Reduced-order models (ROMs) provide lower dimensional representations of complex systems, capturing their salient features while simplifying control design. Building on previous work, this paper presents an overarching framework for the integration of ROMs and control barrier functions, enabling the use of simplified models to construct safety-critical controllers while providing safety guarantees for complex full-order models. To achieve this, we formalize the connection between full and ROMs by defining projection mappings that relate the states and inputs of these models and leverage simulation functions to establish conditions under which safety guarantees may be transferred from a ROM to its corresponding full-order model. The efficacy of our framework is illustrated through simulation results on a drone and hardware demonstrations on ARCHER, a 3D hopping robot.

Interactive search can provide a better experience by incorporating interaction feedback from the users. This can significantly improve search accuracy as it helps avoid irrelevant information and captures the users' search intents. Existing state-of-the-art (SOTA) systems use reinforcement learning (RL) models to incorporate the interactions but focus on item-level feedback, ignoring the fine-grained information found in sentence-level feedback. Yet such feedback requires extensive RL action space exploration and large amounts of annotated data. This work addresses these challenges by proposing a new deep Q-learning (DQ) approach, DQrank. DQrank adapts BERT-based models, the SOTA in natural language processing, to select crucial sentences based on users' engagement and rank the items to obtain more satisfactory responses. We also propose two mechanisms to better explore optimal actions. DQrank further utilizes the experience replay mechanism in DQ to store the feedback sentences to obtain a better initial ranking performance. We validate the effectiveness of DQrank on three search datasets. The results show that DQRank performs at least 12% better than the previous SOTA RL approaches. We also conduct detailed ablation studies. The ablation results demonstrate that each model component can efficiently extract and accumulate long-term engagement effects from the users' sentence-level feedback. This structure offers new technologies with promised performance to construct a search system with sentence-level interaction.

Bayesian synthetic likelihood (BSL) is a popular method for estimating the parameter posterior distribution for complex statistical models and stochastic processes that possess a computationally intractable likelihood function. Instead of evaluating the likelihood, BSL approximates the likelihood of a judiciously chosen summary statistic of the data via model simulation and density estimation. Compared to alternative methods such as approximate Bayesian computation (ABC), BSL requires little tuning and requires less model simulations than ABC when the chosen summary statistic is high-dimensional. The original synthetic likelihood relies on a multivariate normal approximation of the intractable likelihood, where the mean and covariance are estimated by simulation. An extension of BSL considers replacing the sample covariance with a penalised covariance estimator to reduce the number of required model simulations. Further, a semi-parametric approach has been developed to relax the normality assumption. In this paper, we present an R package called BSL that amalgamates the aforementioned methods and more into a single, easy-to-use and coherent piece of software. The R package also includes several examples to illustrate how to use the package and demonstrate the utility of the methods.

We examine techniques for combining generalized policies with search algorithms to exploit the strengths and overcome the weaknesses of each when solving probabilistic planning problems. The Action Schema Network (ASNet) is a recent contribution to planning that uses deep learning and neural networks to learn generalized policies for probabilistic planning problems. ASNets are well suited to problems where local knowledge of the environment can be exploited to improve performance, but may fail to generalize to problems they were not trained on. Monte-Carlo Tree Search (MCTS) is a forward-chaining state space search algorithm for optimal decision making which performs simulations to incrementally build a search tree and estimate the values of each state. Although MCTS can achieve state-of-the-art results when paired with domain-specific knowledge, without this knowledge, MCTS requires a large number of simulations in order to obtain reliable state-value estimates. By combining ASNets with MCTS, we are able to improve the capability of an ASNet to generalize beyond the distribution of problems it was trained on, as well as enhance the navigation of the search space by MCTS.

In this post I want to present the notion of curse of dimensionality following a suggested excercise (Chapter 4 - Ex. 4) of the book An Introduction to Statistical Learning, writen by Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani. When the number of features \(p\) is large, there tends to be a deterioration in the performance of KNN and other local approaches that perform prediction using only observations that are near the test observation for which a prediction must be made. This phenomenon is known as the curse of dimensionality, and it ties into the fact that non-parametric approaches often perform poorly when \(p\) is large. We will now investigate this curse. Let us prepare the notebook.