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In a recent work, Moshkovitz [FOCS '14] presented a transformation on two-player games called ``fortification'', and gave an elementary proof of an (exponential decay) parallel repetition theorem for fortified two-player projection games. In this paper, we give an \emph{analytic reformulation} of Moshkovitz's fortification framework, which was originally cast in combinatorial terms. This reformulation allows us to expand the scope of the fortification method to new settings. First, we show \emph{any} game (not just projection games) can be fortified, and give a simple proof of parallel repetition for general fortified games. Then, we prove parallel repetition and fortification theorems for games with players sharing quantum entanglement, as well as games with more than two players. This gives a new gap amplification method for general games in the quantum and multiplayer settings, two problems which have recently received much attention. An important component of our work is a variant of the fortification transformation, called ``ordered fortification", that preserves the entangled value of a game. The original fortification of Moshkovitz does not in general preserve the entangled value of a game, and this was a barrier to extending the fortification framework to the quantum setting.
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A Continuous Information Gain Measure to Find the Most Discriminatory Problems for AI Benchmarking
This paper introduces an information-theoretic method for selecting a subset of problems which gives the most information about a group of problem-solving algorithms. This method was tested on the games in the General Video Game AI (GVGAI) framework, allowing us to identify a smaller set of games that still gives a large amount of information about the abilities of different game-playing agents. This approach can be used to make agent testing more efficient. We can achieve almost as good discriminatory accuracy when testing on only a handful of games as when testing on more than a hundred games, something which is often computationally infeasible. Furthermore, this method can be extended to study the dimensions of the effective variance in game design between these games, allowing us to identify which games differentiate between agents in the most complementary ways.
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- Award ID(s):
- 1717324
- PAR ID:
- 10231871
- Date Published:
- Journal Name:
- IEEE Congress on Evolutionary Computation
- Page Range / eLocation ID:
- 1 to 8
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/CEC48606.2020.9185834
