Some real-world decision-making problems require making probabilistic forecasts over multiple steps at once. However, methods for probabilistic forecasting may fail to capture correlations in the underlying time-series that exist over long time horizons as errors accumulate. One such application is with resource scheduling under uncertainty in a grid environment, which requires forecasting electricity demand that is inherently noisy, but often cyclic. In this paper, we introduce the conditional approximate normalizing flow (CANF) to make probabilistic multi-step time-series forecasts when correlations are present over long time horizons. We first demonstrate our method's efficacy on estimating the density of a toy distribution, finding that CANF improves the KL divergence by one-third compared to that of a Gaussian mixture model while still being amenable to explicit conditioning. We then use a publicly available household electricity consumption dataset to showcase the effectiveness of CANF on joint probabilistic multi-step forecasting. Empirical results show that conditional approximate normalizing flows outperform other methods in terms of multi-step forecast accuracy and lead to up to 10x better scheduling decisions. Our implementation is available at https://github.com/sisl/JointDemandForecasting.
Safe navigation in dense, urban driving environments remains an open problem and an active area of research. Unlike typical predict-thenplan approaches, game-theoretic planning considers how one vehicle's plan will affect the actions of another. Recent work has demonstrated significant improvements in the time required to find local Nash equilibria in general-sum games with nonlinear objectives and constraints. When applied trivially to driving, these works assume all vehicles in a scene play a game together, which can result in intractable computation times for dense traffic. We formulate a decentralized approach to game-theoretic planning by assuming that agents only play games within their observational vicinity, which we believe to be a more reasonable assumption for human driving. Games are played in parallel for all strongly connected components of an interaction graph, significantly reducing the number of players and constraints in each game, and therefore the time required for planning. We demonstrate that our approach can achieve collision-free, efficient driving in urban environments by comparing performance against an adaptation of the Intelligent Driver Model and centralized game-theoretic planning when navigating roundabouts in the INTER-ACTION dataset. Our implementation is available at http://github.com/sisl/DecNashPlanning.
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