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  1. Free, publicly-accessible full text available May 31, 2024
  2. Fang, F. (Ed.)
  3. Fang, F. (Ed.)
  4. We consider a prototypical path planning problem on a graph with uncertain cost of mobility on its edges. At a given node, the planning agent can access the true cost for edges to its neighbors and uses a noisy simulator to estimate the cost-to-go from the neighboring nodes. The objective of the planning agent is to select a neighboring node such that, with high probability, the cost-to-go is minimized for the worst possible realization of uncertain parameters in the simulator. By modeling the cost-to-go as a Gaussian process (GP) for every realization of the uncertain parameters, we apply a scenario approach in which we draw fixed independent samples of the uncertain parameter. We present a scenario-based iterative algorithm using the upper confidence bound (UCB) of the fixed independent scenarios to compute the choice of the neighbor to go to. We characterize the performance of the proposed algorithm in terms of a novel notion of regret defined with respect to an additional draw of the uncertain parameter, termed as scenario regret under re-draw. In particular, we characterize a high probability upper bound on the regret under re-draw for any finite number of iterations of the algorithm, and show that this upper bound tends to zero asymptotically with the number of iterations. We supplement our analysis with numerical results. 
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