Yujie Tang

Huaiyi Mu, Yujie Tang, Jie Song et al.

This paper investigates distributed zeroth-order optimization for smooth nonconvex problems, targeting the trade-off between convergence rate and sampling cost per zeroth-order gradient estimation in current algorithms that use either the $2$-point or $2d$-point gradient estimators. We propose a novel variance-reduced gradient estimator that either randomly renovates a single orthogonal direction of the true gradient or calculates the gradient estimation across all dimensions for variance correction, based on a Bernoulli distribution. Integrating this estimator with gradient tracking mechanism allows us to address the trade-off. We show that the oracle complexity of our proposed algorithm is upper bounded by $O(d/ε)$ for smooth nonconvex functions and by $O(dκ\ln (1/ε))$ for smooth and gradient dominated nonconvex functions, where $d$ denotes the problem dimension and $κ$ is the condition number. Numerical simulations comparing our algorithm with existing methods confirm the effectiveness and efficiency of the proposed gradient estimator.

Yujie Tang, Liang Hu, Qingrui Zhang et al.

Inertial measurement units are widely used in different fields to estimate the attitude. Many algorithms have been proposed to improve estimation performance. However, most of them still suffer from 1) inaccurate initial estimation, 2) inaccurate initial filter gain, and 3) non-Gaussian process and/or measurement noise. In this paper, we leverage reinforcement learning to compensate for the classical extended Kalman filter estimation, i.e., to learn the filter gain from the sensor measurements. We also analyse the convergence of the estimate error. The effectiveness of the proposed algorithm is validated on both simulated data and real data.