditions under which PG3 is optimal or admissible. We then study a specific instantiation of policy search where planning problems are PDDL-based and policies are lifted decision lists. Empirical results in six domains confirm that PG3 learns generalized policies more efficiently and effectively than several baselines. Code: https://github.com/ryangpeixu/pg3
ROJun 21, 2022
Learning Neuro-Symbolic Skills for Bilevel PlanningTom Silver, Ashay Athalye, Joshua B. Tenenbaum et al. · mit
Decision-making is challenging in robotics environments with continuous object-centric states, continuous actions, long horizons, and sparse feedback. Hierarchical approaches, such as task and motion planning (TAMP), address these challenges by decomposing decision-making into two or more levels of abstraction. In a setting where demonstrations and symbolic predicates are given, prior work has shown how to learn symbolic operators and neural samplers for TAMP with manually designed parameterized policies. Our main contribution is a method for learning parameterized polices in combination with operators and samplers. These components are packaged into modular neuro-symbolic skills and sequenced together with search-then-sample TAMP to solve new tasks. In experiments in four robotics domains, we show that our approach -- bilevel planning with neuro-symbolic skills -- can solve a wide range of tasks with varying initial states, goals, and objects, outperforming six baselines and ablations. Video: https://youtu.be/PbFZP8rPuGg Code: https://tinyurl.com/skill-learning
AIMar 17, 2022
Predicate Invention for Bilevel PlanningTom Silver, Rohan Chitnis, Nishanth Kumar et al. · mit
Efficient planning in continuous state and action spaces is fundamentally hard, even when the transition model is deterministic and known. One way to alleviate this challenge is to perform bilevel planning with abstractions, where a high-level search for abstract plans is used to guide planning in the original transition space. Previous work has shown that when state abstractions in the form of symbolic predicates are hand-designed, operators and samplers for bilevel planning can be learned from demonstrations. In this work, we propose an algorithm for learning predicates from demonstrations, eliminating the need for manually specified state abstractions. Our key idea is to learn predicates by optimizing a surrogate objective that is tractable but faithful to our real efficient-planning objective. We use this surrogate objective in a hill-climbing search over predicate sets drawn from a grammar. Experimentally, we show across four robotic planning environments that our learned abstractions are able to quickly solve held-out tasks, outperforming six baselines. Code: https://tinyurl.com/predicators-release
RONov 17, 2022
SE(3)-Equivariant Relational Rearrangement with Neural Descriptor FieldsAnthony Simeonov, Yilun Du, Lin Yen-Chen et al. · mit
We present a method for performing tasks involving spatial relations between novel object instances initialized in arbitrary poses directly from point cloud observations. Our framework provides a scalable way for specifying new tasks using only 5-10 demonstrations. Object rearrangement is formalized as the question of finding actions that configure task-relevant parts of the object in a desired alignment. This formalism is implemented in three steps: assigning a consistent local coordinate frame to the task-relevant object parts, determining the location and orientation of this coordinate frame on unseen object instances, and executing an action that brings these frames into the desired alignment. We overcome the key technical challenge of determining task-relevant local coordinate frames from a few demonstrations by developing an optimization method based on Neural Descriptor Fields (NDFs) and a single annotated 3D keypoint. An energy-based learning scheme to model the joint configuration of the objects that satisfies a desired relational task further improves performance. The method is tested on three multi-object rearrangement tasks in simulation and on a real robot. Project website, videos, and code: https://anthonysimeonov.github.io/r-ndf/
ROFeb 7, 2023
Local Neural Descriptor Fields: Locally Conditioned Object Representations for ManipulationEthan Chun, Yilun Du, Anthony Simeonov et al. · mit
A robot operating in a household environment will see a wide range of unique and unfamiliar objects. While a system could train on many of these, it is infeasible to predict all the objects a robot will see. In this paper, we present a method to generalize object manipulation skills acquired from a limited number of demonstrations, to novel objects from unseen shape categories. Our approach, Local Neural Descriptor Fields (L-NDF), utilizes neural descriptors defined on the local geometry of the object to effectively transfer manipulation demonstrations to novel objects at test time. In doing so, we leverage the local geometry shared between objects to produce a more general manipulation framework. We illustrate the efficacy of our approach in manipulating novel objects in novel poses -- both in simulation and in the real world.
LGFeb 10, 2025
Guided Exploration for Efficient Relational Model LearningAnnie Feng, Nishanth Kumar, Tomas Lozano-Perez et al.
Efficient exploration is critical for learning relational models in large-scale environments with complex, long-horizon tasks. Random exploration methods often collect redundant or irrelevant data, limiting their ability to learn accurate relational models of the environment. Goal-literal babbling (GLIB) improves upon random exploration by setting and planning to novel goals, but its reliance on random actions and random novel goal selection limits its scalability to larger domains. In this work, we identify the principles underlying efficient exploration in relational domains: (1) operator initialization with demonstrations that cover the distinct lifted effects necessary for planning and (2) refining preconditions to collect maximally informative transitions by selecting informative goal-action pairs and executing plans to them. To demonstrate these principles, we introduce Baking-Large, a challenging domain with extensive state-action spaces and long-horizon tasks. We evaluate methods using oracle-driven demonstrations for operator initialization and precondition-targeting guidance to efficiently gather critical transitions. Experiments show that both the oracle demonstrations and precondition-targeting oracle guidance significantly improve sample efficiency and generalization, paving the way for future methods to use these principles to efficiently learn accurate relational models in complex domains.
ROOct 28, 2021
From Machine Learning to Robotics: Challenges and Opportunities for Embodied IntelligenceNicholas Roy, Ingmar Posner, Tim Barfoot et al.
Machine learning has long since become a keystone technology, accelerating science and applications in a broad range of domains. Consequently, the notion of applying learning methods to a particular problem set has become an established and valuable modus operandi to advance a particular field. In this article we argue that such an approach does not straightforwardly extended to robotics -- or to embodied intelligence more generally: systems which engage in a purposeful exchange of energy and information with a physical environment. In particular, the purview of embodied intelligent agents extends significantly beyond the typical considerations of main-stream machine learning approaches, which typically (i) do not consider operation under conditions significantly different from those encountered during training; (ii) do not consider the often substantial, long-lasting and potentially safety-critical nature of interactions during learning and deployment; (iii) do not require ready adaptation to novel tasks while at the same time (iv) effectively and efficiently curating and extending their models of the world through targeted and deliberate actions. In reality, therefore, these limitations result in learning-based systems which suffer from many of the same operational shortcomings as more traditional, engineering-based approaches when deployed on a robot outside a well defined, and often narrow operating envelope. Contrary to viewing embodied intelligence as another application domain for machine learning, here we argue that it is in fact a key driver for the advancement of machine learning technology. In this article our goal is to highlight challenges and opportunities that are specific to embodied intelligence and to propose research directions which may significantly advance the state-of-the-art in robot learning.
ROSep 23, 2021
Discovering State and Action Abstractions for Generalized Task and Motion PlanningAidan Curtis, Tom Silver, Joshua B. Tenenbaum et al.
Generalized planning accelerates classical planning by finding an algorithm-like policy that solves multiple instances of a task. A generalized plan can be learned from a few training examples and applied to an entire domain of problems. Generalized planning approaches perform well in discrete AI planning problems that involve large numbers of objects and extended action sequences to achieve the goal. In this paper, we propose an algorithm for learning features, abstractions, and generalized plans for continuous robotic task and motion planning (TAMP) and examine the unique difficulties that arise when forced to consider geometric and physical constraints as a part of the generalized plan. Additionally, we show that these simple generalized plans learned from only a handful of examples can be used to improve the search efficiency of TAMP solvers.
AIMay 28, 2021
Learning Neuro-Symbolic Relational Transition Models for Bilevel PlanningRohan Chitnis, Tom Silver, Joshua B. Tenenbaum et al.
In robotic domains, learning and planning are complicated by continuous state spaces, continuous action spaces, and long task horizons. In this work, we address these challenges with Neuro-Symbolic Relational Transition Models (NSRTs), a novel class of models that are data-efficient to learn, compatible with powerful robotic planning methods, and generalizable over objects. NSRTs have both symbolic and neural components, enabling a bilevel planning scheme where symbolic AI planning in an outer loop guides continuous planning with neural models in an inner loop. Experiments in four robotic planning domains show that NSRTs can be learned after only tens or hundreds of training episodes, and then used for fast planning in new tasks that require up to 60 actions and involve many more objects than were seen during training. Video: https://tinyurl.com/chitnis-nsrts
ROFeb 28, 2021
Learning Symbolic Operators for Task and Motion PlanningTom Silver, Rohan Chitnis, Joshua Tenenbaum et al.
Robotic planning problems in hybrid state and action spaces can be solved by integrated task and motion planners (TAMP) that handle the complex interaction between motion-level decisions and task-level plan feasibility. TAMP approaches rely on domain-specific symbolic operators to guide the task-level search, making planning efficient. In this work, we formalize and study the problem of operator learning for TAMP. Central to this study is the view that operators define a lossy abstraction of the transition model of a domain. We then propose a bottom-up relational learning method for operator learning and show how the learned operators can be used for planning in a TAMP system. Experimentally, we provide results in three domains, including long-horizon robotic planning tasks. We find our approach to substantially outperform several baselines, including three graph neural network-based model-free approaches from the recent literature. Video: https://youtu.be/iVfpX9BpBRo Code: https://git.io/JCT0g
LGNov 6, 2020
Learning Object-Based State Estimators for Household RobotsYilun Du, Tomas Lozano-Perez, Leslie Kaelbling
A robot operating in a household makes observations of multiple objects as it moves around over the course of days or weeks. The objects may be moved by inhabitants, but not completely at random. The robot may be called upon later to retrieve objects and will need a long-term object-based memory in order to know how to find them. Existing work in semantic slam does not attempt to capture the dynamics of object movement. In this paper, we combine some aspects of classic techniques for data-association filtering with modern attention-based neural networks to construct object-based memory systems that operate on high-dimensional observations and hypotheses. We perform end-to-end learning on labeled observation trajectories to learn both the transition and observation models. We demonstrate the system's effectiveness in maintaining memory of dynamically changing objects in both simulated environment and real images, and demonstrate improvements over classical structured approaches as well as unstructured neural approaches. Additional information available at project website: https://yilundu.github.io/obm/.
LGSep 22, 2020
Tailoring: encoding inductive biases by optimizing unsupervised objectives at prediction timeFerran Alet, Maria Bauza, Kenji Kawaguchi et al.
From CNNs to attention mechanisms, encoding inductive biases into neural networks has been a fruitful source of improvement in machine learning. Adding auxiliary losses to the main objective function is a general way of encoding biases that can help networks learn better representations. However, since auxiliary losses are minimized only on training data, they suffer from the same generalization gap as regular task losses. Moreover, by adding a term to the loss function, the model optimizes a different objective than the one we care about. In this work we address both problems: first, we take inspiration from \textit{transductive learning} and note that after receiving an input but before making a prediction, we can fine-tune our networks on any unsupervised loss. We call this process {\em tailoring}, because we customize the model to each input to ensure our prediction satisfies the inductive bias. Second, we formulate {\em meta-tailoring}, a nested optimization similar to that in meta-learning, and train our models to perform well on the task objective after adapting them using an unsupervised loss. The advantages of tailoring and meta-tailoring are discussed theoretically and demonstrated empirically on a diverse set of examples.
LGSep 11, 2020
Planning with Learned Object Importance in Large Problem Instances using Graph Neural NetworksTom Silver, Rohan Chitnis, Aidan Curtis et al.
Real-world planning problems often involve hundreds or even thousands of objects, straining the limits of modern planners. In this work, we address this challenge by learning to predict a small set of objects that, taken together, would be sufficient for finding a plan. We propose a graph neural network architecture for predicting object importance in a single inference pass, thus incurring little overhead while greatly reducing the number of objects that must be considered by the planner. Our approach treats the planner and transition model as black boxes, and can be used with any off-the-shelf planner. Empirically, across classical planning, probabilistic planning, and robotic task and motion planning, we find that our method results in planning that is significantly faster than several baselines, including other partial grounding strategies and lifted planners. We conclude that learning to predict a sufficient set of objects for a planning problem is a simple, powerful, and general mechanism for planning in large instances. Video: https://youtu.be/FWsVJc2fvCE Code: https://git.io/JIsqX
LGJul 26, 2020
CAMPs: Learning Context-Specific Abstractions for Efficient Planning in Factored MDPsRohan Chitnis, Tom Silver, Beomjoon Kim et al.
Meta-planning, or learning to guide planning from experience, is a promising approach to improving the computational cost of planning. A general meta-planning strategy is to learn to impose constraints on the states considered and actions taken by the agent. We observe that (1) imposing a constraint can induce context-specific independences that render some aspects of the domain irrelevant, and (2) an agent can take advantage of this fact by imposing constraints on its own behavior. These observations lead us to propose the context-specific abstract Markov decision process (CAMP), an abstraction of a factored MDP that affords efficient planning. We then describe how to learn constraints to impose so the CAMP optimizes a trade-off between rewards and computational cost. Our experiments consider five planners across four domains, including robotic navigation among movable obstacles (NAMO), robotic task and motion planning for sequential manipulation, and classical planning. We find planning with learned CAMPs to consistently outperform baselines, including Stilman's NAMO-specific algorithm. Video: https://youtu.be/wTXt6djcAd4 Code: https://git.io/JTnf6
LGMar 11, 2020
Meta-learning curiosity algorithmsFerran Alet, Martin F. Schneider, Tomas Lozano-Perez et al.
We hypothesize that curiosity is a mechanism found by evolution that encourages meaningful exploration early in an agent's life in order to expose it to experiences that enable it to obtain high rewards over the course of its lifetime. We formulate the problem of generating curious behavior as one of meta-learning: an outer loop will search over a space of curiosity mechanisms that dynamically adapt the agent's reward signal, and an inner loop will perform standard reinforcement learning using the adapted reward signal. However, current meta-RL methods based on transferring neural network weights have only generalized between very similar tasks. To broaden the generalization, we instead propose to meta-learn algorithms: pieces of code similar to those designed by humans in ML papers. Our rich language of programs combines neural networks with other building blocks such as buffers, nearest-neighbor modules and custom loss functions. We demonstrate the effectiveness of the approach empirically, finding two novel curiosity algorithms that perform on par or better than human-designed published curiosity algorithms in domains as disparate as grid navigation with image inputs, acrobot, lunar lander, ant and hopper.
AIJan 22, 2020
GLIB: Efficient Exploration for Relational Model-Based Reinforcement Learning via Goal-Literal BabblingRohan Chitnis, Tom Silver, Joshua Tenenbaum et al.
We address the problem of efficient exploration for transition model learning in the relational model-based reinforcement learning setting without extrinsic goals or rewards. Inspired by human curiosity, we propose goal-literal babbling (GLIB), a simple and general method for exploration in such problems. GLIB samples relational conjunctive goals that can be understood as specific, targeted effects that the agent would like to achieve in the world, and plans to achieve these goals using the transition model being learned. We provide theoretical guarantees showing that exploration with GLIB will converge almost surely to the ground truth model. Experimentally, we find GLIB to strongly outperform existing methods in both prediction and planning on a range of tasks, encompassing standard PDDL and PPDDL planning benchmarks and a robotic manipulation task implemented in the PyBullet physics simulator. Video: https://youtu.be/F6lmrPT6TOY Code: https://git.io/JIsTB
ROOct 1, 2019
Omnipush: accurate, diverse, real-world dataset of pushing dynamics with RGB-D videoMaria Bauza, Ferran Alet, Yen-Chen Lin et al.
Pushing is a fundamental robotic skill. Existing work has shown how to exploit models of pushing to achieve a variety of tasks, including grasping under uncertainty, in-hand manipulation and clearing clutter. Such models, however, are approximate, which limits their applicability. Learning-based methods can reason directly from raw sensory data with accuracy, and have the potential to generalize to a wider diversity of scenarios. However, developing and testing such methods requires rich-enough datasets. In this paper we introduce Omnipush, a dataset with high variety of planar pushing behavior. In particular, we provide 250 pushes for each of 250 objects, all recorded with RGB-D and a high precision tracking system. The objects are constructed so as to systematically explore key factors that affect pushing -- the shape of the object and its mass distribution -- which have not been broadly explored in previous datasets, and allow to study generalization in model learning. Omnipush includes a benchmark for meta-learning dynamic models, which requires algorithms that make good predictions and estimate their own uncertainty. We also provide an RGB video prediction benchmark and propose other relevant tasks that can be suited with this dataset. Data and code are available at \url{https://web.mit.edu/mcube/omnipush-dataset/}.
LGMay 28, 2019
Differentiable Algorithm Networks for Composable Robot LearningPeter Karkus, Xiao Ma, David Hsu et al.
This paper introduces the Differentiable Algorithm Network (DAN), a composable architecture for robot learning systems. A DAN is composed of neural network modules, each encoding a differentiable robot algorithm and an associated model; and it is trained end-to-end from data. DAN combines the strengths of model-driven modular system design and data-driven end-to-end learning. The algorithms and models act as structural assumptions to reduce the data requirements for learning; end-to-end learning allows the modules to adapt to one another and compensate for imperfect models and algorithms, in order to achieve the best overall system performance. We illustrate the DAN methodology through a case study on a simulated robot system, which learns to navigate in complex 3-D environments with only local visual observations and an image of a partially correct 2-D floor map.
LGApr 18, 2019
Graph Element Networks: adaptive, structured computation and memoryFerran Alet, Adarsh K. Jeewajee, Maria Bauza et al.
We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational process defined on the graph to model the relationship between an initial function defined over a space and a resulting function in the same space. We use GNNs as a computational substrate, and show that the locations of the nodes in space as well as their connectivity can be optimized to focus on the most complex parts of the space. Moreover, this representational strategy allows the learned input-output relationship to generalize over the size of the underlying space and run the same model at different levels of precision, trading computation for accuracy. We demonstrate this method on a traditional PDE problem, a physical prediction problem from robotics, and learning to predict scene images from novel viewpoints.
LGDec 19, 2018
Modular meta-learning in abstract graph networks for combinatorial generalizationFerran Alet, Maria Bauza, Alberto Rodriguez et al.
Modular meta-learning is a new framework that generalizes to unseen datasets by combining a small set of neural modules in different ways. In this work we propose abstract graph networks: using graphs as abstractions of a system's subparts without a fixed assignment of nodes to system subparts, for which we would need supervision. We combine this idea with modular meta-learning to get a flexible framework with combinatorial generalization to new tasks built in. We then use it to model the pushing of arbitrarily shaped objects from little or no training data.
ROJul 26, 2018
Learning to guide task and motion planning using score-space representationBeomjoon Kim, Zi Wang, Leslie Pack Kaelbling et al.
In this paper, we propose a learning algorithm that speeds up the search in task and motion planning problems. Our algorithm proposes solutions to three different challenges that arise in learning to improve planning efficiency: what to predict, how to represent a planning problem instance, and how to transfer knowledge from one problem instance to another. We propose a method that predicts constraints on the search space based on a generic representation of a planning problem instance, called score-space, where we represent a problem instance in terms of the performance of a set of solutions attempted so far. Using this representation, we transfer knowledge, in the form of constraints, from previous problems based on the similarity in score space. We design a sequential algorithm that efficiently predicts these constraints, and evaluate it in three different challenging task and motion planning problems. Results indicate that our approach performs orders of magnitudes faster than an unguided planner
AIMay 8, 2018
Finding Frequent Entities in Continuous DataFerran Alet, Rohan Chitnis, Leslie P. Kaelbling et al.
In many applications that involve processing high-dimensional data, it is important to identify a small set of entities that account for a significant fraction of detections. Rather than formalize this as a clustering problem, in which all detections must be grouped into hard or soft categories, we formalize it as an instance of the frequent items or heavy hitters problem, which finds groups of tightly clustered objects that have a high density in the feature space. We show that the heavy hitters formulation generates solutions that are more accurate and effective than the clustering formulation. In addition, we present a novel online algorithm for heavy hitters, called HAC, which addresses problems in continuous space, and demonstrate its effectiveness on real video and household domains.
AINov 4, 2017
Guiding the search in continuous state-action spaces by learning an action sampling distribution from off-target samplesBeomjoon Kim, Leslie Pack Kaelbling, Tomas Lozano-Perez
In robotics, it is essential to be able to plan efficiently in high-dimensional continuous state-action spaces for long horizons. For such complex planning problems, unguided uniform sampling of actions until a path to a goal is found is hopelessly inefficient, and gradient-based approaches often fall short when the optimization manifold of a given problem is not smooth. In this paper we present an approach that guides the search of a state-space planner, such as A*, by learning an action-sampling distribution that can generalize across different instances of a planning problem. The motivation is that, unlike typical learning approaches for planning for continuous action space that estimate a policy, an estimated action sampler is more robust to error since it has a planner to fall back on. We use a Generative Adversarial Network (GAN), and address an important issue: search experience consists of a relatively large number of actions that are not on a solution path and a relatively small number of actions that actually are on a solution path. We introduce a new technique, based on an importance-ratio estimation method, for using samples from a non-target distribution to make GAN learning more data-efficient. We provide theoretical guarantees and empirical evaluation in three challenging continuous robot planning problems to illustrate the effectiveness of our algorithm.
ROAug 3, 2016
FFRob: Leveraging Symbolic Planning for Efficient Task and Motion PlanningCaelan Reed Garrett, Tomas Lozano-Perez, Leslie Pack Kaelbling
Mobile manipulation problems involving many objects are challenging to solve due to the high dimensionality and multi-modality of their hybrid configuration spaces. Planners that perform a purely geometric search are prohibitively slow for solving these problems because they are unable to factor the configuration space. Symbolic task planners can efficiently construct plans involving many variables but cannot represent the geometric and kinematic constraints required in manipulation. We present the FFRob algorithm for solving task and motion planning problems. First, we introduce Extended Action Specification (EAS) as a general purpose planning representation that supports arbitrary predicates as conditions. We adapt existing heuristic search ideas for solving \proc{strips} planning problems, particularly delete-relaxations, to solve EAS problem instances. We then apply the EAS representation and planners to manipulation problems resulting in FFRob. FFRob iteratively discretizes task and motion planning problems using batch sampling of manipulation primitives and a multi-query roadmap structure that can be conditionalized to evaluate reachability under different placements of movable objects. This structure enables the EAS planner to efficiently compute heuristics that incorporate geometric and kinematic planning constraints to give a tight estimate of the distance to the goal. Additionally, we show FFRob is probabilistically complete and has finite expected runtime. Finally, we empirically demonstrate FFRob's effectiveness on complex and diverse task and motion planning tasks including rearrangement planning and navigation among movable objects.
AIAug 3, 2016
Learning to Rank for Synthesizing Planning HeuristicsCaelan Reed Garrett, Leslie Pack Kaelbling, Tomas Lozano-Perez
We investigate learning heuristics for domain-specific planning. Prior work framed learning a heuristic as an ordinary regression problem. However, in a greedy best-first search, the ordering of states induced by a heuristic is more indicative of the resulting planner's performance than mean squared error. Thus, we instead frame learning a heuristic as a learning to rank problem which we solve using a RankSVM formulation. Additionally, we introduce new methods for computing features that capture temporal interactions in an approximate plan. Our experiments on recent International Planning Competition problems show that the RankSVM learned heuristics outperform both the original heuristics and heuristics learned through ordinary regression.
ROApr 12, 2016
Backward-Forward Search for Manipulation PlanningCaelan Reed Garrett, Tomas Lozano-Perez, Leslie Pack Kaelbling
In this paper we address planning problems in high-dimensional hybrid configuration spaces, with a particular focus on manipulation planning problems involving many objects. We present the hybrid backward-forward (HBF) planning algorithm that uses a backward identification of constraints to direct the sampling of the infinite action space in a forward search from the initial state towards a goal configuration. The resulting planner is probabilistically complete and can effectively construct long manipulation plans requiring both prehensile and nonprehensile actions in cluttered environments.
AIJun 26, 2012
CAPIR: Collaborative Action Planning with Intention RecognitionTruong-Huy Dinh Nguyen, David Hsu, Wee-Sun Lee et al.
We apply decision theoretic techniques to construct non-player characters that are able to assist a human player in collaborative games. The method is based on solving Markov decision processes, which can be difficult when the game state is described by many variables. To scale to more complex games, the method allows decomposition of a game task into subtasks, each of which can be modelled by a Markov decision process. Intention recognition is used to infer the subtask that the human is currently performing, allowing the helper to assist the human in performing the correct task. Experiments show that the method can be effective, giving near-human level performance in helping a human in a collaborative game.