There has been growing progress on theoretical analyses for provably efficient learning in MDPs with linear function approximation, but much of the existing work has made strong assumptions to enable exploration by conventional exploration frameworks. Typically these assumptions are stronger than what is needed to find good solutions in the batch setting. In this work, we show how under a more standard notion of low inherent Bellman error, typically employed in least-square value iteration-style algorithms, we can provide strong PAC guarantees on learning a near optimal value function provided that the linear space is sufficiently ``explorable''. We present a computationally tractable algorithm for the reward-free setting and show how it can be used to learn a near optimal policy for any (linear) reward function, which is revealed only once learning has completed. If this reward function is also estimated from the samples gathered during pure exploration, our results also provide same-order PAC guarantees on the performance of the resulting policy for this setting.
Operating Earth observing satellites requires efficient planning methods that coordinate activities of multiple spacecraft. The satellite task planning problem entails selecting actions that best satisfy mission objectives for autonomous execution. Task scheduling is often performed by human operators assisted by heuristic or rule-based planning tools. This approach does not efficiently scale to multiple assets as heuristics frequently fail to properly coordinate actions of multiple vehicles over long horizons. Additionally, the problem becomes more difficult to solve for large constellations as the complexity of the problem scales exponentially in the number of requested observations and linearly in the number of spacecraft. It is expected that new commercial optical and radar imaging constellations will require automated planning methods to meet stated responsiveness and throughput objectives. This paper introduces a new approach for solving the satellite scheduling problem by generating an infeasibility-based graph representation of the problem and finding a maximal independent set of vertices for the graph. The approach is tested on a scenarios of up to 10,000 requested imaging locations for the Skysat constellation of optical satellites as well as simulated constellations of up to 24 satellites. Performance is compared with contemporary graph-traversal and mixed-integer linear programming approaches. Empirical results demonstrate improvements in both the solution time along with the number of scheduled collections beyond baseline methods. For large problems, the maximum independent set approach is able find a feasible schedule with 8% more collections in 75% less time.
We can use driving data collected over a long period of time to extract rich information about how vehicles behave in different areas of the roads. In this paper, we introduce the concept of directional primitives, which is a representation of prior information of road networks. Specifically, we represent the uncertainty of directions using a mixture of von Mises distributions and associated speeds using gamma distributions. These location-dependent primitives can be combined with motion information of surrounding vehicles to predict their future behavior in the form of probability distributions. Experiments conducted on highways, intersections, and roundabouts in the Carla simulator, as well as real-world urban driving datasets, indicate that primitives lead to better uncertainty-aware motion estimation.
System identification is a key step for model-based control, estimator design, and output prediction. This work considers the offline identification of partially observed nonlinear systems. We empirically show that the certainty-equivalent approximation to expectation-maximization can be a reliable and scalable approach for high-dimensional deterministic systems, which are common in robotics. We formulate certainty-equivalent expectation-maximization as block coordinate-ascent, and provide an efficient implementation. The algorithm is tested on a simulated system of coupled Lorenz attractors, demonstrating its ability to identify high-dimensional systems that can be intractable for particle-based approaches. Our approach is also used to identify the dynamics of an aerobatic helicopter. By augmenting the state with unobserved fluid states, a model is learned that predicts the acceleration of the helicopter better than state-of-the-art approaches. The codebase for this work is available at https://github.com/sisl/CEEM.
Multi-agent reinforcement learning (MARL) requires coordination to efficiently solve certain tasks. Fully centralized control is often infeasible in such domains due to the size of joint action spaces. Coordination graph based formalization allows reasoning about the joint action based on the structure of interactions. However, they often require domain expertise in their design. This paper introduces the deep implicit coordination graph (DICG) architecture for such scenarios. DICG consists of a module for inferring the dynamic coordination graph structure which is then used by a graph neural network based module to learn to implicitly reason about the joint actions or values. DICG allows learning the tradeoff between full centralization and decentralization via standard actor-critic methods to significantly improve coordination for domains with large number of agents. We apply DICG to both centralized-training-centralized-execution and centralized-training-decentralized-execution regimes. We demonstrate that DICG solves the relative overgeneralization pathology in predatory-prey tasks as well as outperforms various MARL baselines on the challenging StarCraft II Multi-agent Challenge (SMAC) and traffic junction environments.
Stochastic processes generated by non-stationary distributions are difficult to represent with conventional models such as Gaussian processes. This work presents Recurrent Autoregressive Flows as a method toward general stochastic process modeling with normalizing flows. The proposed method defines a conditional distribution for each variable in a sequential process by conditioning the parameters of a normalizing flow with recurrent neural connections. Complex conditional relationships are learned through the recurrent network parameters. In this work, we present an initial design for a recurrent flow cell and a method to train the model to match observed empirical distributions. We demonstrate the effectiveness of this class of models through a series of experiments in which models are trained on three complex stochastic processes. We highlight the shortcomings of our current formulation and suggest some potential solutions.
We study the problem of sequential task assignment and collision-free routing for large teams of robots in applications with inter-task precedence constraints (e.g., task $A$ and task $B$ must both be completed before task $C$ may begin). Such problems commonly occur in assembly planning for robotic manufacturing applications, in which sub-assemblies must be completed before they can be combined to form the final product. We propose a hierarchical algorithm for computing makespan-optimal solutions to the problem. The algorithm is evaluated on a set of randomly generated problem instances where robots must transport objects between stations in a "factory "grid world environment. In addition, we demonstrate in high-fidelity simulation that the output of our algorithm can be used to generate collision-free trajectories for non-holonomic differential-drive robots.
We present a review and taxonomy of 200 models from the literature on driver behavior modeling. We begin by introducing a mathematical formulation based on the partially observable stochastic game, which serves as a common framework for comparing and contrasting different driver models. Our taxonomy is constructed around the core modeling tasks of state estimation, intention estimation, trait estimation, and motion prediction, and also discusses the auxiliary tasks of risk estimation, anomaly detection, behavior imitation and microscopic traffic simulation. Existing driver models are categorized based on the specific tasks they address and key attributes of their approach.
Designing reward functions is a challenging problem in AI and robotics. Humans usually have a difficult time directly specifying all the desirable behaviors that a robot needs to optimize. One common approach is to learn reward functions from collected expert demonstrations. However, learning reward functions from demonstrations introduces many challenges: some methods require highly structured models, e.g. reward functions that are linear in some predefined set of features, while others adopt less structured reward functions that on the other hand require tremendous amount of data. In addition, humans tend to have a difficult time providing demonstrations on robots with high degrees of freedom, or even quantifying reward values for given demonstrations. To address these challenges, we present a preference-based learning approach, where as an alternative, the human feedback is only in the form of comparisons between trajectories. Furthermore, we do not assume highly constrained structures on the reward function. Instead, we model the reward function using a Gaussian Process (GP) and propose a mathematical formulation to actively find a GP using only human preferences. Our approach enables us to tackle both inflexibility and data-inefficiency problems within a preference-based learning framework. Our results in simulations and a user study suggest that our approach can efficiently learn expressive reward functions for robotics tasks.
We consider the problem of dynamically allocating tasks to multiple agents under time window constraints and task completion uncertainty. Our objective is to minimize the number of unsuccessful tasks at the end of the operation horizon. We present a multi-robot allocation algorithm that decouples the key computational challenges of sequential decision-making under uncertainty and multi-agent coordination and addresses them in a hierarchical manner. The lower layer computes policies for individual agents using dynamic programming with tree search, and the upper layer resolves conflicts in individual plans to obtain a valid multi-agent allocation. Our algorithm, Stochastic Conflict-Based Allocation (SCoBA), is optimal in expectation and complete under some reasonable assumptions. In practice, SCoBA is computationally efficient enough to interleave planning and execution online. On the metric of successful task completion, SCoBA consistently outperforms a number of baseline methods and shows strong competitive performance against an oracle with complete lookahead. It also scales well with the number of tasks and agents. We validate our results over a wide range of simulations on two distinct domains: multi-arm conveyor belt pick-and-place and multi-drone delivery dispatch in a city.