Closed-Loop Statistical Verification of Stochastic Nonlinear Systems Subject to Parametric Uncertainties

This paper proposes a statistical verification framework using Gaussian processes (GPs) for simulation-based verification of stochastic nonlinear systems with parametric uncertainties. Given a small number of stochastic simulations, the proposed framework constructs a GP regression model and predicts the system's performance over the entire set of possible uncertainties. Included in the framework is a new metric to estimate the confidence in those predictions based on the variance of the GP's cumulative distribution function. This variance-based metric forms the basis of active sampling algorithms that aim to minimize prediction error through careful selection of simulations. In three case studies, the new active sampling algorithms demonstrate up to a 35% improvement in prediction error over other approaches and are able to correctly identify regions with low prediction confidence through the variance metric.Comment: 8 pages, submitted to ACC 201

Gaussian Process Decentralized Data Fusion Meets Transfer Learning in Large-Scale Distributed Cooperative Perception

This paper presents novel Gaussian process decentralized data fusion algorithms exploiting the notion of agent-centric support sets for distributed cooperative perception of large-scale environmental phenomena. To overcome the limitations of scale in existing works, our proposed algorithms allow every mobile sensing agent to choose a different support set and dynamically switch to another during execution for encapsulating its own data into a local summary that, perhaps surprisingly, can still be assimilated with the other agents' local summaries (i.e., based on their current choices of support sets) into a globally consistent summary to be used for predicting the phenomenon. To achieve this, we propose a novel transfer learning mechanism for a team of agents capable of sharing and transferring information encapsulated in a summary based on a support set to that utilizing a different support set with some loss that can be theoretically bounded and analyzed. To alleviate the issue of information loss accumulating over multiple instances of transfer learning, we propose a new information sharing mechanism to be incorporated into our algorithms in order to achieve memory-efficient lazy transfer learning. Empirical evaluation on real-world datasets show that our algorithms outperform the state-of-the-art methods.Comment: 32nd AAAI Conference on Artificial Intelligence (AAAI 2018), Extended version with proofs, 14 page

Gaussian Process Planning with Lipschitz Continuous Reward Functions: Towards Unifying Bayesian Optimization, Active Learning, and Beyond

This paper presents a novel nonmyopic adaptive Gaussian process planning (GPP) framework endowed with a general class of Lipschitz continuous reward functions that can unify some active learning/sensing and Bayesian optimization criteria and offer practitioners some flexibility to specify their desired choices for defining new tasks/problems. In particular, it utilizes a principled Bayesian sequential decision problem framework for jointly and naturally optimizing the exploration-exploitation trade-off. In general, the resulting induced GPP policy cannot be derived exactly due to an uncountable set of candidate observations. A key contribution of our work here thus lies in exploiting the Lipschitz continuity of the reward functions to solve for a nonmyopic adaptive epsilon-optimal GPP (epsilon-GPP) policy. To plan in real time, we further propose an asymptotically optimal, branch-and-bound anytime variant of epsilon-GPP with performance guarantee. We empirically demonstrate the effectiveness of our epsilon-GPP policy and its anytime variant in Bayesian optimization and an energy harvesting task.Comment: 30th AAAI Conference on Artificial Intelligence (AAAI 2016), Extended version with proofs, 17 page

Gaussian Process Planning with Lipschitz Continuous Reward Functions

This paper presents a novel nonmyopic adaptive Gaussian process planning (GPP) framework endowed with a general class of Lipschitz continuous reward functions that can unify some active learning/sensing and Bayesian optimization criteria and offer practitioners some flexibility to specify their desired choices for defining new tasks/problems. In particular, it utilizes a principled Bayesian sequential decision problem framework for jointly and naturally optimizing the exploration-exploitation trade-off. In general, the resulting induced GPP policy cannot be derived exactly due to an uncountable set of candidate observations. A key contribution of our work here thus lies in exploiting the Lipschitz continuity of the reward functions to solve for a nonmyopic adaptive ε-optimal GPP (ε-GPP) policy. To plan in real time, we further propose an asymptotically optimal, branch-and-bound anytime variant of ε-GPP with performance guarantee. We empirically demonstrate the effectiveness of our ε-GPP policy and its anytime variant in Bayesian optimization and an energy harvesting task.Singapore-MIT Alliance for Research and Technology (SMART) (52 R-252-000-550-592