Safe Learning for Near Optimal Scheduling

In this paper, we investigate the combination of synthesis, model-based learning, and online sampling techniques to obtain safe and near-optimal schedulers for a preemptible task scheduling problem. Our algorithms can handle Markov decision processes (MDPs) that have 1020 states and beyond which cannot be handled with state-of-the art probabilistic model-checkers. We provide probably approximately correct (PAC) guarantees for learning the model. Additionally, we extend Monte-Carlo tree search with advice, computed using safety games or obtained using the earliest-deadline-first scheduler, to safely explore the learned model online. Finally, we implemented and compared our algorithms empirically against shielded deep Q-learning on large task systems

Scheduling for Urban Air Mobility using Safe Learning

This work considers the scheduling problem for Urban Air Mobility (UAM) vehicles travelling between origin-destination pairs with both hard and soft trip deadlines. Each route is described by a discrete probability distribution over trip completion times (or delay) and over inter-arrival times of requests (or demand) for the route along with a fixed hard or soft deadline. Soft deadlines carry a cost that is incurred when the deadline is missed. An online, safe scheduler is developed that ensures that hard deadlines are never missed, and that average cost of missing soft deadlines is minimized. The system is modelled as a Markov Decision Process (MDP) and safe model-based learning is used to find the probabilistic distributions over route delays and demand. Monte Carlo Tree Search (MCTS) Earliest Deadline First (EDF) is used to safely explore the learned models in an online fashion and develop a near-optimal non-preemptive scheduling policy. These results are compared with Value Iteration (VI) and MCTS (Random) scheduling solutions.Comment: In Proceedings FMAS2022 ASYDE2022, arXiv:2209.1318

Learning Algorithms for Minimizing Queue Length Regret

We consider a system consisting of a single transmitter/receiver pair and $N$ channels over which they may communicate. Packets randomly arrive to the transmitter's queue and wait to be successfully sent to the receiver. The transmitter may attempt a frame transmission on one channel at a time, where each frame includes a packet if one is in the queue. For each channel, an attempted transmission is successful with an unknown probability. The transmitter's objective is to quickly identify the best channel to minimize the number of packets in the queue over $T$ time slots. To analyze system performance, we introduce queue length regret, which is the expected difference between the total queue length of a learning policy and a controller that knows the rates, a priori. One approach to designing a transmission policy would be to apply algorithms from the literature that solve the closely-related stochastic multi-armed bandit problem. These policies would focus on maximizing the number of successful frame transmissions over time. However, we show that these methods have $\Omega(\log{T})$ queue length regret. On the other hand, we show that there exists a set of queue-length based policies that can obtain order optimal $O(1)$ queue length regret. We use our theoretical analysis to devise heuristic methods that are shown to perform well in simulation.Comment: 28 Pages, 11 figure