The recent advances in Machine Learning and high-dimensional gradient-based optimization has led to increased interest in the question of whether we can use such methods to optimize the design of future detectors for high-level physics objectives. However this program faces a fundamental obstacle: The quality of a detector design must be judged on the physics inference it enables, but both simulation and reconstruction of events are to a large degree described by discrete and thus naively non-differentiable stochastic branching (e.g. particle showers, ) and clustering processes (e.g. jet algorithms). In this work we explore the use of gradient estimation techniques based on differentiable and probabilistic programming that provide sufficiently stable estimates such that they may be used in an optimization loop. We showcase the effectiveness of such methods in benchmark scenarios ranging from a few to many thousands of optimizable parameters and discuss current limitations and future directions.
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