Neural network-based Combinatorial Optimization (CO) methods have shown promising results in solving various NP-complete (NPC) problems without relying on hand-crafted domain knowledge. This paper broadens the current scope of neural solvers for NPC problems by introducing a new graph-based diffusion framework, namely DIFUSCO. Our framework casts NPC problems as discrete {0,1}-vector optimization problems and leverages graph-based denoising diffusion models to generate high-quality solutions. We investigate two types of diffusion models with Gaussian and Bernoulli noise, respectively, and devise an effective inference schedule to enhance the solution quality. We evaluate our methods on two well-studied NPC combinatorial optimization problems: Traveling Salesman Problem (TSP) and Maximal Independent Set (MIS). Experimental results show that DIFUSCO strongly outperforms the previous state-of-the-art neural solvers, improving the performance gap between ground-truth and neural solvers from 1.76% to 0.46% on TSP-500, from 2.46% to 1.17% on TSP-1000, and from 3.19% to 2.58% on TSP-10000. For the MIS problem, DIFUSCO outperforms the previous state-of-the-art neural solver on the challenging SATLIB benchmark.

This paper investigates fairness and bias in Canonical Correlation Analysis (CCA), a widely used statistical technique for examining the relationship between two sets of variables. We present a framework that alleviates unfairness by minimizing the correlation disparity error associated with protected attributes. Our approach enables CCA to learn global projection matrices from all data points while ensuring that these matrices yield comparable correlation levels to group-specific projection matrices. Experimental evaluation on both synthetic and real-world datasets demonstrates the efficacy of our method in reducing correlation disparity error without compromising CCA accuracy.

A.1 Connection to online learning In Section 2 we motivated the update (2) as a way to adjust the size of our prediction sets in response to the realized historical miscoverage frequency. Alternatively, one could also derive (2) as an online gradient descent algorithm with respect to the pinball loss. To be more precise let t:= sup{: Yt 2 Cˆt()}, where we remark that Cˆt( t) can be thought of as the smallest prediction set containing Yt. Because the pinball loss is convex, this gradient descent update falls within a well understood class of algorithms that have been extensively studied in the online learning literature (see e.g. Unfortunately, this notion of regret fails to capture our intuition that t is adaptively tracking the moving target .

We present a novel method for reconstructing 3D objects from a single RGB image. Our method leverages the latest image generation models to infer the hidden 3D structure while remaining faithful to the input image. While existing methods[1, 2] obtain impressive results in generating 3D models from text prompts, they do not provide an easy approach for conditioning on input RGB data. Naïve extensions of these methods often lead to improper alignment in appearance between the input image and the 3D reconstructions. We address these challenges by introducing Image Constrained Radiance Fields (ConRad), a novel variant of neural radiance fields. ConRad is an efficient 3D representation that explicitly captures the appearance of an input image in one viewpoint. We propose a training algorithm that leverages the single RGB image in conjunction with pretrained Diffusion Models to optimize the parameters of a ConRad representation. Extensive experiments show that ConRad representations can simplify preservation of image details while producing a realistic 3D reconstruction. Compared to existing state-of-the-art baselines, we show that our 3D reconstructions remain more faithful to the input and produce more consistent 3D models while demonstrating significantly improved quantitative performance on a ShapeNet object benchmark.

Real-world decision-making systems are often subject to uncertainties that have to be resolved through observational data. Therefore, we are frequently confronted with combinatorial optimization problems of which the objective function is unknown and thus has to be debunked using empirical evidence. In contrast to the common practice that relies on a learning-and-optimization strategy, we consider the regression between combinatorial spaces, aiming to infer high-quality optimization solutions from samples of input-solution pairs - without the need to learn the objective function. Our main deliverable is a universal solver that is able to handle abstract undetermined stochastic combinatorial optimization problems.

Recently, auto-bidding technique has become an essential tool to increase the revenue of advertisers. Facing the complex and ever-changing bidding environments in the real-world advertising system (RAS), state-of-the-art auto-bidding policies usually leverage reinforcement learning (RL) algorithms to generate realtime bids on behalf of the advertisers. Due to safety concerns, it was believed that the RL training process can only be carried out in an offline virtual advertising system (VAS) that is built based on the historical data generated in the RAS. In this paper, we argue that there exists significant gaps between the VAS and RAS, making the RL training process suffer from the problem of inconsistency between online and offline (IBOO). Firstly, we formally define the IBOO and systematically analyze its causes and influences. Then, to avoid the IBOO, we propose a sustainable online RL (SORL) framework that trains the auto-bidding policy by directly interacting with the RAS, instead of learning in the VAS. Specifically, based on our proof of the Lipschitz smooth property of the Q function, we design a safe and efficient online exploration (SER) policy for continuously collecting data from the RAS. Meanwhile, we derive the theoretical lower bound on the safety degree of the SER policy. We also develop a variance-suppressed conservative Q-learning (V-CQL) method to effectively and stably learn the auto-bidding policy with the collected data.