4,253 research outputs found
Imperfect-Recall Abstractions with Bounds in Games
Imperfect-recall abstraction has emerged as the leading paradigm for
practical large-scale equilibrium computation in incomplete-information games.
However, imperfect-recall abstractions are poorly understood, and only weak
algorithm-specific guarantees on solution quality are known. In this paper, we
show the first general, algorithm-agnostic, solution quality guarantees for
Nash equilibria and approximate self-trembling equilibria computed in
imperfect-recall abstractions, when implemented in the original
(perfect-recall) game. Our results are for a class of games that generalizes
the only previously known class of imperfect-recall abstractions where any
results had been obtained. Further, our analysis is tighter in two ways, each
of which can lead to an exponential reduction in the solution quality error
bound.
We then show that for extensive-form games that satisfy certain properties,
the problem of computing a bound-minimizing abstraction for a single level of
the game reduces to a clustering problem, where the increase in our bound is
the distance function. This reduction leads to the first imperfect-recall
abstraction algorithm with solution quality bounds. We proceed to show a divide
in the class of abstraction problems. If payoffs are at the same scale at all
information sets considered for abstraction, the input forms a metric space.
Conversely, if this condition is not satisfied, we show that the input does not
form a metric space. Finally, we use these results to experimentally
investigate the quality of our bound for single-level abstraction
Theoretical and Practical Advances on Smoothing for Extensive-Form Games
Sparse iterative methods, in particular first-order methods, are known to be
among the most effective in solving large-scale two-player zero-sum
extensive-form games. The convergence rates of these methods depend heavily on
the properties of the distance-generating function that they are based on. We
investigate the acceleration of first-order methods for solving extensive-form
games through better design of the dilated entropy function---a class of
distance-generating functions related to the domains associated with the
extensive-form games. By introducing a new weighting scheme for the dilated
entropy function, we develop the first distance-generating function for the
strategy spaces of sequential games that has no dependence on the branching
factor of the player. This result improves the convergence rate of several
first-order methods by a factor of , where is the branching
factor of the player, and is the depth of the game tree.
Thus far, counterfactual regret minimization methods have been faster in
practice, and more popular, than first-order methods despite their
theoretically inferior convergence rates. Using our new weighting scheme and
practical tuning we show that, for the first time, the excessive gap technique
can be made faster than the fastest counterfactual regret minimization
algorithm, CFR+, in practice
The Complexity of Synthesizing Uniform Strategies
We investigate uniformity properties of strategies. These properties involve
sets of plays in order to express useful constraints on strategies that are not
\mu-calculus definable. Typically, we can state that a strategy is
observation-based. We propose a formal language to specify uniformity
properties, interpreted over two-player turn-based arenas equipped with a
binary relation between plays. This way, we capture e.g. games with winning
conditions expressible in epistemic temporal logic, whose underlying
equivalence relation between plays reflects the observational capabilities of
agents (for example, synchronous perfect recall). Our framework naturally
generalizes many other situations from the literature. We establish that the
problem of synthesizing strategies under uniformity constraints based on
regular binary relations between plays is non-elementary complete.Comment: In Proceedings SR 2013, arXiv:1303.007
A marriage between adversarial team games and 2-player games: enabling abstractions, no-regret learning, and subgame solving
Ex ante correlation is becoming the mainstream approach for sequential adversarial team games,where a team of players faces another team in a
zero-sum game. It is known that team members’asymmetric information makes both equilibrium computation APX-hard and team’s strategies not
directly representable on the game tree. This latter issue prevents the adoption of successful tools for huge 2-player zero-sum games such as,
e.g., abstractions, no-regret learning, and sub game solving. This work shows that we can re cover from this weakness by bridging the gap be tween sequential adversarial team games and 2-player games. In particular, we propose a new,suitable game representation that we call team public-information, in which a team is repre sented as a single coordinator who only knows information common to the whole team and pre scribes to each member an action for any pos sible private state. The resulting representation is highly explainable, being a 2-player tree in
which the team’s strategies are behavioral with a direct interpretation and more expressive than he original extensive form when designing ab stractions. Furthermore, we prove payoff equiva lence of our representation, and we provide tech niques that, starting directly from the extensive form, generate dramatically more compact repre sentations without information loss. Finally, we experimentally evaluate our techniques when ap plied to a standard testbed, comparing their per formance with the current state of the art
Public Information Representation for Adversarial Team Games
The peculiarity of adversarial team games resides in the asymmetric
information available to the team members during the play, which makes the
equilibrium computation problem hard even with zero-sum payoffs. The algorithms
available in the literature work with implicit representations of the strategy
space and mainly resort to Linear Programming and column generation techniques
to enlarge incrementally the strategy space. Such representations prevent the
adoption of standard tools such as abstraction generation, game solving, and
subgame solving, which demonstrated to be crucial when solving huge, real-world
two-player zero-sum games. Differently from these works, we answer the question
of whether there is any suitable game representation enabling the adoption of
those tools. In particular, our algorithms convert a sequential team game with
adversaries to a classical two-player zero-sum game. In this converted game,
the team is transformed into a single coordinator player who only knows
information common to the whole team and prescribes to the players an action
for any possible private state. Interestingly, we show that our game is more
expressive than the original extensive-form game as any state/action
abstraction of the extensive-form game can be captured by our representation,
while the reverse does not hold. Due to the NP-hard nature of the problem, the
resulting Public Team game may be exponentially larger than the original one.
To limit this explosion, we provide three algorithms, each returning an
information-lossless abstraction that dramatically reduces the size of the
tree. These abstractions can be produced without generating the original game
tree. Finally, we show the effectiveness of the proposed approach by presenting
experimental results on Kuhn and Leduc Poker games, obtained by applying
state-of-art algorithms for two-player zero-sum games on the converted gamesComment: 19 pages, 7 figures, Best Paper Award in Cooperative AI Workshop at
NeurIPS 202
Using a high-level language to build a poker playing agent
Tese de mestrado integrado. Engenharia Informática e Computação. Faculdade de Engenharia. Universidade do Porto. 200
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