CHARDA: Causal Hybrid Automata Recovery via Dynamic Analysis

Abstract

We propose and evaluate a new technique for learning hybrid automata automatically by observing the runtime behavior of a dynamical system. Working from a sequence of continuous state values and predicates about the environment, CHARDA recovers the distinct dynamic modes, learns a model for each mode from a given set of templates, and postulates causal guard conditions which trigger transitions between modes. Our main contribution is the use of information-theoretic measures (1) as a cost function for data segmentation and model selection to penalize over-fitting and (2) to determine the likely causes of each transition. CHARDA is easily extended with different classes of model templates, fitting methods, or predicates. In our experiments on a complex videogame character, CHARDA successfully discovers a reasonable over-approximation of the character's true behaviors. Our results also compare favorably against recent work in automatically learning probabilistic timed automata in an aircraft domain: CHARDA exactly learns the modes of these simpler automata.

Refining operational logics

“…As an example of the bene ts of this approach, the authors have seen productive connections between the theory of hybrid automata (a combination of nite state machines and switched systems of di erential equations) [1] and graphical logic games; this has led to work both in modeling languages (as in Fig. 3) and in reverse-engineering game mechanics [16], recovering hybrid automata speci cations from game characters [17], and automatically mapping game levels (as in Fig. 4) from observations of game play [12].…”

“…ideas [3,21] and a variety of projects in player/game modeling and generation [4,6,7,[16][17][18]. e key move in all these cases has been to step away from considering games as bags of mechanics and towards viewing them as assemblages of abstract operations from diverse logics.…”

Automated game design learning

“…If we also have access to player inputs (e.g. a timed sequence of button presses), we can attempt causal reasoning, blaming changes in character behavior on player actions [52]. Sometimes we can observe the game's internal runtime behavior including its memory address space or, for games run in emulation, the states of memory and registers of the emulated hardware [53].…”

“…MARIO [53] assumes a per-character state machine structure and ignores collisions, learning only parameters on the physics equations associated with each state; CHARDA [52] generalizes this to learn state machine structure and physics parameters, with collisions being among the possible causes for transitions between discrete states (along with the axis and button inputs of input logics). A reasonable extension for games like Mega Man or Metroid where some behaviors require and expend a resource like health or ammunition would be to incorporate resource transactions as a possible set of effects (and augment our causal language with resource availability); such resources can generally be treated abstractly as full, sufficient, or insufficient for particular outcomes, and these qualitative constraints should be straightforward to learn.…”

Membership-Based Synthesis of Linear Hybrid Automata

“…This strict separation inherently makes their approach offline. The work by Summerville et al based on least-squares regression requires an exhaustive construction of all possible models for later optimizing a cost function over all of them [20]. Lamrani et al learn a completely deterministic model with urgent transitions using ideas from information theory [12].…”