Changyu Gao

Charles Dickens, Connor Pryor, Changyu Gao et al.

The field of Neural-Symbolic (NeSy) systems is growing rapidly. Proposed approaches show great promise in achieving symbiotic unions of neural and symbolic methods. However, a unifying framework is needed to organize common NeSy modeling patterns and develop general learning approaches. In this paper, we introduce Neural-Symbolic Energy-Based Models (NeSy-EBMs), a unifying mathematical framework for discriminative and generative NeSy modeling. Importantly, NeSy-EBMs allow the derivation of general expressions for gradients of prominent learning losses, and we introduce a suite of four learning approaches that leverage methods from multiple domains, including bilevel and stochastic policy optimization. Finally, we ground the NeSy-EBM framework with Neural Probabilistic Soft Logic (NeuPSL), an open-source NeSy-EBM library designed for scalability and expressivity, facilitating the real-world application of NeSy systems. Through extensive empirical analysis across multiple datasets, we demonstrate the practical advantages of NeSy-EBMs in various tasks, including image classification, graph node labeling, autonomous vehicle situation awareness, and question answering.

Changyu Gao, Stephen J. Wright

We develop simple differentially private optimization algorithms that move along directions of (expected) descent to find an approximate second-order solution for nonconvex ERM. We use line search, mini-batching, and a two-phase strategy to improve the speed and practicality of the algorithm. Numerical experiments demonstrate the effectiveness of these approaches.

Changyu Gao, Andrew Lowy, Xingyu Zhou et al.

We revisit the problem of federated learning (FL) with private data from people who do not trust the server or other silos/clients. In this context, every silo (e.g. hospital) has data from several people (e.g. patients) and needs to protect the privacy of each person's data (e.g. health records), even if the server and/or other silos try to uncover this data. Inter-Silo Record-Level Differential Privacy (ISRL-DP) prevents each silo's data from being leaked, by requiring that silo i's communications satisfy item-level differential privacy. Prior work arXiv:2106.09779 characterized the optimal excess risk bounds for ISRL-DP algorithms with homogeneous (i.i.d.) silo data and convex loss functions. However, two important questions were left open: (1) Can the same excess risk bounds be achieved with heterogeneous (non-i.i.d.) silo data? (2) Can the optimal risk bounds be achieved with fewer communication rounds? In this paper, we give positive answers to both questions. We provide novel ISRL-DP FL algorithms that achieve the optimal excess risk bounds in the presence of heterogeneous silo data. Moreover, our algorithms are more communication-efficient than the prior state-of-the-art. For smooth loss functions, our algorithm achieves the optimal excess risk bound and has communication complexity that matches the non-private lower bound. Additionally, our algorithms are more computationally efficient than the previous state-of-the-art.

Charles Dickens, Changyu Gao, Connor Pryor et al.

We leverage convex and bilevel optimization techniques to develop a general gradient-based parameter learning framework for neural-symbolic (NeSy) systems. We demonstrate our framework with NeuPSL, a state-of-the-art NeSy architecture. To achieve this, we propose a smooth primal and dual formulation of NeuPSL inference and show learning gradients are functions of the optimal dual variables. Additionally, we develop a dual block coordinate descent algorithm for the new formulation that naturally exploits warm-starts. This leads to over 100x learning runtime improvements over the current best NeuPSL inference method. Finally, we provide extensive empirical evaluations across 8 datasets covering a range of tasks and demonstrate our learning framework achieves up to a 16% point prediction performance improvement over alternative learning methods.

Changyu Gao, Andrew Lowy, Xingyu Zhou et al.

Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the $ε$-contamination model, where an adversary can inspect and replace up to an $ε$-fraction of the samples, a fundamental open problem is determining the optimal rates for robust stochastic convex optimization (SCO) under such contamination. We develop novel algorithms that achieve minimax-optimal excess risk (up to logarithmic factors) under the $ε$-contamination model. Our approach improves over existing algorithms, which are not only suboptimal but also require stringent assumptions, including Lipschitz continuity and smoothness of individual sample functions. By contrast, our optimal algorithms do not require these stringent assumptions, assuming only population-level smoothness of the loss. Moreover, our algorithms can be adapted to handle the case in which the covariance parameter is unknown, and can be extended to nonsmooth population risks via convolutional smoothing. We complement our algorithmic developments with a tight information-theoretic lower bound for robust SCO.