3,390 research outputs found
Iterated Regret Minimization in Game Graphs
Iterated regret minimization has been introduced recently by J.Y. Halpern and
R. Pass in classical strategic games. For many games of interest, this new
solution concept provides solutions that are judged more reasonable than
solutions offered by traditional game concepts -- such as Nash equilibrium --.
Although computing iterated regret on explicit matrix game is conceptually and
computationally easy, nothing is known about computing the iterated regret on
games whose matrices are defined implicitly using game tree, game DAG or, more
generally game graphs. In this paper, we investigate iterated regret
minimization for infinite duration two-player quantitative non-zero sum games
played on graphs.
We consider reachability objectives that are not necessarily antagonist.
Edges are weighted by integers -- one for each player --, and the payoffs are
defined by the sum of the weights along the paths. Depending on the class of
graphs, we give either polynomial or pseudo-polynomial time algorithms to
compute a strategy that minimizes the regret for a fixed player. We finally
give algorithms to compute the strategies of the two players that minimize the
iterated regret for trees, and for graphs with strictly positive weights only.Comment: 19 pages. Bug in introductive example fixed
Positive multi-criteria models in agriculture for energy and environmental policy analysis
Environmental consciousness and accompanying actions have been paralleled by the evolution of multi-criteria methods which have provided tools to assist policy makers in discovering compromises in order to muddle through. This paper recalls the development of multi-criteria methods in agriculture, focusing on their contribution to produce input or output functions useful for environmental and/or energy policy. Response curves generated by MC models can more accurately predict farmersâ response to market and policy parameters compared with classic profit maximizing behavior. Concrete examples from recent literature illustrate the above statements and ideas for further research are provided.multi-criteria models, interval programming, supply curves, bio-energy, policy analysis
Private Multiplicative Weights Beyond Linear Queries
A wide variety of fundamental data analyses in machine learning, such as
linear and logistic regression, require minimizing a convex function defined by
the data. Since the data may contain sensitive information about individuals,
and these analyses can leak that sensitive information, it is important to be
able to solve convex minimization in a privacy-preserving way.
A series of recent results show how to accurately solve a single convex
minimization problem in a differentially private manner. However, the same data
is often analyzed repeatedly, and little is known about solving multiple convex
minimization problems with differential privacy. For simpler data analyses,
such as linear queries, there are remarkable differentially private algorithms
such as the private multiplicative weights mechanism (Hardt and Rothblum, FOCS
2010) that accurately answer exponentially many distinct queries. In this work,
we extend these results to the case of convex minimization and show how to give
accurate and differentially private solutions to *exponentially many* convex
minimization problems on a sensitive dataset
Trend Detection based Regret Minimization for Bandit Problems
We study a variation of the classical multi-armed bandits problem. In this
problem, the learner has to make a sequence of decisions, picking from a fixed
set of choices. In each round, she receives as feedback only the loss incurred
from the chosen action. Conventionally, this problem has been studied when
losses of the actions are drawn from an unknown distribution or when they are
adversarial. In this paper, we study this problem when the losses of the
actions also satisfy certain structural properties, and especially, do show a
trend structure. When this is true, we show that using \textit{trend
detection}, we can achieve regret of order with
respect to a switching strategy for the version of the problem where a single
action is chosen in each round and when actions
are chosen each round. This guarantee is a significant improvement over the
conventional benchmark. Our approach can, as a framework, be applied in
combination with various well-known bandit algorithms, like Exp3. For both
versions of the problem, we give regret guarantees also for the
\textit{anytime} setting, i.e. when the length of the choice-sequence is not
known in advance. Finally, we pinpoint the advantages of our method by
comparing it to some well-known other strategies
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