University of Münster

In imperfect-information games with ordered state spaces, cumulative regrets are no longer stored cell by cell for every information set; they are transformed into Haar wavelet coefficients and only the largest are kept. Tabular CFR+ previously grew memory linearly with the game tree under fine discretization, while Deep CFR traded memory for neural inference latency. On Deep-Stack Kuhn poker, growing the state count from one thousand to ten million raised memory only from 0.6 MB to 2.1 MB, a compression ratio above 99.9%; on Flop Hold'em, reaching comparable exploitability took about one-sixth the wall-clock time of Deep CFR.

In imperfect-information games with ordered state spaces, cumulative regrets are no longer stored cell by cell for every information set; they are transformed into Haar wavelet coefficients and only the largest are kept. Tabular CFR+ previously grew memory linearly with the game tree under fine discretization, while Deep CFR traded memory for neural inference latency. On Deep-Stack Kuhn poker, growing the state count from one thousand to ten million raised memory only from 0.6 MB to 2.1 MB, a compression ratio above 99.9%; on Flop Hold'em, reaching comparable exploitability took about one-sixth the wall-clock time of Deep CFR.

Simulation of stochastic hybrid systems previously handled only discrete nondeterministic choices, while an action allowed to fire anywhere in a time interval gives a single state infinitely many options. The new method discretizes each action's time interval separately, learns a scheduler with Q-learning over the finite abstraction, and uses precomputed symbolic reachable states to steer simulation and prune unreachable regions in a correct-by-construction way. On the water tank benchmark the simulation reproduces the maximum reachability probabilities reported by an existing method; on a water tank variant with a low-probability underflow objective, guidance makes learning clearly faster than unguided simulation and yields a reachability probability of at least 45%.

Simulation of stochastic hybrid systems previously handled only discrete nondeterministic choices, while an action allowed to fire anywhere in a time interval gives a single state infinitely many options. The new method discretizes each action's time interval separately, learns a scheduler with Q-learning over the finite abstraction, and uses precomputed symbolic reachable states to steer simulation and prune unreachable regions in a correct-by-construction way. On the water tank benchmark the simulation reproduces the maximum reachability probabilities reported by an existing method; on a water tank variant with a low-probability underflow objective, guidance makes learning clearly faster than unguided simulation and yields a reachability probability of at least 45%.