Search for: All records

This paper leverages the framework of algorithms-with-predictions to design data structures for two fundamental dynamic graph problems: incremental topological ordering and cycle detection. In these problems, the input is a directed graph on n nodes, and the m edges arrive one by one. The data structure must maintain a topological ordering of the vertices at all times and detect if the newly inserted edge creates a cycle. The theoretically best worst-case algorithms for these problems have high update cost (polynomial in n and m). In practice, greedy heuristics (that recompute the solution from scratch each time) perform well but can have high update cost in the worst case. In this paper, we bridge this gap by leveraging predictions to design a learned new data structure for the problems. Our data structure guarantees consistency, robustness, and smoothness with respect to predictions--that is, it has the best possible running time under perfect predictions, never performs worse than the best-known worst-case methods, and its running time degrades smoothly with the prediction error. Moreover, we demonstrate empirically that predictions, learned from a very small training dataset, are sufficient to provide significant speed-ups on real datasets. 

We propose VecKM, a local point cloud geometry encoder that is descriptive and efficient to compute. VecKM leverages a unique approach by vectorizing a kernel mixture to represent the local point cloud. Such representation's descriptiveness is supported by two theorems that validate its ability to reconstruct and preserve the similarity of the local shape. Unlike existing encoders down-sampling the local point cloud, VecKM constructs the local geometry encoding using all neighboring points, producing a more descriptive encoding. Moreover, VecKM is efficient to compute and scalable to large point cloud inputs: VecKM reduces the memory cost from (n2 + nKd) to (nd + np); and reduces the major runtime cost from computing nK MLPs to n MLPs, where n is the size of the point cloud, K is the neighborhood size, d is the encoding dimension, and p is a marginal factor. The efficiency is due to VecKM's unique factorizable property that eliminates the need of explicitly grouping points into neighbors. In the normal estimation task, VecKM demonstrates not only 100× faster inference speed but also highest accuracy and strongest robustness. In classification and segmentation tasks, integrating VecKM as a preprocessing module achieves consistently better performance than the PointNet, PointNet++, and point transformer baselines, and runs consistently faster by up to 10 times. 

To mitigate the limitation that the classical reinforcement learning (RL) framework heavily relies on identical training and test environments, Distributionally Robust RL (DRRL) has been proposed to enhance performance across a range of environments, possibly including unknown test environments. As a price for robustness gain, DRRL involves optimizing over a set of distributions, which is inherently more challenging than optimizing over a fixed distribution in the non-robust case. Existing DRRL algorithms are either model-based or fail to learn from a single sample trajectory. In this paper, we design a first fully model-free DRRL algorithm, called distributionally robust Q-learning with single trajectory (DRQ). We delicately design a multi-timescale framework to fully utilize each incrementally arriving sample and directly learn the optimal distributionally robust policy without modeling the environment, thus the algorithm can be trained along a single trajectory in a model-free fashion. Despite the algorithm’s complexity, we provide asymptotic convergence guarantees by generalizing classical stochastic approximation tools. Comprehensive experimental results demonstrate the superior robustness and sample complexity of our proposed algorithm, compared to non-robust methods and other robust RL algorithms. 

Replica exchange stochastic gradient Langevin dynamics (reSGLD) is an effective sampler for non-convex learning in large-scale datasets. However, the simulation may encounter stagnation issues when the high-temperature chain delves too deeply into the distribution tails. To tackle this issue, we propose reflected reSGLD (r2SGLD): an algorithm tailored for constrained non-convex exploration by utilizing reflection steps within a bounded domain. Theoretically, we observe that reducing the diameter of the domain enhances mixing rates, exhibiting a quadratic behavior. Empirically, we test its performance through extensive experiments, including identifying dynamical systems with physical constraints, simulations of constrained multi-modal distributions, and image classification tasks. The theoretical and empirical findings highlight the crucial role of constrained exploration in improving the simulation efficiency. 

To mitigate the limitation that the classical reinforcement learning (RL) framework heavily relies on identical training and test environments, Distributionally Robust RL (DRRL) has been proposed to enhance performance across a range of environments, possibly including unknown test environments. As a price for robustness gain, DRRL involves optimizing over a set of distributions, which is inherently more challenging than optimizing over a fixed distribution in the non-robust case. Existing DRRL algorithms are either model-based or fail to learn from a single sample trajectory. In this paper, we design a first fully model-free DRRL algorithm, called distributionally robust Q-learning with single trajectory (DRQ). We delicately design a multi-timescale framework to fully utilize each incrementally arriving sample and directly learn the optimal distributionally robust policy without modeling the environment, thus the algorithm can be trained along a single trajectory in a model-free fashion. Despite the algorithm's complexity, we provide asymptotic convergence guarantees by generalizing classical stochastic approximation tools. Comprehensive experimental results demonstrate the superior robustness and sample complexity of our proposed algorithm, compared to non-robust methods and other robust RL algorithms. 

Rankings are ubiquitous across many applications, from search engines to hiring committees. In practice, many rankings are derived from the output of predictors. However, when predictors trained for classification tasks have intrinsic uncertainty, it is not obvious how this uncertainty should be represented in the derived rankings. Our work considers ranking functions: maps from individual predictions for a classification task to distributions over rankings. We focus on two aspects of ranking functions: stability to perturbations in predictions and fairness towards both individuals and subgroups. Not only is stability an important requirement for its own sake, but — as we show — it composes harmoniously with individual fairness in the sense of Dwork et al. (2012). While deterministic ranking functions cannot be stable aside from trivial scenarios, we show that the recently proposed uncertainty aware (UA) ranking functions of Singh et al. (2021) are stable. Our main result is that UA rankings also achieve group fairness through successful composition with multiaccurate or multicalibrated predictors. Our work demonstrates that UA rankings naturally interpolate between group and individual level fairness guarantees, while simultaneously satisfying stability guarantees important whenever machine-learned predictions are used.