A framework capable of computing optimal control policies for a continuous system in the presence of both action and environment uncertainty is presented in this work. The framework decomposes the planning problem into two stages: an offline phase that reasons only over action uncertainty and an online phase that quickly reacts to the uncertain environment. Offline, a bounded-parameter Markov decision process (BMDP) is employed to model the evolution of the stochastic system over a discretization of the environment. Online, an optimal control policy over the BMDP is computed. Upon the discovery of an unknown environment feature during policy execution, the BMDP is updated and the optimal control policy is efficiently recomputed. Depending on the desired quality of the control policy, a suite of methods is presented to incorporate new information into the BMDP with varying degrees of detail online. Experiments confirm that the framework recomputes high-quality policies in seconds and is orders of magnitude faster than existing methods.

In multi-robot task allocation problems with in-schedule dependencies, tasks with high costs have a large influence on the total time required for a team of robots to complete all tasks. We reduce this influence by calculating a novel task cost dispersion value that measures robots' collective preference for each task. By modifying the winner determination phase of sequential single-item auctions, our approach inspects the bids for every task to identify tasks which robots collectively consider to be high cost and ensures these tasks are allocated prior to other tasks.Our empirical results show this method provides a significant reduction in the total time required to complete all tasks.

We present a ping-pong-playing robot that learns to improve its swings with human advice. Our method learns a reward function over the joint space of task and policy parameters T×P, so the robot can explore policy space more intelligently in a way that trades off exploration vs. exploitation to maximize the total cumulative reward over time. Multimodal stochastic polices can also easily be learned with this approach when the reward function is multimodal in the policy parameters. We extend the recently-developed Gaussian Process Bandit Optimization framework to include exploration-bias advice from human domain experts, using a novel algorithm called Exploration Bias with Directional Advice (EBDA).

In heterogeneous multi-robot teams, robustness and flexibility are increased by the diversity of the robots, each contributing different capabilities. Yet platform-independence is desirable when planning actions for the various robots. We propose a platform-independent model of robot capabilities which we use as a planning domain. We extend existing planning techniques to support two requirements: generating new objects during planning; and, required concurrency of actions due to data flow which can be cyclic. The first requires online action instantiation, the second a small extension of the Planning Domain Definition Language (PDDL): allowing predicates in continuous effects. We evaluate the planner on benchmark domains and present results on an example object transportation task in simulation.

Manipulating natural objects of irregular shapes, such as rocks, is an essential capability of robots operating in outdoor environments. Physics-based simulators are commonly used to plan stable grasps for man-made objects. However, planning is an expensive process that is based on simulating hand and object trajectories in different configurations, and evaluating the outcome of each trajectory. This problem is particularly concerning when the objects are irregular or cluttered, because the space of feasible grasps is significantly smaller, and more configurations need to be evaluated before finding a good one. In this paper, we first present a learning technique for fast detection of an initial set of potentially stable grasps in a cluttered scene. The best detected grasps are further optimized by fine-tuning the configuration of the hand in simulation. To reduce the computational burden of this last operation, we model the outcomes of the grasps as a Gaussian Process, and use an entropy-search method in order to focus the optimization on regions where the best grasp is most likely to be. This approach is tested on the task of clearing piles of real, unknown, rock debris with an autonomous robot. Empirical results show a clear advantage of the proposed approach when the time window for decision is short.

Partially observable Markov decision processes (POMDPs) provide a principled mathematical framework for modeling autonomous decision-making problems. A POMDP solution is often represented by a value function comprised of a set of vectors. In the case of factored models, the size of these vectors grows exponentially with the number of state factors, leading to scalability issues. We consider an approximate value function representation based on a linear combination of basis functions. In particular, we present a backup operator that can be used in any point-based POMDP solver. Furthermore, we show how under certain conditions independence between observation factors can be exploited for large computational gains. We experimentally verify our contributions and show that they have the potential to improve point-based methods in policy quality and solution size.

In this paper, we solve cooperative decentralized stochastic planning problems, where the interactions between agents (specified using transition and reward functions) are dependent on the number of agents (and not on the identity of the individual agents) involved in the interaction. A collision of robots in a narrow corridor, defender teams coordinating patrol activities to secure a target, etc. are examples of such anonymous interactions. Formally, we consider problems that are a subset of the well known Decentralized MDP (DEC-MDP) model, where the anonymity in interactions is specified within the joint reward and transition functions. In this paper, not only do we introduce a general model model called D-SPAIT to capture anonymity in interactions, but also provide optimization based optimal and local-optimal solutions for generalizable sub-categories of D-SPAIT.

Probabilistic inference can be realized using weighted model counting. Despite a lot of progress, computing weighted model counts exactly is still infeasible for many problems of interest, and one typically has to resort to approximation methods. We contribute a new bounded approximation method for weighted model counting based on probabilistic logic programming principles. Our bounded approximation algorithm is an anytime algorithm that provides lower and upper bounds on the weighted model count. An empirical evaluation on probabilistic logic programs shows that our approach is effective in many cases that are currently beyond the reach of exact methods.

Recently, there has been a growing interest in modeling planning with information constraints. Accordingly, an agent maximizes a regularized expected utility known as the free energy, where the regularizer is given by the information divergence from a prior to a posterior policy. While this approach can be justified in various ways, including from statistical mechanics and information theory, it is still unclear how it relates to decision-making against adversarial environments. This connection has previously been suggested in work relating the free energy to risk-sensitive control and to extensive form games. Here, we show that a single-agent free energy optimization is equivalent to a game between the agent and an imaginary adversary. The adversary can, by paying an exponential penalty, generate costs that diminish the decision maker's payoffs. It turns out that the optimal strategy of the adversary consists in choosing costs so as to render the decision maker indifferent among its choices, which is a definining property of a Nash equilibrium, thus tightening the connection between free energy optimization and game theory.

We present a new Markov Chain Monte Carlo (MCMC) sampling algorithm for probabilistic programs. Our approach and tool, called R2, has the unique feature of employing program analysis in order to improve the efficiencyof MCMC sampling. Given an input program P, R2 propagates observations in P backwards to obtaina semantically equivalent program P' in which every probabilistic assignment is immediately followed by an observe statement. Inference is performed by a suitably modified version of the Metropolis-Hastings algorithm that exploits the structure of the program P'. This has the overall effect of preventing rejections due to program executions that fail to satisfy observations in P. We formalize the semantics of probabilistic programs and rigorously prove the correctness of R2. We also empirically demonstrate the effectiveness of R2—in particular, we show that R2 is able to produce results of similar quality as the CHURCH and STAN probabilistic programming tools with much shorter execution time.