Xiuyuan Lu

Ian Osband, Zheng Wen, Seyed Mohammad Asghari et al. · stanford

Thompson sampling (TS) is a popular heuristic for action selection, but it requires sampling from a posterior distribution. Unfortunately, this can become computationally intractable in complex environments, such as those modeled using neural networks. Approximate posterior samples can produce effective actions, but only if they reasonably approximate joint predictive distributions of outputs across inputs. Notably, accuracy of marginal predictive distributions does not suffice. Epistemic neural networks (ENNs) are designed to produce accurate joint predictive distributions. We compare a range of ENNs through computational experiments that assess their performance in approximating TS across bandit and reinforcement learning environments. The results indicate that ENNs serve this purpose well and illustrate how the quality of joint predictive distributions drives performance. Further, we demonstrate that the \textit{epinet} -- a small additive network that estimates uncertainty -- matches the performance of large ensembles at orders of magnitude lower computational cost. This enables effective application of TS with computation that scales gracefully to complex environments.

Chao Qin, Zheng Wen, Xiuyuan Lu et al. · deepmind, stanford

Ensemble sampling serves as a practical approximation to Thompson sampling when maintaining an exact posterior distribution over model parameters is computationally intractable. In this paper, we establish a regret bound that ensures desirable behavior when ensemble sampling is applied to the linear bandit problem. This represents the first rigorous regret analysis of ensemble sampling and is made possible by leveraging information-theoretic concepts and novel analytic techniques that may prove useful beyond the scope of this paper.

Vikranth Dwaracherla, Zheng Wen, Ian Osband et al. · deepmind, stanford

In machine learning, an agent needs to estimate uncertainty to efficiently explore and adapt and to make effective decisions. A common approach to uncertainty estimation maintains an ensemble of models. In recent years, several approaches have been proposed for training ensembles, and conflicting views prevail with regards to the importance of various ingredients of these approaches. In this paper, we aim to address the benefits of two ingredients -- prior functions and bootstrapping -- which have come into question. We show that prior functions can significantly improve an ensemble agent's joint predictions across inputs and that bootstrapping affords additional benefits if the signal-to-noise ratio varies across inputs. Our claims are justified by both theoretical and experimental results.

Xiuyuan Lu, Ian Osband, Seyed Mohammad Asghari et al. · stanford

Recent work introduced the epinet as a new approach to uncertainty modeling in deep learning. An epinet is a small neural network added to traditional neural networks, which, together, can produce predictive distributions. In particular, using an epinet can greatly improve the quality of joint predictions across multiple inputs, a measure of how well a neural network knows what it does not know. In this paper, we examine whether epinets can offer similar advantages under distributional shifts. We find that, across ImageNet-A/O/C, epinets generally improve robustness metrics. Moreover, these improvements are more significant than those afforded by even very large ensembles at orders of magnitude lower computational costs. However, these improvements are relatively small compared to the outstanding issues in distributionally-robust deep learning. Epinets may be a useful tool in the toolbox, but they are far from the complete solution.

Jinghang Li, Bangyan Liao, Xiuyuan LU et al.

Predicting a potential collision with leading vehicles is an essential functionality of any autonomous/assisted driving system. One bottleneck of existing vision-based solutions is that their updating rate is limited to the frame rate of standard cameras used. In this paper, we present a novel method that estimates the time to collision using a neuromorphic event-based camera, a biologically inspired visual sensor that can sense at exactly the same rate as scene dynamics. The core of the proposed algorithm consists of a two-step approach for efficient and accurate geometric model fitting on event data in a coarse-to-fine manner. The first step is a robust linear solver based on a novel geometric measurement that overcomes the partial observability of event-based normal flow. The second step further refines the resulting model via a spatio-temporal registration process formulated as a nonlinear optimization problem. Experiments on both synthetic and real data demonstrate the effectiveness of the proposed method, outperforming other alternative methods in terms of efficiency and accuracy.

Jiayao Mai, Xiuyuan Lu, Kuan Dai et al.

Event cameras generate asynchronous signals in response to pixel-level brightness changes, offering a sensing paradigm with theoretically microsecond-scale latency that can significantly enhance the performance of multi-sensor systems. Extrinsic calibration is a critical prerequisite for effective sensor fusion; however, the configuration that involves event cameras remains an understudied topic. In this paper, we propose a motion-based temporal and rotational calibration framework tailored for event-centric multi-sensor systems, eliminating the need for dedicated calibration targets. Our method uses as input the rotational motion estimates obtained from event cameras and other heterogeneous sensors, respectively. Different from conventional approaches that rely on event-to-frame conversion, our method efficiently estimates angular velocity from normal flow observations, which are derived from the spatio-temporal profile of event data. The overall calibration pipeline adopts a two-step approach: it first initializes the temporal offset and rotational extrinsics by exploiting kinematic correlations in the spirit of Canonical Correlation Analysis (CCA), and then refines both temporal and rotational parameters through a joint non-linear optimization using a continuous-time parametrization in SO(3). Extensive evaluations on both publicly available and self-collected datasets validate that the proposed method achieves calibration accuracy comparable to target-based methods, while exhibiting superior stability over purely CCA-based methods, and highlighting its precision, robustness and flexibility. To facilitate future research, our implementation will be made open-source. Code: https://github.com/NAIL-HNU/EvMultiCalib.

Ian Osband, Zheng Wen, Seyed Mohammad Asghari et al.

Predictive distributions quantify uncertainties ignored by point estimates. This paper introduces The Neural Testbed: an open-source benchmark for controlled and principled evaluation of agents that generate such predictions. Crucially, the testbed assesses agents not only on the quality of their marginal predictions per input, but also on their joint predictions across many inputs. We evaluate a range of agents using a simple neural network data generating process. Our results indicate that some popular Bayesian deep learning agents do not fare well with joint predictions, even when they can produce accurate marginal predictions. We also show that the quality of joint predictions drives performance in downstream decision tasks. We find these results are robust across choice a wide range of generative models, and highlight the practical importance of joint predictions to the community.

Yi Zhou, Guillermo Gallego, Xiuyuan Lu et al.

Identifying independently moving objects is an essential task for dynamic scene understanding. However, traditional cameras used in dynamic scenes may suffer from motion blur or exposure artifacts due to their sampling principle. By contrast, event-based cameras are novel bio-inspired sensors that offer advantages to overcome such limitations. They report pixelwise intensity changes asynchronously, which enables them to acquire visual information at exactly the same rate as the scene dynamics. We develop a method to identify independently moving objects acquired with an event-based camera, i.e., to solve the event-based motion segmentation problem. We cast the problem as an energy minimization one involving the fitting of multiple motion models. We jointly solve two subproblems, namely event cluster assignment (labeling) and motion model fitting, in an iterative manner by exploiting the structure of the input event data in the form of a spatio-temporal graph. Experiments on available datasets demonstrate the versatility of the method in scenes with different motion patterns and number of moving objects. The evaluation shows state-of-the-art results without having to predetermine the number of expected moving objects. We release the software and dataset under an open source licence to foster research in the emerging topic of event-based motion segmentation.

Seyed Mohammad Asghari, Chris Chute, Vikranth Dwaracherla et al.

We develop an online learning algorithm that dramatically improves the data efficiency of reinforcement learning from human feedback (RLHF). Our algorithm incrementally updates reward and language models as choice data is received. The reward model is fit to the choice data, while the language model is updated by a variation of reinforce, with reinforcement signals provided by the reward model. Several features enable the efficiency gains: a small affirmative nudge added to each reinforcement signal, an epistemic neural network that models reward uncertainty, and information-directed exploration. With Gemma large language models (LLMs), our algorithm matches the performance of offline RLHF trained on 200K labels using fewer than 20K labels, representing more than a 10x gain in data efficiency. Extrapolating from our results, we expect our algorithm trained on 1M labels to match offline RLHF trained on 1B labels. This represents a 1,000x gain. To our knowledge, these are the first results to demonstrate that such large improvements are possible.

Junkai Niu, Sheng Zhong, Xiuyuan Lu et al.

Event-based visual odometry is a specific branch of visual Simultaneous Localization and Mapping (SLAM) techniques, which aims at solving tracking and mapping subproblems (typically in parallel), by exploiting the special working principles of neuromorphic (i.e., event-based) cameras. Due to the motion-dependent nature of event data, explicit data association (i.e., feature matching) under large-baseline view-point changes is difficult to establish, making direct methods a more rational choice. However, state-of-the-art direct methods are limited by the high computational complexity of the mapping sub-problem and the degeneracy of camera pose tracking in certain degrees of freedom (DoF) in rotation. In this paper, we tackle these issues by building an event-based stereo visual-inertial odometry system on top of a direct pipeline. Specifically, to speed up the mapping operation, we propose an efficient strategy for sampling contour points according to the local dynamics of events. The mapping performance is also improved in terms of structure completeness and local smoothness by merging the temporal stereo and static stereo results. To circumvent the degeneracy of camera pose tracking in recovering the pitch and yaw components of general 6-DoF motion, we introduce IMU measurements as motion priors via pre-integration. To this end, a compact back-end is proposed for continuously updating the IMU bias and predicting the linear velocity, enabling an accurate motion prediction for camera pose tracking. The resulting system scales well with modern high-resolution event cameras and leads to better global positioning accuracy in large-scale outdoor environments. Extensive evaluations on five publicly available datasets featuring different resolutions and scenarios justify the superior performance of the proposed system against five state-of-the-art methods.

Ian Osband, Zheng Wen, Seyed Mohammad Asghari et al.

Most work on supervised learning research has focused on marginal predictions. In decision problems, joint predictive distributions are essential for good performance. Previous work has developed methods for assessing low-order predictive distributions with inputs sampled i.i.d. from the testing distribution. With low-dimensional inputs, these methods distinguish agents that effectively estimate uncertainty from those that do not. We establish that the predictive distribution order required for such differentiation increases greatly with input dimension, rendering these methods impractical. To accommodate high-dimensional inputs, we introduce \textit{dyadic sampling}, which focuses on predictive distributions associated with random \textit{pairs} of inputs. We demonstrate that this approach efficiently distinguishes agents in high-dimensional examples involving simple logistic regression as well as complex synthetic and empirical data.

Xiuyuan Lu, Yi Zhou, Shaojie Shen

Among prerequisites for a synthetic agent to interact with dynamic scenes, the ability to identify independently moving objects is specifically important. From an application perspective, nevertheless, standard cameras may deteriorate remarkably under aggressive motion and challenging illumination conditions. In contrast, event-based cameras, as a category of novel biologically inspired sensors, deliver advantages to deal with these challenges. Its rapid response and asynchronous nature enables it to capture visual stimuli at exactly the same rate of the scene dynamics. In this paper, we present a cascaded two-level multi-model fitting method for identifying independently moving objects (i.e., the motion segmentation problem) with a monocular event camera. The first level leverages tracking of event features and solves the feature clustering problem under a progressive multi-model fitting scheme. Initialized with the resulting motion model instances, the second level further addresses the event clustering problem using a spatio-temporal graph-cut method. This combination leads to efficient and accurate event-wise motion segmentation that cannot be achieved by any of them alone. Experiments demonstrate the effectiveness and versatility of our method in real-world scenes with different motion patterns and an unknown number of independently moving objects.

Zheng Wen, Ian Osband, Chao Qin et al.

A fundamental challenge for any intelligent system is prediction: given some inputs, can you predict corresponding outcomes? Most work on supervised learning has focused on producing accurate marginal predictions for each input. However, we show that for a broad class of decision problems, accurate joint predictions are required to deliver good performance. In particular, we establish several results pertaining to combinatorial decision problems, sequential predictions, and multi-armed bandits to elucidate the essential role of joint predictive distributions. Our treatment of multi-armed bandits introduces an approximate Thompson sampling algorithm and analytic techniques that lead to a new kind of regret bound.

Ian Osband, Zheng Wen, Seyed Mohammad Asghari et al.

Intelligence relies on an agent's knowledge of what it does not know. This capability can be assessed based on the quality of joint predictions of labels across multiple inputs. In principle, ensemble-based approaches produce effective joint predictions, but the computational costs of training large ensembles can become prohibitive. We introduce the epinet: an architecture that can supplement any conventional neural network, including large pretrained models, and can be trained with modest incremental computation to estimate uncertainty. With an epinet, conventional neural networks outperform very large ensembles, consisting of hundreds or more particles, with orders of magnitude less computation. The epinet does not fit the traditional framework of Bayesian neural networks. To accommodate development of approaches beyond BNNs, such as the epinet, we introduce the epistemic neural network (ENN) as an interface for models that produce joint predictions.

Shaozu Cao, Xiuyuan Lu, Shaojie Shen

Visual-Inertial odometry (VIO) is known to suffer from drifting especially over long-term runs. In this paper, we present GVINS, a non-linear optimization based system that tightly fuses GNSS raw measurements with visual and inertial information for real-time and drift-free state estimation. Our system aims to provide accurate global 6-DoF estimation under complex indoor-outdoor environment where GNSS signals may be intermittent or even totally unavailable. To connect global measurements with local states, a coarse-to-fine initialization procedure is proposed to efficiently calibrate the transformation online and initialize GNSS states from only a short window of measurements. The GNSS code pseudorange and Doppler shift measurements, along with visual and inertial information, are then modelled and used to constrain the system states in a factor graph framework. For complex and GNSS-unfriendly areas, the degenerate cases are discussed and carefully handled to ensure robustness. Thanks to the tightly-coupled multi-sensor approach and system design, our system fully exploits the merits of three types of sensors and is capable to seamlessly cope with the transition between indoor and outdoor environments, where satellites are lost and reacquired. We extensively evaluate the proposed system by both simulation and real-world experiments, and the result demonstrates that our system substantially eliminates the drift of VIO and preserves the local accuracy in spite of noisy GNSS measurements. The challenging indoor-outdoor and urban driving experiments verify the availability and robustness of GVINS in complex environments. In addition, experiments also show that our system can gain from even a single satellite while conventional GNSS algorithms need four at least.

Xiuyuan Lu, Benjamin Van Roy, Vikranth Dwaracherla et al.

Reinforcement learning agents have demonstrated remarkable achievements in simulated environments. Data efficiency poses an impediment to carrying this success over to real environments. The design of data-efficient agents calls for a deeper understanding of information acquisition and representation. We discuss concepts and regret analysis that together offer principled guidance. This line of thinking sheds light on questions of what information to seek, how to seek that information, and what information to retain. To illustrate concepts, we design simple agents that build on them and present computational results that highlight data efficiency.

Vikranth Dwaracherla, Xiuyuan Lu, Morteza Ibrahimi et al.

We study the use of hypermodels to represent epistemic uncertainty and guide exploration. This generalizes and extends the use of ensembles to approximate Thompson sampling. The computational cost of training an ensemble grows with its size, and as such, prior work has typically been limited to ensembles with tens of elements. We show that alternative hypermodels can enjoy dramatic efficiency gains, enabling behavior that would otherwise require hundreds or thousands of elements, and even succeed in situations where ensemble methods fail to learn regardless of size. This allows more accurate approximation of Thompson sampling as well as use of more sophisticated exploration schemes. In particular, we consider an approximate form of information-directed sampling and demonstrate performance gains relative to Thompson sampling. As alternatives to ensembles, we consider linear and neural network hypermodels, also known as hypernetworks. We prove that, with neural network base models, a linear hypermodel can represent essentially any distribution over functions, and as such, hypernetworks are no more expressive.

Xiuyuan Lu, Benjamin Van Roy

We integrate information-theoretic concepts into the design and analysis of optimistic algorithms and Thompson sampling. By making a connection between information-theoretic quantities and confidence bounds, we obtain results that relate the per-period performance of the agent with its information gain about the environment, thus explicitly characterizing the exploration-exploitation tradeoff. The resulting cumulative regret bound depends on the agent's uncertainty over the environment and quantifies the value of prior information. We show applicability of this approach to several environments, including linear bandits, tabular MDPs, and factored MDPs. These examples demonstrate the potential of a general information-theoretic approach for the design and analysis of reinforcement learning algorithms.

Xiuyuan Lu, Benjamin Van Roy

Thompson sampling has emerged as an effective heuristic for a broad range of online decision problems. In its basic form, the algorithm requires computing and sampling from a posterior distribution over models, which is tractable only for simple special cases. This paper develops ensemble sampling, which aims to approximate Thompson sampling while maintaining tractability even in the face of complex models such as neural networks. Ensemble sampling dramatically expands on the range of applications for which Thompson sampling is viable. We establish a theoretical basis that supports the approach and present computational results that offer further insight.