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Prophet inequalities are a central object of study in optimal stopping theory. In the iid model, a gambler sees values in an online fashion, sampled independently from a given distribution. Upon observing each value, the gambler either accepts it as a reward or irrevocably rejects it and proceeds to observe the next value. The goal of the gambler, who cannot see the future, is maximising the expected value of the reward while competing against the expectation of a prophet (the offline maximum). In other words, one seeks to maximise the gambler-to-prophet ratio of the expectations. This model has been studied with infinite, finite and unknown number of values. When the gambler faces a random number of values, the model is said to have random horizon. We consider the model in which the gambler is given a priori knowledge of the horizon's distribution. Alijani et al. (2020) designed a single-threshold algorithms achieving a ratio of $1/2$ when the random horizon has an increasing hazard rate and is independent of the values. We prove that with a single-threshold, a ratio of $1/2$ is actually achievable for several larger classes of horizon distributions, with the largest being known as the $\mathcal{G}$ class in reliability theory. Moreover, we extend this result to its dual, the $\overline{\mathcal{G}}$ class (which includes the decreasing hazard rate class), and to low-variance horizons. Finally, we construct the first example of a family of horizons, for which multiple thresholds are necessary to achieve a nonzero ratio. We establish that the Secretary Problem optimal stopping rule provides one such algorithm, paving the way towards the study of the model beyond single-threshold algorithms.

We present a method for controlling a simulated humanoid to grasp an object and move it to follow an object trajectory. Due to the challenges in controlling a humanoid with dexterous hands, prior methods often use a disembodied hand and only consider vertical lifts or short trajectories. This limited scope hampers their applicability for object manipulation required for animation and simulation. To close this gap, we learn a controller that can pick up a large number (>1200) of objects and carry them to follow randomly generated trajectories. Our key insight is to leverage a humanoid motion representation that provides human-like motor skills and significantly speeds up training. Using only simplistic reward, state, and object representations, our method shows favorable scalability on diverse object and trajectories. For training, we do not need dataset of paired full-body motion and object trajectories. At test time, we only require the object mesh and desired trajectories for grasping and transporting. To demonstrate the capabilities of our method, we show state-of-the-art success rates in following object trajectories and generalizing to unseen objects. Code and models will be released.

Offline reinforcement learning (RL) is a promising direction that allows RL agents to pre-train on large datasets, avoiding the recurrence of expensive data collection. To advance the field, it is crucial to generate large-scale datasets. Compositional RL is particularly appealing for generating such large datasets, since 1)~it permits creating many tasks from few components, 2)~the task structure may enable trained agents to solve new tasks by combining relevant learned components, and 3)~the compositional dimensions provide a notion of task relatedness. This paper provides four offline RL datasets for simulated robotic manipulation created using the $256$ tasks from CompoSuite [Mendez at al., 2022a]. Each dataset is collected from an agent with a different degree of performance, and consists of $256$ million transitions. We provide training and evaluation settings for assessing an agent's ability to learn compositional task policies. Our benchmarking experiments show that current offline RL methods can learn the training tasks to some extent and that compositional methods outperform non-compositional methods. Yet current methods are unable to extract the compositional structure to generalize to unseen tasks, highlighting a need for future research in offline compositional RL.

Model predictive control (MPC) has played a more crucial role in various robotic control tasks, but its high computational requirements are concerning, especially for nonlinear dynamical models. This paper presents a $\textbf{la}$tent $\textbf{l}$inear $\textbf{q}$uadratic $\textbf{r}$egulator (LaLQR) that maps the state space into a latent space, on which the dynamical model is linear and the cost function is quadratic, allowing the efficient application of LQR. We jointly learn this alternative system by imitating the original MPC. Experiments show LaLQR's superior efficiency and generalization compared to other baselines.

Representing and rendering dynamic scenes has been an important but challenging task. Especially, to accurately model complex motions, high efficiency is usually hard to guarantee. To achieve real-time dynamic scene rendering while also enjoying high training and storage efficiency, we propose 4D Gaussian Splatting (4D-GS) as a holistic representation for dynamic scenes rather than applying 3D-GS for each individual frame. In 4D-GS, a novel explicit representation containing both 3D Gaussians and 4D neural voxels is proposed. A decomposed neural voxel encoding algorithm inspired by HexPlane is proposed to efficiently build Gaussian features from 4D neural voxels and then a lightweight MLP is applied to predict Gaussian deformations at novel timestamps. Our 4D-GS method achieves real-time rendering under high resolutions, 82 FPS at an 800$\times$800 resolution on an RTX 3090 GPU while maintaining comparable or better quality than previous state-of-the-art methods. More demos and code are available at //guanjunwu.github.io/4dgs/.

Model Predictive Control (MPC) relies heavily on the robot model for its control law. However, a gap always exists between the reduced-order control model with uncertainties and the real robot, which degrades its performance. To address this issue, we propose the controller of integrating a data-driven error model into traditional MPC for quadruped robots. Our approach leverages real-world data from sensors to compensate for defects in the control model. Specifically, we employ the Autoregressive Moving Average Vector (ARMAV) model to construct the state error model of the quadruped robot using data. The predicted state errors are then used to adjust the predicted future robot states generated by MPC. By such an approach, our proposed controller can provide more accurate inputs to the system, enabling it to achieve desired states even in the presence of model parameter inaccuracies or disturbances. The proposed controller exhibits the capability to partially eliminate the disparity between the model and the real-world robot, thereby enhancing the locomotion performance of quadruped robots. We validate our proposed method through simulations and real-world experimental trials on a large-size quadruped robot that involves carrying a 20 kg un-modeled payload (84% of body weight).

Deep learning models have shown considerable vulnerability to adversarial attacks, particularly as attacker strategies become more sophisticated. While traditional adversarial training (AT) techniques offer some resilience, they often focus on defending against a single type of attack, e.g., the $\ell_\infty$-norm attack, which can fail for other types. This paper introduces a computationally efficient multilevel $\ell_p$ defense, called the Efficient Robust Mode Connectivity (EMRC) method, which aims to enhance a deep learning model's resilience against multiple $\ell_p$-norm attacks. Similar to analytical continuation approaches used in continuous optimization, the method blends two $p$-specific adversarially optimal models, the $\ell_1$- and $\ell_\infty$-norm AT solutions, to provide good adversarial robustness for a range of $p$. We present experiments demonstrating that our approach performs better on various attacks as compared to AT-$\ell_\infty$, E-AT, and MSD, for datasets/architectures including: CIFAR-10, CIFAR-100 / PreResNet110, WideResNet, ViT-Base.

Large language models in the past have typically relied on some form of reinforcement learning with human feedback (RLHF) to better align model responses with human preferences. However, because of oft-observed instabilities when implementing these RLHF pipelines, various reparameterization techniques have recently been introduced to sidestep the need for separately learning an RL reward model. Instead, directly fine-tuning for human preferences is achieved via the minimization of a single closed-form training objective, a process originally referred to as direct preference optimization (DPO) and followed by several notable descendants. Although effective in certain real-world settings, we introduce new evaluation criteria that serve to highlight unresolved shortcomings in the ability of existing DPO methods to interpolate between a pre-trained reference model and empirical measures of human preferences, as well as unavoidable trade-offs in how low- and high-quality responses are regularized and constraints are handled. Our insights then motivate an alternative DPO-like loss that provably mitigates these limitations. Empirical results serve to corroborate notable aspects of our analyses.

In LiDAR-based 3D object detection for autonomous driving, the ratio of the object size to input scene size is significantly smaller compared to 2D detection cases. Overlooking this difference, many 3D detectors directly follow the common practice of 2D detectors, which downsample the feature maps even after quantizing the point clouds. In this paper, we start by rethinking how such multi-stride stereotype affects the LiDAR-based 3D object detectors. Our experiments point out that the downsampling operations bring few advantages, and lead to inevitable information loss. To remedy this issue, we propose Single-stride Sparse Transformer (SST) to maintain the original resolution from the beginning to the end of the network. Armed with transformers, our method addresses the problem of insufficient receptive field in single-stride architectures. It also cooperates well with the sparsity of point clouds and naturally avoids expensive computation. Eventually, our SST achieves state-of-the-art results on the large scale Waymo Open Dataset. It is worth mentioning that our method can achieve exciting performance (83.8 LEVEL 1 AP on validation split) on small object (pedestrian) detection due to the characteristic of single stride. Codes will be released at //github.com/TuSimple/SST

It is important to detect anomalous inputs when deploying machine learning systems. The use of larger and more complex inputs in deep learning magnifies the difficulty of distinguishing between anomalous and in-distribution examples. At the same time, diverse image and text data are available in enormous quantities. We propose leveraging these data to improve deep anomaly detection by training anomaly detectors against an auxiliary dataset of outliers, an approach we call Outlier Exposure (OE). This enables anomaly detectors to generalize and detect unseen anomalies. In extensive experiments on natural language processing and small- and large-scale vision tasks, we find that Outlier Exposure significantly improves detection performance. We also observe that cutting-edge generative models trained on CIFAR-10 may assign higher likelihoods to SVHN images than to CIFAR-10 images; we use OE to mitigate this issue. We also analyze the flexibility and robustness of Outlier Exposure, and identify characteristics of the auxiliary dataset that improve performance.