We introduce a new zeroth-order algorithm for private stochastic optimization on nonconvex and nonsmooth objectives. Given a dataset of size $M$, our algorithm ensures $(\alpha,\alpha\rho^2/2)$-Renyi differential privacy and finds a $(\delta,\epsilon)$-stationary point so long as $M=\tilde\Omega(\frac{d}{\delta\epsilon^3} + \frac{d^{3/2}}{\rho\delta\epsilon^2})$. This matches the optimal complexity found in its non-private zeroth-order analog. Notably, although the objective is not smooth, we have privacy ``for free'' when $\rho \ge \sqrt{d}\epsilon$.

We develop a new algorithm for non-convex stochastic optimization that finds an $\epsilon$-critical point in the optimal $O(\epsilon^{-3})$ stochastic gradient and Hessian-vector product computations. Our algorithm uses Hessian-vector products to "correct'' a bias term in the momentum of SGD with momentum. This leads to better gradient estimates in a manner analogous to variance reduction methods. In contrast to prior work, we do not require excessively large batch sizes and are able to provide an adaptive algorithm whose convergence rate automatically improves with decreasing variance in the gradient estimates. We validate our results on a variety of large-scale deep learning architectures and benchmarks tasks.

We introduce new algorithms and convergence guarantees for privacy-preserving non-convex Empirical Risk Minimization (ERM) on smooth $d$-dimensional objectives. We develop an improved sensitivity analysis of stochastic gradient descent on smooth objectives that exploits the recurrence of examples in different epochs. By combining this new approach with recent analysis of momentum with private aggregation techniques, we provide an $(\epsilon,\delta)$-differential private algorithm that finds a gradient of norm $O\left(\frac{d^{1/3}}{(\epsilon N)^{2/3}}\right)$ in $O\left(\frac{N^{7/3}\epsilon^{4/3}}{d^{2/3}}\right)$ gradient evaluations, improving the previous best gradient bound of $\tilde O\left(\frac{d^{1/4}}{\sqrt{\epsilon N}}\right)$.

We develop a new reduction that converts any online convex optimization algorithm suffering $O(\sqrt{T})$ regret into an $\epsilon$-differentially private stochastic convex optimization algorithm with the optimal convergence rate $\tilde O(1/\sqrt{T} + 1/\epsilon T)$ on smooth losses in linear time, forming a direct analogy to the classical non-private ``online-to-batch'' conversion. By applying our techniques to more advanced adaptive online algorithms, we produce adaptive differentially private counterparts whose convergence rates depend on apriori unknown variances or parameter norms.

The growing prevalence and computational demands of Artificial Intelligence (AI) workloads has led to widespread use of hardware accelerators in their execution. Scaling the performance of AI accelerators across generations is pivotal to their success in commercial deployments. The intrinsic error-resilient nature of AI workloads present a unique opportunity for performance/energy improvement through precision scaling. Motivated by the recent algorithmic advances in precision scaling for inference and training, we designed RaPiD1, a 4-core AI accelerator chip supporting a spectrum of precisions, namely, 16 and 8-bit floating-point and 4 and 2-bit fixed-point. The 36mm2RaPiD chip fabricated in 7nm EUV technology delivers a peak 3.5 TFLOPS/W in HFP8 mode and 16.5 TOPS/W in INT4 mode at nominal voltage. Using a performance model calibrated to within 1% of the measurement results, we evaluated DNN inference using 4-bit fixed-point representation for a 4-core 1 RaPiD chip system and DNN training using 8-bit floating point representation for a 768 TFLOPs AI system comprising 4 32-core RaPiD chips. Our results show INT4 inference for batch size of 1 achieves 3 - 13.5 (average 7) TOPS/W and FP8 training for a mini-batch of 512 achieves a sustained 102 - 588 (average 203) TFLOPS across a wide range of applications.

We consider the problem of minimizing multi-modal loss functions with a large number of local optima. Since the local gradient points to the direction of the steepest slope in an infinitesimal neighborhood, an optimizer guided by the local gradient is often trapped in a local minimum. To address this issue, we develop a novel nonlocal gradient to skip small local minima by capturing major structures of the loss’s landscape in black-box optimization. The nonlocal gradient is defined by a directional Gaussian smoothing (DGS) approach. The key idea of DGS is to conducts 1D long-range exploration with a large smoothing radius along $d$ orthogonal directions in $R^d$, each of which defines a nonlocal directional derivative as a 1D integral. Such long-range exploration enables the nonlocal gradient to skip small local minima. The $d$ directional derivatives are then assembled to form the nonlocal gradient. We use the Gauss-Hermite quadrature rule to approximate the $d$ 1D integrals to obtain an accurate estimator. The superior performance of our method is demonstrated in three sets of examples, including benchmark functions for global optimization, and two real-world scientific problems.