Learning an Optimal Assortment Policy under Observational Data

We study the fundamental problem of offline assortment optimization under the Multinomial Logit (MNL) model, where sellers must determine the optimal subset of the products to offer based solely on historical customer choice data. While most existing approaches to learning-based assortment optimization focus on the online learning of the optimal assortment through repeated interactions with customers, such exploration can be costly or even impractical in many real-world settings. In this paper, we consider the offline learning paradigm and investigate the minimal data requirements for efficient offline assortment optimization. To this end, we introduce Pessimistic Rank-Breaking (PRB), an algorithm that combines rank-breaking with pessimistic estimation. We prove that PRB is nearly minimax optimal by establishing the tight suboptimality upper bound and a nearly matching lower bound. This further shows that "optimal item coverage" - where each item in the optimal assortment appears sufficiently often in the historical data - is both sufficient and necessary for efficient offline learning. This significantly relaxes the previous requirement of observing the complete optimal assortment in the data. Our results provide fundamental insights into the data requirements for offline assortment optimization under the MNL model.

On the Precise Asymptotics and Refined Regret of the Variance-Aware UCB Algorithm

In this paper, we study the behavior of the Upper Confidence Bound-Variance (UCB-V) algorithm for Multi-Armed Bandit (MAB) problems, a variant of the canonical Upper Confidence Bound (UCB) algorithm that incorporates variance estimates into its decision-making process. More precisely, we provide an asymptotic characterization of the arm-pulling rates of UCB-V, extending recent results for the canonical UCB in Kalvit and Zeevi (2021) and Khamaru and Zhang (2024). In an interesting contrast to the canonical UCB, we show that the behavior of UCB-V can exhibit instability, meaning that the arm-pulling rates may not always be asymptotically deterministic. Besides the asymptotic characterization, we also provide non-asymptotic bounds for arm-pulling rates in the high probability regime, offering insights into regret analysis. As an application of this high probability result, we show that UCB-V can achieve a refined regret bound, previously unknown even for more complicate and advanced variance-aware online decision-making algorithms.

PRTGaussian: Efficient Relighting Using 3D Gaussians with Precomputed Radiance Transfer

We present PRTGaussian, a realtime relightable novel-view synthesis method made possible by combining 3D Gaussians and Precomputed Radiance Transfer (PRT). By fitting relightable Gaussians to multi-view OLAT data, our method enables real-time, free-viewpoint relighting. By estimating the radiance transfer based on high-order spherical harmonics, we achieve a balance between capturing detailed relighting effects and maintaining computational efficiency. We utilize a two-stage process: in the first stage, we reconstruct a coarse geometry of the object from multi-view images. In the second stage, we initialize 3D Gaussians with the obtained point cloud, then simultaneously refine the coarse geometry and learn the light transport for each Gaussian. Extensive experiments on synthetic datasets show that our approach can achieve fast and high-quality relighting for general objects. Code and data are available at https://github.com/zhanglbthu/PRTGaussian.

RL in Markov Games with Independent Function Approximation: Improved Sample Complexity Bound under the Local Access Model

Efficiently learning equilibria with large state and action spaces in general-sum Markov games while overcoming the curse of multi-agency is a challenging problem. Recent works have attempted to solve this problem by employing independent linear function classes to approximate the marginal $Q$-value for each agent. However, existing sample complexity bounds under such a framework have a suboptimal dependency on the desired accuracy $\varepsilon$ or the action space. In this work, we introduce a new algorithm, Lin-Confident-FTRL, for learning coarse correlated equilibria (CCE) with local access to the simulator, i.e., one can interact with the underlying environment on the visited states. Up to a logarithmic dependence on the size of the state space, Lin-Confident-FTRL learns $\epsilon$-CCE with a provable optimal accuracy bound $O(\epsilon^{-2})$ and gets rids of the linear dependency on the action space, while scaling polynomially with relevant problem parameters (such as the number of agents and time horizon). Moreover, our analysis of Linear-Confident-FTRL generalizes the virtual policy iteration technique in the single-agent local planning literature, which yields a new computationally efficient algorithm with a tighter sample complexity bound when assuming random access to the simulator.

PC-NeRF: Parent-Child Neural Radiance Fields Using Sparse LiDAR Frames in Autonomous Driving Environments

Large-scale 3D scene reconstruction and novel view synthesis are vital for autonomous vehicles, especially utilizing temporally sparse LiDAR frames. However, conventional explicit representations remain a significant bottleneck towards representing the reconstructed and synthetic scenes at unlimited resolution. Although the recently developed neural radiance fields (NeRF) have shown compelling results in implicit representations, the problem of large-scale 3D scene reconstruction and novel view synthesis using sparse LiDAR frames remains unexplored. To bridge this gap, we propose a 3D scene reconstruction and novel view synthesis framework called parent-child neural radiance field (PC-NeRF). Based on its two modules, parent NeRF and child NeRF, the framework implements hierarchical spatial partitioning and multi-level scene representation, including scene, segment, and point levels. The multi-level scene representation enhances the efficient utilization of sparse LiDAR point cloud data and enables the rapid acquisition of an approximate volumetric scene representation. With extensive experiments, PC-NeRF is proven to achieve high-precision novel LiDAR view synthesis and 3D reconstruction in large-scale scenes. Moreover, PC-NeRF can effectively handle situations with sparse LiDAR frames and demonstrate high deployment efficiency with limited training epochs. Our approach implementation and the pre-trained models are available at https://github.com/biter0088/pc-nerf.

High-Quality Facial Geometry and Appearance Capture at Home

Facial geometry and appearance capture have demonstrated tremendous success in 3D scanning real humans in studios. Recent works propose to democratize this technique while keeping the results high quality. However, they are still inconvenient for daily usage. In addition, they focus on an easier problem of only capturing facial skin. This paper proposes a novel method for high-quality face capture, featuring an easy-to-use system and the capability to model the complete face with skin, mouth interior, hair, and eyes. We reconstruct facial geometry and appearance from a single co-located smartphone flashlight sequence captured in a dim room where the flashlight is the dominant light source (e.g. rooms with curtains or at night). To model the complete face, we propose a novel hybrid representation to effectively model both eyes and other facial regions, along with novel techniques to learn it from images. We apply a combined lighting model to compactly represent real illuminations and exploit a morphable face albedo model as a reflectance prior to disentangle diffuse and specular. Experiments show that our method can capture high-quality 3D relightable scans.

PC-NeRF: Parent-Child Neural Radiance Fields under Partial Sensor Data Loss in Autonomous Driving Environments

Reconstructing large-scale 3D scenes is essential for autonomous vehicles, especially when partial sensor data is lost. Although the recently developed neural radiance fields (NeRF) have shown compelling results in implicit representations, the large-scale 3D scene reconstruction using partially lost LiDAR point cloud data still needs to be explored. To bridge this gap, we propose a novel 3D scene reconstruction framework called parent-child neural radiance field (PC-NeRF). The framework comprises two modules, the parent NeRF and the child NeRF, to simultaneously optimize scene-level, segment-level, and point-level scene representations. Sensor data can be utilized more efficiently by leveraging the segment-level representation capabilities of child NeRFs, and an approximate volumetric representation of the scene can be quickly obtained even with limited observations. With extensive experiments, our proposed PC-NeRF is proven to achieve high-precision 3D reconstruction in large-scale scenes. Moreover, PC-NeRF can effectively tackle situations where partial sensor data is lost and has high deployment efficiency with limited training time. Our approach implementation and the pre-trained models will be available at https://github.com/biter0088/pc-nerf.

Learning a 3D Morphable Face Reflectance Model from Low-cost Data

Modeling non-Lambertian effects such as facial specularity leads to a more realistic 3D Morphable Face Model. Existing works build parametric models for diffuse and specular albedo using Light Stage data. However, only diffuse and specular albedo cannot determine the full BRDF. In addition, the requirement of Light Stage data is hard to fulfill for the research communities. This paper proposes the first 3D morphable face reflectance model with spatially varying BRDF using only low-cost publicly-available data. We apply linear shiness weighting into parametric modeling to represent spatially varying specular intensity and shiness. Then an inverse rendering algorithm is developed to reconstruct the reflectance parameters from non-Light Stage data, which are used to train an initial morphable reflectance model. To enhance the model's generalization capability and expressive power, we further propose an update-by-reconstruction strategy to finetune it on an in-the-wild dataset. Experimental results show that our method obtains decent rendering results with plausible facial specularities. Our code is released \href{https://yxuhan.github.io/ReflectanceMM/index.html}{\textcolor{magenta}{here}}.

On Private Online Convex Optimization: Optimal Algorithms in $\ell_p$-Geometry and High Dimensional Contextual Bandits

Differentially private (DP) stochastic convex optimization (SCO) is ubiquitous in trustworthy machine learning algorithm design. This paper studies the DP-SCO problem with streaming data sampled from a distribution and arrives sequentially. We also consider the continual release model where parameters related to private information are updated and released upon each new data, often known as the online algorithms. Despite that numerous algorithms have been developed to achieve the optimal excess risks in different $\ell_p$ norm geometries, yet none of the existing ones can be adapted to the streaming and continual release setting. To address such a challenge as the online convex optimization with privacy protection, we propose a private variant of online Frank-Wolfe algorithm with recursive gradients for variance reduction to update and reveal the parameters upon each data. Combined with the adaptive differential privacy analysis, our online algorithm achieves in linear time the optimal excess risk when $1<p\leq 2$ and the state-of-the-art excess risk meeting the non-private lower ones when $2<p\leq\infty$. Our algorithm can also be extended to the case $p=1$ to achieve nearly dimension-independent excess risk. While previous variance reduction results on recursive gradient have theoretical guarantee only in the independent and identically distributed sample setting, we establish such a guarantee in a non-stationary setting. To demonstrate the virtues of our method, we design the first DP algorithm for high-dimensional generalized linear bandits with logarithmic regret. Comparative experiments with a variety of DP-SCO and DP-Bandit algorithms exhibit the efficacy and utility of the proposed algorithms.

Single-View View Synthesis in the Wild with Learned Adaptive Multiplane Images

This paper deals with the challenging task of synthesizing novel views for in-the-wild photographs. Existing methods have shown promising results leveraging monocular depth estimation and color inpainting with layered depth representations. However, these methods still have limited capability to handle scenes with complex 3D geometry. We propose a new method based on the multiplane image (MPI) representation. To accommodate diverse scene layouts in the wild and tackle the difficulty in producing high-dimensional MPI contents, we design a network structure that consists of two novel modules, one for plane depth adjustment and another for depth-aware color prediction. The former adjusts the initial plane positions using the RGBD context feature and an attention mechanism. Given adjusted depth values, the latter predicts the color and density for each plane separately with proper inter-plane interactions achieved via a feature masking strategy. To train our method, we construct large-scale stereo training data using only unconstrained single-view image collections by a simple yet effective warp-back strategy. The experiments on both synthetic and real datasets demonstrate that our trained model works remarkably well and achieves state-of-the-art results.