Penalised FTRL With Time-Varying Constraints

In this paper we extend the classical Follow-The-Regularized-Leader (FTRL) algorithm to encompass time-varying constraints, through adaptive penalization. We establish sufficient conditions for the proposed Penalized FTRL algorithm to achieve $O(\sqrt{t})$ regret and violation with respect to strong benchmark $\hat{X}^{max}_t$. Lacking prior knowledge of the constraints, this is probably the largest benchmark set that we can reasonably hope for. Our sufficient conditions are necessary in the sense that when they are violated there exist examples where $O(\sqrt{t})$ regret and violation is not achieved. Compared to the best existing primal-dual algorithms, Penalized FTRL substantially extends the class of problems for which $O(\sqrt{t})$ regret and violation performance is achievable.

Lazy Lagrangians with Predictions for Online Learning

We consider the general problem of online convex optimization with time-varying additive constraints in the presence of predictions for the next cost and constraint functions. A novel primal-dual algorithm is designed by combining a Follow-The-Regularized-Leader iteration with prediction-adaptive dynamic steps. The algorithm achieves $\mathcal O(T^{\frac{3-\beta}{4}})$ regret and $\mathcal O(T^{\frac{1+\beta}{2}})$ constraint violation bounds that are tunable via parameter $\beta\!\in\![1/2,1)$ and have constant factors that shrink with the predictions quality, achieving eventually $\mathcal O(1)$ regret for perfect predictions. Our work extends the FTRL framework for this constrained OCO setting and outperforms the respective state-of-the-art greedy-based solutions, without imposing conditions on the quality of predictions, the cost functions or the geometry of constraints, beyond convexity.

Measurement-Based Evaluation Of Google/Apple Exposure Notification API For Proximity Detection in a Commuter Bus

We report on the results of a measurement study carried out on a commuter bus in Dublin, Ireland using the Google/Apple Exposure Notification (GAEN) API. This API is likely to be widely used by Covid-19 contact tracing apps. Measurements were collected between 60 pairs of handset locations and are publicly available. We find that the attenuation level reported by the GAEN API need not increase with distance between handsets, consistent with there being a complex radio environment inside a bus caused by the metal-rich environment. Changing the people holding a pair of handsets, with the location of the handsets otherwise remaining unchanged, can cause variations of +/-10dB in the attenuation level reported by the GAEN API. Applying the rule used by the Swiss Covid-19 contact tracing app to trigger an exposure notification to our bus measurements we find that no exposure notifications would have been triggered despite the fact that all pairs of handsets were within 2m of one another for at least 15 mins. Applying an alternative threshold-based exposure notification rule can somewhat improve performance to a detection rate of 5% when an exposure duration threshold of 15 minutes is used, increasing to 8% when the exposure duration threshold is reduced to 10 mins. Stratifying the data by distance between pairs of handsets indicates that there is only a weak dependence of detection rate on distance.

Coronavirus Contact Tracing: Evaluating The Potential Of Using Bluetooth Received Signal Strength For Proximity Detection

We report on measurements of Bluetooth Low Energy (LE) received signal strength taken on mobile handsets in a variety of common, real-world settings. We note that a key difficulty is obtaining the ground truth as to when people are in close proximity to one another. Knowledge of this ground truth is important for accurately evaluating the accuracy with which contact events are detected by Bluetooth LE. We approach this by adopting a scenario-based approach. In summary, we find that the Bluetooth LE received signal strength can vary substantially depending on the relative orientation of handsets, on absorption by the human body, reflection/absorption of radio signals in buildings and trains. Indeed we observe that the received signal strength need not decrease with increasing distance. This suggests that the development of accurate methods for proximity detection based on Bluetooth LE received signal strength is likely to be challenging. Our measurements also suggest that combining use of Bluetooth LE contact tracing apps with adoption of new social protocols may yield benefits but this requires further investigation. For example, placing phones on the table during meetings is likely to simplify proximity detection using received signal strength. Similarly, carrying handbags with phones placed close to the outside surface. In locations where the complexity of signal propagation makes proximity detection using received signal strength problematic entry/exit from the location might instead be logged in an app by e.g. scanning a time-varying QR code or the like.

Learning The Best Expert Efficiently

We consider online learning problems where the aim is to achieve regret which is efficient in the sense that it is the same order as the lowest regret amongst K experts. This is a substantially stronger requirement that achieving $O(\sqrt{n})$ or $O(\log n)$ regret with respect to the best expert and standard algorithms are insufficient, even in easy cases where the regrets of the available actions are very different from one another. We show that a particular lazy form of the online subgradient algorithm can be used to achieve minimal regret in a number of "easy" regimes while retaining an $O(\sqrt{n})$ worst-case regret guarantee. We also show that for certain classes of problem minimal regret strategies exist for some of the remaining "hard" regimes.