NeurIPS 2023 论文列表

Designing efficient algorithms to compute a Nash Equilibrium (NE) in multiplayer games is still an open challenge. In this paper, we focus on computing an NE that optimizes a given objective function. For example, when there is a team of players independently playing against an adversary in a game (e.g., several groups in a forest trying to interdict illegal loggers in green security games), these team members may need to find an NE minimizing the adversary’s utility. Finding an optimal NE in multiplayer games can be formulated as a mixed-integer bilinear program by introducing auxiliary variables to represent bilinear terms, leading to a huge number of bilinear terms, making it hard to solve. To overcome this challenge, we first propose a general framework for this formulation based on a set of correlation plans. We then develop a novel algorithm called CRM based on this framework, which uses correlation plans with their relations to strictly reduce the feasible solution space after the convex relaxation of bilinear terms while minimizing the number of correlation plans to significantly reduce the number of bilinear terms. We show that our techniques can significantly reduce the time complexity and CRM can be several orders of magnitude faster than the state-of-the-art baseline.

Recent works in dimensionality reduction for regression tasks have introduced the notion of sensitivity, an estimate of the importance of a specific datapoint in a dataset, offering provable guarantees on the quality of the approximation after removing low-sensitivity datapoints via subsampling. However, fast algorithms for approximating sensitivities, which we show is equivalent to approximate regression, are known for only the $\ell_2$ setting, in which they are popularly termed leverage scores. In this work, we provide the first efficient algorithms for approximating $\ell_p$ sensitivities and other summary statistics of a given matrix. In particular, for a given $n \times d$ matrix, we compute $\alpha$-approximation to its $\ell_1$ sensitivities at the cost of $n/\alpha$ sensitivity computations. For estimating the total $\ell_p$ sensitivity (i.e. the sum of $\ell_p$ sensitivities), we provide an algorithm based on importance sampling of $\ell_p$ Lewis weights, which computes a constant factor approximation at the cost of roughly $\sqrt{d}$ sensitivity computations, with no polynomial dependence on $n$. Furthermore, we estimate the maximum $\ell_1$ sensitivity up to a $\sqrt{d}$ factor in $O(d)$ sensitivity computations. We also generalize these results to $\ell_p$ norms. Lastly, we experimentally show that for a wide class of structured matrices in real-world datasets, the total sensitivity can be quickly approximated and is significantly smaller than the theoretical prediction, demonstrating that real-world datasets have on average low intrinsic effective dimensionality.

In this paper, we present continuous parametric optical flow, a parametric representation of dense and continuous motion over arbitrary time interval. In contrast to existing discrete-time representations (i.e., flow in between consecutive frames), this new representation transforms the frame-to-frame pixel correspondences to dense continuous flow. In particular, we present a temporal-parametric model that employs B-splines to fit point trajectories using a limited number of frames. To further improve the stability and robustness of the trajectories, we also add an encoder with a neural ordinary differential equation (NODE) to represent features associated with specific times. We also contribute a synthetic dataset and introduce two evaluation perspectives to measure the accuracy and robustness of continuous flow estimation. Benefiting from the combination of explicit parametric modeling and implicit feature optimization, our model focuses on motion continuity and outperforms the flow-based and point-tracking approaches for fitting long-term and variable sequences.