Approximate Decentralized Bayesian Inference

This paper presents an approximate method for performing Bayesian inference in models with conditional independence over a decentralized network of learning agents. The method first employs variational inference on each individual learning agent to generate a local approximate posterior, the agents transmit their local posteriors to other agents in the network, and finally each agent combines its set of received local posteriors. The key insight in this work is that, for many Bayesian models, approximate inference schemes destroy symmetry and dependencies in the model that are crucial to the correct application of Bayes' rule when combining the local posteriors. The proposed method addresses this issue by including an additional optimization step in the combination procedure that accounts for these broken dependencies. Experiments on synthetic and real data demonstrate that the decentralized method provides advantages in computational performance and predictive test likelihood over previous batch and distributed methods.Comment: This paper was presented at UAI 2014. Please use the following BibTeX citation: @inproceedings{Campbell14_UAI, Author = {Trevor Campbell and Jonathan P. How}, Title = {Approximate Decentralized Bayesian Inference}, Booktitle = {Uncertainty in Artificial Intelligence (UAI)}, Year = {2014}

Active Perception in Adversarial Scenarios using Maximum Entropy Deep Reinforcement Learning

We pose an active perception problem where an autonomous agent actively interacts with a second agent with potentially adversarial behaviors. Given the uncertainty in the intent of the other agent, the objective is to collect further evidence to help discriminate potential threats. The main technical challenges are the partial observability of the agent intent, the adversary modeling, and the corresponding uncertainty modeling. Note that an adversary agent may act to mislead the autonomous agent by using a deceptive strategy that is learned from past experiences. We propose an approach that combines belief space planning, generative adversary modeling, and maximum entropy reinforcement learning to obtain a stochastic belief space policy. By accounting for various adversarial behaviors in the simulation framework and minimizing the predictability of the autonomous agent's action, the resulting policy is more robust to unmodeled adversarial strategies. This improved robustness is empirically shown against an adversary that adapts to and exploits the autonomous agent's policy when compared with a standard Chance-Constraint Partially Observable Markov Decision Process robust approach

Truncated Random Measures

Completely random measures (CRMs) and their normalizations are a rich source of Bayesian nonparametric priors. Examples include the beta, gamma, and Dirichlet processes. In this paper we detail two major classes of sequential CRM representations---series representations and superposition representations---within which we organize both novel and existing sequential representations that can be used for simulation and posterior inference. These two classes and their constituent representations subsume existing ones that have previously been developed in an ad hoc manner for specific processes. Since a complete infinite-dimensional CRM cannot be used explicitly for computation, sequential representations are often truncated for tractability. We provide truncation error analyses for each type of sequential representation, as well as their normalized versions, thereby generalizing and improving upon existing truncation error bounds in the literature. We analyze the computational complexity of the sequential representations, which in conjunction with our error bounds allows us to directly compare representations and discuss their relative efficiency. We include numerous applications of our theoretical results to commonly-used (normalized) CRMs, demonstrating that our results enable a straightforward representation and analysis of CRMs that has not previously been available in a Bayesian nonparametric context.Comment: To appear in Bernoulli; 58 pages, 3 figure

Transferable Pedestrian Motion Prediction Models at Intersections

One desirable capability of autonomous cars is to accurately predict the pedestrian motion near intersections for safe and efficient trajectory planning. We are interested in developing transfer learning algorithms that can be trained on the pedestrian trajectories collected at one intersection and yet still provide accurate predictions of the trajectories at another, previously unseen intersection. We first discussed the feature selection for transferable pedestrian motion models in general. Following this discussion, we developed one transferable pedestrian motion prediction algorithm based on Inverse Reinforcement Learning (IRL) that infers pedestrian intentions and predicts future trajectories based on observed trajectory. We evaluated our algorithm on a dataset collected at two intersections, trained at one intersection and tested at the other intersection. We used the accuracy of augmented semi-nonnegative sparse coding (ASNSC), trained and tested at the same intersection as a baseline. The result shows that the proposed algorithm improves the baseline accuracy by 40% in the non-transfer task, and 16% in the transfer task

Quantifying Nonlocal Informativeness in High-Dimensional, Loopy Gaussian Graphical Models

We consider the problem of selecting informative observations in Gaussian graphical models containing both cycles and nuisances. More specifically, we consider the subproblem of quantifying conditional mutual information measures that are nonlocal on such graphs. The ability to efficiently quantify the information content of observations is crucial for resource-constrained data acquisition (adaptive sampling) and data processing (active learning) systems. While closed-form expressions for Gaussian mutual information exist, standard linear algebraic techniques, with complexity cubic in the network size, are intractable for high-dimensional distributions. We investigate the use of embedded trees for computing nonlocal pairwise mutual information and demonstrate through numerical simulations that the presented approach achieves a significant reduction in computational cost over inversion-based methods.United States. Defense Advanced Research Projects Agency (Mathematics of Sensing, Exploitation and Execution

Gradient Projection Anti-windup Scheme on Constrained Planar LTI Systems

The gradient projection anti-windup (GPAW) scheme was recently proposed as an anti-windup method for nonlinear multi-input-multi-output systems/controllers, the solution of which was recognized as a largely open problem in a recent survey paper. This report analyzes the properties of the GPAW scheme applied to an input constrained first order linear time invariant (LTI) system driven by a first order LTI controller, where the objective is to regulate the system state about the origin. We show that the GPAW compensated system is in fact a projected dynamical system (PDS), and use results in the PDS literature to assert existence and uniqueness of its solutions. The main result is that the GPAW scheme can only maintain/enlarge the exact region of attraction of the uncompensated system. We illustrate the qualitative weaknesses of some results in establishing true advantages of anti-windup methods, and propose a new paradigm to address the anti-windup problem, where results relative to the uncompensated system are sought.DSO National Laboratories, Singapore and AFOSR grant FA9550-08-1-008

Socially Aware Motion Planning with Deep Reinforcement Learning

For robotic vehicles to navigate safely and efficiently in pedestrian-rich environments, it is important to model subtle human behaviors and navigation rules (e.g., passing on the right). However, while instinctive to humans, socially compliant navigation is still difficult to quantify due to the stochasticity in people's behaviors. Existing works are mostly focused on using feature-matching techniques to describe and imitate human paths, but often do not generalize well since the feature values can vary from person to person, and even run to run. This work notes that while it is challenging to directly specify the details of what to do (precise mechanisms of human navigation), it is straightforward to specify what not to do (violations of social norms). Specifically, using deep reinforcement learning, this work develops a time-efficient navigation policy that respects common social norms. The proposed method is shown to enable fully autonomous navigation of a robotic vehicle moving at human walking speed in an environment with many pedestrians.Comment: 8 page

On Approximate Dynamic Inversion

Approximate Dynamic Inversion has been established as a method to control minimum-phase, nonaffine-in-control systems [1]. In this report, we re-state the main results of [1], clarify some minor notational errors, and prove the same results in an expanded form. In the large, the main results of [1] still stand. The development follows [1] closely, and no novelty is claimed herein. The purpose of this report is mainly to supplement our existing results in [2]–[4] that rely heavily on the results of [1].DSO National Laboratories (Singapore), AFOSR grant FA9550-08-1-008