Xuchen Gong

Junfei Sun, Dixi Yao, Xuchen Gong et al.

Heavy-tailed stochastic gradient noise, commonly observed in transformer models, can destabilize the optimization process. Recent works mainly focus on developing and understanding approaches to address heavy-tailed noise in the centralized or distributed, synchronous setting, leaving the interactions between such noise and asynchronous optimization underexplored. In this work, we investigate two communication schemes that handle stragglers with asynchronous updates in the presence of heavy-tailed gradient noise. We propose and theoretically analyze algorithmic modifications based on delay-aware learning rate scheduling and delay compensation to enhance the performance of asynchronous algorithms. Our convergence guarantees under heavy-tailed noise match the rate of the synchronous counterparts and improve delay tolerance compared with existing asynchronous approaches. Empirically, our approaches outperform prior synchronous and asynchronous methods in terms of accuracy/runtime trade-offs and are more robust to hyperparameters in both image and language tasks.

Xuchen Gong, Tian Li

One of the major bottlenecks for deploying popular first-order differentially private (DP) machine learning algorithms (e.g., DP-SGD) lies in their high computation and memory cost, despite the existence of optimized implementations. Zeroth-order methods have promise in mitigating the overhead, as they leverage function evaluations to approximate the gradients, hence significantly easier to privatize. While recent works have explored zeroth-order approaches in both private and non-private settings, they still suffer from relatively low utilities compared with DP-SGD, and have only been evaluated in limited application domains. In this work, we propose to leverage public information to guide and improve gradient approximation of private zeroth-order algorithms. We explore a suite of public-data-assisted zeroth-order optimizers (PAZO) with minimal overhead. We provide theoretical analyses of the PAZO framework under an assumption of the similarity between public and private data. Empirically, we demonstrate that PAZO achieves superior privacy/utility tradeoffs across vision and text tasks in both pre-training and fine-tuning settings, outperforming the best first-order baselines (with public data) especially in highly private regimes, while offering up to $16\times$ runtime speedup.

Xuchen Gong, Tian Li

Classic zeroth-order optimization approaches typically optimize for a smoothed version of the original function, i.e., the expected objective under randomly perturbed model parameters. This can be interpreted as encouraging the loss values in the perturbation set to be small on average. Popular sharpness-aware minimization (SAM) objectives, however, typically focus on the largest loss within the neighborhood to arrive at flat minima more effectively. In this work, we connect zeroth-order optimization (and its corresponding objectives) with SAM approaches explicitly, through an exponential tilting objective that provides a smooth transition between the average- and the max-loss formulations. We explore new zeroth-order algorithms to solve a soft SAM objective parameterized by a tilting parameter $t$. We provide precise characterizations of the sharpness notions of the tilted SAM framework. Practically, our approach can be used as a gradient-free and memory-efficient alternative to SAM variants, and it achieves better generalization compared to vanilla zeroth-order baselines on a wide range of downstream tasks, including classification, multiple choice QA, and language generation.