Chasing Convex Functions with Long-term Constraints

We introduce and study a family of online metric problems with long-term constraints. In these problems, an online player makes decisions $\mathbf{x}_t$ in a metric space $(X,d)$ to simultaneously minimize their hitting cost $f_t(\mathbf{x}_t)$ and switching cost as determined by the metric. Over the time horizon $T$, the player must satisfy a long-term demand constraint $\sum_{t} c(\mathbf{x}_t) \geq 1$, where $c(\mathbf{x}_t)$ denotes the fraction of demand satisfied at time $t$. Such problems can find a wide array of applications to online resource allocation in sustainable energy and computing systems. We devise optimal competitive and learning-augmented algorithms for specific instantiations of these problems, and further show that our proposed algorithms perform well in numerical experiments.

Online Conversion with Switching Costs: Robust and Learning-Augmented Algorithms

We introduce and study online conversion with switching costs, a family of online problems that capture emerging problems at the intersection of energy and sustainability. In this problem, an online player attempts to purchase (alternatively, sell) fractional shares of an asset during a fixed time horizon with length $T$. At each time step, a cost function (alternatively, price function) is revealed, and the player must irrevocably decide an amount of asset to convert. The player also incurs a switching cost whenever their decision changes in consecutive time steps, i.e., when they increase or decrease their purchasing amount. We introduce competitive (robust) threshold-based algorithms for both the minimization and maximization variants of this problem, and show they are optimal among deterministic online algorithms. We then propose learning-augmented algorithms that take advantage of untrusted black-box advice (such as predictions from a machine learning model) to achieve significantly better average-case performance without sacrificing worst-case competitive guarantees. Finally, we empirically evaluate our proposed algorithms using a carbon-aware EV charging case study, showing that our algorithms substantially improve on baseline methods for this problem.

Time Fairness in Online Knapsack Problems

The online knapsack problem is a classic problem in the field of online algorithms. Its canonical version asks how to pack items of different values and weights arriving online into a capacity-limited knapsack so as to maximize the total value of the admitted items. Although optimal competitive algorithms are known for this problem, they may be fundamentally unfair, i.e., individual items may be treated inequitably in different ways. Inspired by recent attention to fairness in online settings, we develop a natural and practically-relevant notion of time fairness for the online knapsack problem, and show that the existing optimal algorithms perform poorly under this metric. We propose a parameterized deterministic algorithm where the parameter precisely captures the Pareto-optimal trade-off between fairness and competitiveness. We show that randomization is theoretically powerful enough to be simultaneously competitive and fair; however, it does not work well in practice, using trace-driven experiments. To further improve the trade-off between fairness and competitiveness, we develop a fair, robust (competitive), and consistent learning-augmented algorithm with substantial performance improvement in trace-driven experiments.

FlowSense: Monitoring Airflow in Building Ventilation Systems Using Audio Sensing

Proper indoor ventilation through buildings' heating, ventilation, and air conditioning (HVAC) systems has become an increasing public health concern that significantly impacts individuals' health and safety at home, work, and school. While much work has progressed in providing energy-efficient and user comfort for HVAC systems through IoT devices and mobile-sensing approaches, ventilation is an aspect that has received lesser attention despite its importance. With a motivation to monitor airflow from building ventilation systems through commodity sensing devices, we present FlowSense, a machine learning-based algorithm to predict airflow rate from sensed audio data in indoor spaces. Our ML technique can predict the state of an air vent-whether it is on or off-as well as the rate of air flowing through active vents. By exploiting a low-pass filter to obtain low-frequency audio signals, we put together a privacy-preserving pipeline that leverages a silence detection algorithm to only sense for sounds of air from HVAC air vent when no human speech is detected. We also propose the Minimum Persistent Sensing (MPS) as a post-processing algorithm to reduce interference from ambient noise, including ongoing human conversation, office machines, and traffic noises. Together, these techniques ensure user privacy and improve the robustness of FlowSense. We validate our approach yielding over 90% accuracy in predicting vent status and 0.96 MSE in predicting airflow rate when the device is placed within 2.25 meters away from an air vent. Additionally, we demonstrate how our approach as a mobile audio-sensing platform is robust to smartphone models, distance, and orientation. Finally, we evaluate FlowSense privacy-preserving pipeline through a user study and a Google Speech Recognition service, confirming that the audio signals we used as input data are inaudible and inconstructible.