A New Perspective and Extension of the Gaussian Filter

The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. GFs represent the belief of the current state by a Gaussian with the mean being an affine function of the measurement. We show that this representation can be too restrictive to accurately capture the dependences in systems with nonlinear observation models, and we investigate how the GF can be generalized to alleviate this problem. To this end, we view the GF from a variational-inference perspective. We analyse how restrictions on the form of the belief can be relaxed while maintaining simplicity and efficiency. This analysis provides a basis for generalizations of the GF. We propose one such generalization which coincides with a GF using a virtual measurement, obtained by applying a nonlinear function to the actual measurement. Numerical experiments show that the proposed Feature Gaussian Filter (FGF) can have a substantial performance advantage over the standard GF for systems with nonlinear observation models.Comment: Will appear in Robotics: Science and Systems (R:SS) 201

The Coordinate Particle Filter - A novel Particle Filter for High Dimensional Systems

Parametric filters, such as the Extended Kalman Filter and the Unscented Kalman Filter, typically scale well with the dimensionality of the problem, but they are known to fail if the posterior state distribution cannot be closely approximated by a density of the assumed parametric form. For nonparametric filters, such as the Particle Filter, the converse holds. Such methods are able to approximate any posterior, but the computational requirements scale exponentially with the number of dimensions of the state space. In this paper, we present the Coordinate Particle Filter which alleviates this problem. We propose to compute the particle weights recursively, dimension by dimension. This allows us to explore one dimension at a time, and resample after each dimension if necessary. Experimental results on simulated as well as real data confirm that the proposed method has a substantial performance advantage over the Particle Filter in high-dimensional systems where not all dimensions are highly correlated. We demonstrate the benefits of the proposed method for the problem of multi-object and robotic manipulator tracking

Robust Gaussian Filtering using a Pseudo Measurement

Many sensors, such as range, sonar, radar, GPS and visual devices, produce measurements which are contaminated by outliers. This problem can be addressed by using fat-tailed sensor models, which account for the possibility of outliers. Unfortunately, all estimation algorithms belonging to the family of Gaussian filters (such as the widely-used extended Kalman filter and unscented Kalman filter) are inherently incompatible with such fat-tailed sensor models. The contribution of this paper is to show that any Gaussian filter can be made compatible with fat-tailed sensor models by applying one simple change: Instead of filtering with the physical measurement, we propose to filter with a pseudo measurement obtained by applying a feature function to the physical measurement. We derive such a feature function which is optimal under some conditions. Simulation results show that the proposed method can effectively handle measurement outliers and allows for robust filtering in both linear and nonlinear systems

Representation with Incomplete Votes

Platforms for online civic participation rely heavily on methods for condensing thousands of comments into a relevant handful, based on whether participants agree or disagree with them. These methods should guarantee fair representation of the participants, as their outcomes may affect the health of the conversation and inform impactful downstream decisions. To that end, we draw on the literature on approval-based committee elections. Our setting is novel in that the approval votes are incomplete since participants will typically not vote on all comments. We prove that this complication renders non-adaptive algorithms impractical in terms of the amount of information they must gather. Therefore, we develop an adaptive algorithm that uses information more efficiently by presenting incoming participants with statements that appear promising based on votes by previous participants. We prove that this method satisfies commonly used notions of fair representation, even when participants only vote on a small fraction of comments. Finally, an empirical evaluation using real data shows that the proposed algorithm provides representative outcomes in practice

Generative Social Choice

Traditionally, social choice theory has only been applicable to choices among a few predetermined alternatives but not to more complex decisions such as collectively selecting a textual statement. We introduce generative social choice, a framework that combines the mathematical rigor of social choice theory with large language models' capability to generate text and extrapolate preferences. This framework divides the design of AI-augmented democratic processes into two components: first, proving that the process satisfies rigorous representation guarantees when given access to oracle queries; second, empirically validating that these queries can be approximately implemented using a large language model. We illustrate this framework by applying it to the problem of generating a slate of statements that is representative of opinions expressed as free-form text, for instance in an online deliberative process

Benchmarking Offline Reinforcement Learning on Real-Robot Hardware

Learning policies from previously recorded data is a promising direction for real-world robotics tasks, as online learning is often infeasible. Dexterous manipulation in particular remains an open problem in its general form. The combination of offline reinforcement learning with large diverse datasets, however, has the potential to lead to a breakthrough in this challenging domain analogously to the rapid progress made in supervised learning in recent years. To coordinate the efforts of the research community toward tackling this problem, we propose a benchmark including: i) a large collection of data for offline learning from a dexterous manipulation platform on two tasks, obtained with capable RL agents trained in simulation; ii) the option to execute learned policies on a real-world robotic system and a simulation for efficient debugging. We evaluate prominent open-sourced offline reinforcement learning algorithms on the datasets and provide a reproducible experimental setup for offline reinforcement learning on real systems.Comment: The Eleventh International Conference on Learning Representations. 2022. Published at ICLR 2023. Datasets available at https://github.com/rr-learning/trifinger_rl_dataset