Decentralized Stochastic Nonconvex Optimization under the Relaxed Smoothness

This paper studies decentralized optimization problem $f(\mathbf{x})=\frac{1}{m}\sum_{i=1}^m f_i(\mathbf{x})$, where each local function has the form of $f_i(\mathbf{x}) = {\mathbb E}\left[F(\mathbf{x};{\xi}_i)\right]$ which is $(L_0,L_1)$-smooth but possibly nonconvex and the random variable ${\xi}_i$ follows distribution ${\mathcal D}_i$. We propose a novel algorithm called decentralized normalized stochastic gradient descent (DNSGD), which can achieve the $\epsilon$-stationary point on each local agent. We present a new framework for analyzing decentralized first-order methods in the relaxed smooth setting, based on the Lyapunov function related to the product of the gradient norm and the consensus error. The analysis shows upper bounds on sample complexity of ${\mathcal O}(m^{-1}(L_f\sigma^2\Delta_f\epsilon^{-4} + \sigma^2\epsilon^{-2} + L_f^{-2}L_1^3\sigma^2\Delta_f\epsilon^{-1} + L_f^{-2}L_1^2\sigma^2))$ per agent and communication complexity of $\tilde{\mathcal O}((L_f\epsilon^{-2} + L_1\epsilon^{-1})\gamma^{-1/2}\Delta_f)$, where $L_f=L_0 +L_1\zeta$, $\sigma^2$ is the variance of the stochastic gradient, $\Delta_f$ is the initial optimal function value gap, $\gamma$ is the spectral gap of the network, and $\zeta$ is the degree of the gradient dissimilarity. In the special case of $L_1=0$, the above results (nearly) match the lower bounds on decentralized nonconvex optimization in the standard smooth setting. We also conduct numerical experiments to show the empirical superiority of our method.

A computer vision-based model for occupancy detection using low-resolution thermal images

Occupancy plays an essential role in influencing the energy consumption and operation of heating, ventilation, and air conditioning (HVAC) systems. Traditional HVAC typically operate on fixed schedules without considering occupancy. Advanced occupant-centric control (OCC) adopted occupancy status in regulating HVAC operations. RGB images combined with computer vision (CV) techniques are widely used for occupancy detection, however, the detailed facial and body features they capture raise significant privacy concerns. Low-resolution thermal images offer a non-invasive solution that mitigates privacy issues. The study developed an occupancy detection model utilizing low-resolution thermal images and CV techniques, where transfer learning was applied to fine-tune the You Only Look Once version 5 (YOLOv5) model. The developed model ultimately achieved satisfactory performance, with precision, recall, mAP50, and mAP50 values approaching 1.000. The contributions of this model lie not only in mitigating privacy concerns but also in reducing computing resource demands.