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

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

Real-Time Predictive Modeling and Robust Avoidance of Pedestrians with Uncertain, Changing Intentions

To plan safe trajectories in urban environments, autonomous vehicles must be able to quickly assess the future intentions of dynamic agents. Pedestrians are particularly challenging to model, as their motion patterns are often uncertain and/or unknown a priori. This paper presents a novel changepoint detection and clustering algorithm that, when coupled with offline unsupervised learning of a Gaussian process mixture model (DPGP), enables quick detection of changes in intent and online learning of motion patterns not seen in prior training data. The resulting long-term movement predictions demonstrate improved accuracy relative to offline learning alone, in terms of both intent and trajectory prediction. By embedding these predictions within a chance-constrained motion planner, trajectories which are probabilistically safe to pedestrian motions can be identified in real-time. Hardware experiments demonstrate that this approach can accurately predict pedestrian motion patterns from onboard sensor/perception data and facilitate robust navigation within a dynamic environment.Comment: Submitted to 2014 International Workshop on the Algorithmic Foundations of Robotic

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

Inverse Reinforcement Learning in Swarm Systems

Inverse reinforcement learning (IRL) has become a useful tool for learning behavioral models from demonstration data. However, IRL remains mostly unexplored for multi-agent systems. In this paper, we show how the principle of IRL can be extended to homogeneous large-scale problems, inspired by the collective swarming behavior of natural systems. In particular, we make the following contributions to the field: 1) We introduce the swarMDP framework, a sub-class of decentralized partially observable Markov decision processes endowed with a swarm characterization. 2) Exploiting the inherent homogeneity of this framework, we reduce the resulting multi-agent IRL problem to a single-agent one by proving that the agent-specific value functions in this model coincide. 3) To solve the corresponding control problem, we propose a novel heterogeneous learning scheme that is particularly tailored to the swarm setting. Results on two example systems demonstrate that our framework is able to produce meaningful local reward models from which we can replicate the observed global system dynamics.Comment: 9 pages, 8 figures; ### Version 2 ### version accepted at AAMAS 201

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

Learning Models of Sequential Decision-Making without Complete State Specification using Bayesian Nonparametric Inference and Active Querying

Learning models of decision-making behavior during sequential tasks is useful across a variety of applications, including human-machine interaction. In this paper, we present an approach to learning such models within Markovian domains based on observing and querying a decision-making agent. In contrast to classical approaches to behavior learning, we do not assume complete knowledge of the state features that impact an agent's decisions. Using tools from Bayesian nonparametric inference and time series of agents decisions, we first provide an inference algorithm to identify the presence of any unmodeled state features that impact decision making, as well as likely candidate models. In order to identify the best model among these candidates, we next provide an active querying approach that resolves model ambiguity by querying the decision maker. Results from our evaluations demonstrate that, using the proposed algorithms, an observer can identify the presence of latent state features, recover their dynamics, and estimate their impact on decisions during sequential tasks

Imitation Learning with Sinkhorn Distances

Imitation learning algorithms have been interpreted as variants of divergence minimization problems. The ability to compare occupancy measures between experts and learners is crucial in their effectiveness in learning from demonstrations. In this paper, we present tractable solutions by formulating imitation learning as minimization of the Sinkhorn distance between occupancy measures. The formulation combines the valuable properties of optimal transport metrics in comparing non-overlapping distributions with a cosine distance cost defined in an adversarially learned feature space. This leads to a highly discriminative critic network and optimal transport plan that subsequently guide imitation learning. We evaluate the proposed approach using both the reward metric and the Sinkhorn distance metric on a number of MuJoCo experiments