281 research outputs found
Thick Subtrees, Games and Experiments
Abstract. We relate the dynamic semantics (games, dealing with interactions) and the static semantics (dealing with results of interactions) of linear logic with polarities, in the spirit of Timeless Game
(Mechanical) Reasoning on Infinite Extensive Games
In order to better understand reasoning involved in analyzing infinite games
in extensive form, we performed experiments in the proof assistant Coq that are
reported here.Comment: 11
Behavior Trees in Robotics and AI: An Introduction
A Behavior Tree (BT) is a way to structure the switching between different
tasks in an autonomous agent, such as a robot or a virtual entity in a computer
game. BTs are a very efficient way of creating complex systems that are both
modular and reactive. These properties are crucial in many applications, which
has led to the spread of BT from computer game programming to many branches of
AI and Robotics. In this book, we will first give an introduction to BTs, then
we describe how BTs relate to, and in many cases generalize, earlier switching
structures. These ideas are then used as a foundation for a set of efficient
and easy to use design principles. Properties such as safety, robustness, and
efficiency are important for an autonomous system, and we describe a set of
tools for formally analyzing these using a state space description of BTs. With
the new analysis tools, we can formalize the descriptions of how BTs generalize
earlier approaches. We also show the use of BTs in automated planning and
machine learning. Finally, we describe an extended set of tools to capture the
behavior of Stochastic BTs, where the outcomes of actions are described by
probabilities. These tools enable the computation of both success probabilities
and time to completion
Collaboration in Social Networks
The very notion of social network implies that linked individuals interact
repeatedly with each other. This allows them not only to learn successful
strategies and adapt to them, but also to condition their own behavior on the
behavior of others, in a strategic forward looking manner. Game theory of
repeated games shows that these circumstances are conducive to the emergence of
collaboration in simple games of two players. We investigate the extension of
this concept to the case where players are engaged in a local contribution game
and show that rationality and credibility of threats identify a class of Nash
equilibria -- that we call "collaborative equilibria" -- that have a precise
interpretation in terms of sub-graphs of the social network. For large network
games, the number of such equilibria is exponentially large in the number of
players. When incentives to defect are small, equilibria are supported by local
structures whereas when incentives exceed a threshold they acquire a non-local
nature, which requires a "critical mass" of more than a given fraction of the
players to collaborate. Therefore, when incentives are high, an individual
deviation typically causes the collapse of collaboration across the whole
system. At the same time, higher incentives to defect typically support
equilibria with a higher density of collaborators. The resulting picture
conforms with several results in sociology and in the experimental literature
on game theory, such as the prevalence of collaboration in denser groups and in
the structural hubs of sparse networks
On Monte-Carlo tree search for deterministic games with alternate moves and complete information
We consider a deterministic game with alternate moves and complete
information, of which the issue is always the victory of one of the two
opponents. We assume that this game is the realization of a random model
enjoying some independence properties. We consider algorithms in the spirit of
Monte-Carlo Tree Search, to estimate at best the minimax value of a given
position: it consists in simulating, successively, well-chosen matches,
starting from this position. We build an algorithm, which is optimal, step by
step, in some sense: once the first matches are simulated, the algorithm
decides from the statistics furnished by the first matches (and the a
priori we have on the game) how to simulate the -th match in such a way
that the increase of information concerning the minimax value of the position
under study is maximal. This algorithm is remarkably quick. We prove that our
step by step optimal algorithm is not globally optimal and that it always
converges in a finite number of steps, even if the a priori we have on the game
is completely irrelevant. We finally test our algorithm, against MCTS, on
Pearl's game and, with a very simple and universal a priori, on the games
Connect Four and some variants. The numerical results are rather disappointing.
We however exhibit some situations in which our algorithm seems efficient
Glueability of Resource Proof-Structures: Inverting the Taylor Expansion
A Multiplicative-Exponential Linear Logic (MELL) proof-structure can be expanded into a set of resource proof-structures: its Taylor expansion. We introduce a new criterion characterizing those sets of resource proof-structures that are part of the Taylor expansion of some MELL proof-structure, through a rewriting system acting both on resource and MELL proof-structures
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