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Sequential posted pricing auctions are popular because of their simplicity in practice and their tractability in theory. A usual assumption in their study is that the Bayesian prior distributions of the buyers are known to the seller, while in reality these priors can only be accessed from historical data. To overcome this assumption, we study sequential posted pricing in the bandit learning model, where the seller interacts with n buyers over T rounds: In each round the seller posts n prices for the n buyers and the first buyer with a valuation higher than the price takes the item. The only feedback that the seller receives in each round is the revenue. Our main results obtain nearly-optimal regret bounds for single-item sequential posted pricing in the bandit learning model. In particular, we achieve an Õ (𝗉𝗈𝗅𝗒(n)T‾^{1/2}) regret for buyers with (Myerson's) regular distributions and an Õ (𝗉𝗈𝗅𝗒(n)T^{2/3}) regret for buyers with general distributions, both of which are tight in the number of rounds T. Our result for regular distributions was previously not known even for the single-buyer setting and relies on a new half-concavity property of the revenue function in the value space. For n sequential buyers, our technique is to run a generalized single-buyer algorithm for all the buyers and to carefully bound the regret from the sub-optimal pricing of the suffix buyers. 

We demonstrate an optical fiber sensor that uses the orbital angular momentum of light in a polarization maintaining fiber to act as a temperature and force sensor. The polarization of the input light is shown to greatly affect the sensitivity of the sensor. In addition, we show how our sensor can be used to resolve the direction and magnitude of a force applied to a fiber.

 

Accurate flood forecasting and efficient emergency response operations are vital, especially in the case of urban flash floods. The dense distribution of power lines in urban areas significantly impacts search and rescue operations during extreme flood events. However, no existing emergency response frameworks have incorporated the impacts of overhead power lines on lifeboat rescue operations. This study aims to determine the necessity and feasibility of incorporating overhead power line information into an emergency response framework using Manville, New Jersey during Hurricane Ida as a test bed. We propose an integrated framework, which includes a building-scale flood model, urban point cloud data, a human vulnerability model, and network analysis, to simulate rescue operation feasibility during Hurricane Ida. Results reveal that during the most severe point of the flood event, 46% of impacted buildings became nonrescuable due to complete isolation from the road network, and a significant 67.7% of the municipality’s areas that became dangerous for pedestrians also became inaccessible to rescue boats due to overhead power line obstruction. Additionally, we identify a continuous 10-hour period during which an average of 43.4% of the 991 impacted buildings faced complete isolation. For these structures, early evacuation emerges as the sole means to prevent isolation. This research highlights the pressing need to consider overhead power lines in emergency response planning to ensure more effective and targeted flood resilience measures for urban areas facing increasingly frequent extreme precipitation events. 

The Prophet Inequality and Pandora's Box problems are fundamental stochastic problem with applications in Mechanism Design, Online Algorithms, Stochastic Optimization, Optimal Stopping, and Operations Research. A usual assumption in these works is that the probability distributions of the n underlying random variables are given as input to the algorithm. Since in practice these distributions need to be learned under limited feedback, we initiate the study of such stochastic problems in the Multi-Armed Bandits model. In the Multi-Armed Bandits model we interact with n unknown distributions over T rounds: in round t we play a policy x(t) and only receive the value of x(t) as feedback. The goal is to minimize the regret, which is the difference over T rounds in the total value of the optimal algorithm that knows the distributions vs. the total value of our algorithm that learns the distributions from the limited feedback. Our main results give near-optimal Õ (poly (n) √T) total regret algorithms for both Prophet Inequality and Pandora's Box. Our proofs proceed by maintaining confidence intervals on the unknown indices of the optimal policy. The exploration-exploitation tradeoff prevents us from directly refining these confidence intervals, so the main technique is to design a regret upper bound function that is learnable while playing low-regret Bandit policies.