Bayesian nonparametric reward learning from demonstration

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 123-132).Learning from demonstration provides an attractive solution to the problem of teaching autonomous systems how to perform complex tasks. Demonstration opens autonomy development to non-experts and is an intuitive means of communication for humans, who naturally use demonstration to teach others. This thesis focuses on a specific form of learning from demonstration, namely inverse reinforcement learning, whereby the reward of the demonstrator is inferred. Formally, inverse reinforcement learning (IRL) is the task of learning the reward function of a Markov Decision Process (MDP) given knowledge of the transition function and a set of observed demonstrations. While reward learning is a promising method of inferring a rich and transferable representation of the demonstrator's intents, current algorithms suffer from intractability and inefficiency in large, real-world domains. This thesis presents a reward learning framework that infers multiple reward functions from a single, unsegmented demonstration, provides several key approximations which enable scalability to large real-world domains, and generalizes to fully continuous demonstration domains without the need for discretization of the state space, all of which are not handled by previous methods. In the thesis, modifications are proposed to an existing Bayesian IRL algorithm to improve its efficiency and tractability in situations where the state space is large and the demonstrations span only a small portion of it. A modified algorithm is presented and simulation results show substantially faster convergence while maintaining the solution quality of the original method. Even with the proposed efficiency improvements, a key limitation of Bayesian IRL (and most current IRL methods) is the assumption that the demonstrator is maximizing a single reward function. This presents problems when dealing with unsegmented demonstrations containing multiple distinct tasks, common in robot learning from demonstration (e.g. in large tasks that may require multiple subtasks to complete). A key contribution of this thesis is the development of a method that learns multiple reward functions from a single demonstration. The proposed method, termed Bayesian nonparametric inverse reinforcement learning (BNIRL), uses a Bayesian nonparametric mixture model to automatically partition the data and find a set of simple reward functions corresponding to each partition. The simple rewards are interpreted intuitively as subgoals, which can be used to predict actions or analyze which states are important to the demonstrator. Simulation results demonstrate the ability of BNIRL to handle cyclic tasks that break existing algorithms due to the existence of multiple subgoal rewards in the demonstration. The BNIRL algorithm is easily parallelized, and several approximations to the demonstrator likelihood function are offered to further improve computational tractability in large domains. Since BNIRL is only applicable to discrete domains, the Bayesian nonparametric reward learning framework is extended to general continuous demonstration domains using Gaussian process reward representations. The resulting algorithm, termed Gaussian process subgoal reward learning (GPSRL), is the only learning from demonstration method that is able to learn multiple reward functions from unsegmented demonstration in general continuous domains. GPSRL does not require discretization of the continuous state space and focuses computation efficiently around the demonstration itself. Learned subgoal rewards are cast as Markov decision process options to enable execution of the learned behaviors by the robotic system and provide a principled basis for future learning and skill refinement. Experiments conducted in the MIT RAVEN indoor test facility demonstrate the ability of both BNIRL and GPSRL to learn challenging maneuvers from demonstration on a quadrotor helicopter and a remote-controlled car.by Bernard J. Michini.Ph. D

Stick-Breaking Policy Learning in Dec-POMDPs

Expectation maximization (EM) has recently been shown to be an efficient algorithm for learning finite-state controllers (FSCs) in large decentralized POMDPs (Dec-POMDPs). However, current methods use fixed-size FSCs and often converge to maxima that are far from optimal. This paper considers a variable-size FSC to represent the local policy of each agent. These variable-size FSCs are constructed using a stick-breaking prior, leading to a new framework called \emph{decentralized stick-breaking policy representation} (Dec-SBPR). This approach learns the controller parameters with a variational Bayesian algorithm without having to assume that the Dec-POMDP model is available. The performance of Dec-SBPR is demonstrated on several benchmark problems, showing that the algorithm scales to large problems while outperforming other state-of-the-art methods

Bayesian Nonparametric Feature and Policy Learning for Decision-Making

Learning from demonstrations has gained increasing interest in the recent past, enabling an agent to learn how to make decisions by observing an experienced teacher. While many approaches have been proposed to solve this problem, there is only little work that focuses on reasoning about the observed behavior. We assume that, in many practical problems, an agent makes its decision based on latent features, indicating a certain action. Therefore, we propose a generative model for the states and actions. Inference reveals the number of features, the features, and the policies, allowing us to learn and to analyze the underlying structure of the observed behavior. Further, our approach enables prediction of actions for new states. Simulations are used to assess the performance of the algorithm based upon this model. Moreover, the problem of learning a driver's behavior is investigated, demonstrating the performance of the proposed model in a real-world scenario

Efficient Probabilistic Performance Bounds for Inverse Reinforcement Learning

In the field of reinforcement learning there has been recent progress towards safety and high-confidence bounds on policy performance. However, to our knowledge, no practical methods exist for determining high-confidence policy performance bounds in the inverse reinforcement learning setting---where the true reward function is unknown and only samples of expert behavior are given. We propose a sampling method based on Bayesian inverse reinforcement learning that uses demonstrations to determine practical high-confidence upper bounds on the $\alpha$-worst-case difference in expected return between any evaluation policy and the optimal policy under the expert's unknown reward function. We evaluate our proposed bound on both a standard grid navigation task and a simulated driving task and achieve tighter and more accurate bounds than a feature count-based baseline. We also give examples of how our proposed bound can be utilized to perform risk-aware policy selection and risk-aware policy improvement. Because our proposed bound requires several orders of magnitude fewer demonstrations than existing high-confidence bounds, it is the first practical method that allows agents that learn from demonstration to express confidence in the quality of their learned policy.Comment: In proceedings AAAI-1

Modeling Human Understanding of Complex Intentional Action with a Bayesian Nonparametric Subgoal Model

Most human behaviors consist of multiple parts, steps, or subtasks. These structures guide our action planning and execution, but when we observe others, the latent structure of their actions is typically unobservable, and must be inferred in order to learn new skills by demonstration, or to assist others in completing their tasks. For example, an assistant who has learned the subgoal structure of a colleague's task can more rapidly recognize and support their actions as they unfold. Here we model how humans infer subgoals from observations of complex action sequences using a nonparametric Bayesian model, which assumes that observed actions are generated by approximately rational planning over unknown subgoal sequences. We test this model with a behavioral experiment in which humans observed different series of goal-directed actions, and inferred both the number and composition of the subgoal sequences associated with each goal. The Bayesian model predicts human subgoal inferences with high accuracy, and significantly better than several alternative models and straightforward heuristics. Motivated by this result, we simulate how learning and inference of subgoals can improve performance in an artificial user assistance task. The Bayesian model learns the correct subgoals from fewer observations, and better assists users by more rapidly and accurately inferring the goal of their actions than alternative approaches.Comment: Accepted at AAAI 1

Bayesian Nonparametric Inverse Reinforcement Learning

Inverse reinforcement learning (IRL) is the task of learning the reward function of a Markov Decision Process (MDP) given the transition function and a set of observed demonstrations in the form of state-action pairs. Current IRL algorithms attempt to find a single reward function which explains the entire observation set. In practice, this leads to a computationally-costly search over a large (typically infinite) space of complex reward functions. This paper proposes the notion that if the observations can be partitioned into smaller groups, a class of much simpler reward functions can be used to explain each group. The proposed method uses a Bayesian nonparametric mixture model to automatically partition the data and find a set of simple reward functions corresponding to each partition. The simple rewards are interpreted intuitively as subgoals, which can be used to predict actions or analyze which states are important to the demonstrator. Experimental results are given for simple examples showing comparable performance to other IRL algorithms in nominal situations. Moreover, the proposed method handles cyclic tasks (where the agent begins and ends in the same state) that would break existing algorithms without modification. Finally, the new algorithm has a fundamentally different structure than previous methods, making it more computationally efficient in a real-world learning scenario where the state space is large but the demonstration set is small

Probabilistic inverse reinforcement learning in unknown environments

We consider the problem of learning by demonstration from agents acting in unknown stochastic Markov environments or games. Our aim is to estimate agent preferences in order to construct improved policies for the same task that the agents are trying to solve. To do so, we extend previous probabilistic approaches for inverse reinforcement learning in known MDPs to the case of unknown dynamics or opponents. We do this by deriving two simplified probabilistic models of the demonstrator's policy and utility. For tractability, we use maximum a posteriori estimation rather than full Bayesian inference. Under a flat prior, this results in a convex optimisation problem. We find that the resulting algorithms are highly competitive against a variety of other methods for inverse reinforcement learning that do have knowledge of the dynamics.Comment: Appears in Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence (UAI2013