Regret minimization in repeated matrix games with variable stage duration

Online Learning with Variable Stage Duration

We consider online learning in repeated decision problems, within the framework of a repeated game against an arbitrary opponent. For repeated matrix games, well known results establish the existence of no-regret strategies; such strategies secure a long-term average payoff that comes close to the maximal payoff that could be obtained, in hindsight, by playing any fixed action against the obser...

Regret Minimization in Signal Space for Repeated Matrix Games with Partial Observations

Logarithmic Regret Algorithms for Strongly Convex Repeated Games

Many problems arising in machine learning can be cast as a convex optimization problem, in which a sum of a loss term and a regularization term is minimized. For example, in Support Vector Machines the loss term is the average hinge-loss of a vector over a training set of examples and the regularization term is the squared Euclidean norm of this vector. In this paper we study an algorithmic fra...

Efficient Regret Minimization in Non-Convex Games

We consider regret minimization in repeated games with non-convex loss functions. Minimizing the standard notion of regret is computationally intractable. Thus, we define a natural notion of regret which permits efficient optimization and generalizes offline guarantees for convergence to an approximate local optimum. We give gradient-based methods that achieve optimal regret, which in turn guar...

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 –. In this paper, we investigate iterated regret minimization for infinite duration two-player qu...