Scalable high-precision reachable set estimation in high-dimensional settings

Develop scalable algorithms and improved sample complexity bounds to estimate, with high precision, the reachable sets of measurement values for dialogue processes with generative models under coarse-grained (gamma-quantized) reachability, particularly when the measurement-value space is high-dimensional or intrinsically complex. Specifically, mitigate the poor scaling of the current Monte Carlo PAC reachability bound with respect to the covering number of the quantized measurement-value space to enable practical estimation in such settings.

Background

The GenCtrl framework introduces Monte Carlo algorithms with PAC guarantees to estimate reachable and controllable sets for generative models in dialogue processes. For continuous-valued attributes, the approach relies on gamma-quantization of the measurement-value space, and the sample complexity depends on the covering number of this space.

While intrinsic dimension can sometimes reduce the effective complexity, the authors note that the proposed reachability bound does not scale well when the reachable set is intrinsically complex and high precision is required. They emphasize that achieving practical, high-precision estimation in high-dimensional settings remains challenging broadly across reachability analysis, citing prior work that highlights similar difficulties in high-dimensional scenarios.