Expanding the Resolution Boundary of Outcome-Based Imperfect-Recall Abstraction in Games with Ordered Signals
arxiv(2024)
摘要
In the development of advanced Texas Hold'em AI systems, abstraction
technology has garnered widespread attention due to its significant effect in
simplifying game complexity. This study adopts a more specific model, the games
of ordered signal, to describe Texas Hold'em-style games and optimizes this
model to streamline its mathematical representation and broaden its
applicability. By transitioning from a broad imperfect information game model
to a game with ordered signals model, we have separated the previously
intertwined infoset abstraction and action abstraction into independent signal
abstraction and action abstraction. Importantly, this signal abstraction
provides a mathematical framework for the hand abstraction task, which is
emphatically discussed in this paper. Additionally, a novel common refinement
principle is introduced, revealing the limit performance of hand abstraction
algorithms. We introduce potential outcome isomorphism (POI) and pinpoint that
it suffers from the issue of excessive abstraction. Futher, We demonstrate that
POI serves as a common refinement for leading outcome-based hand abstraction
algorithms, such as E[HS] and PA&PAEMD. Consequently, excessive abstraction
also inherently affects these algorithms, leading to suboptimal performance.
Our investigation reveals the omission of historical data as a primary
contributor to excessive abstraction. To remedy this, we propose the K-Recall
Outcome Isomorphism (KROI) to incorporate the missing information. Compared
with POI, KROI more accurately mirrors lossless isomorphism (LI), the ground
truth, offering enhanced signal abstraction resolution. Experimental results in
the Numeral211 Hold'em indicate that strategies developed through KROI
approximate the exploitability of those developed through LI more closely than
those trained through POI.
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