We study two-player zero-sum games over infinite-state graphs with boundedness conditions. Our first contribution is about the strategy complexity, i.e the memory required for winning strategies: we prove that over general infinite-state graphs, memoryless strategies are sufficient for finitary Büchi games, and finite-memory suffices for finitary parity games. We then study pushdown boundedness...

X iv :0 70 9. 42 29 v1 [ m at h. FA ] 2 6 Se p 20 07 An Extrapolation of Operator Valued Dyadic Paraproducts Tao MEI 1 Abstract We consider the dyadic paraproducts πφ on T associated with an M-valued function φ. Here T is the unit circle and M is a tracial von Neumann algebra. We prove that their boundedness on L(T, L(M)) for some 1 < p < ∞ implies their boundedness on L(T, L(M)) for all 1 < p ...

This paper considers a batch gradient method with penalty for training feedforward neural networks. The role of the penalty term is to control the magnitude of the weights and to improve the generalization performance of the network. An usual penalty is considered, which is a term proportional to the norm of the weights. The boundedness of the weights of the network is proved. The boundedness i...

Reinforcement Learning (RL) is a simulation-based counterpart of stochastic dynamic programming. In recent years, it has been used in solving complex Markov decision problems (MDPs). Watkins’ Q-Learning is by far the most popular RL algorithm used for solving discounted-reward MDPs. The boundedness of the iterates in Q-Learning plays a critical role in its convergence analysis and in making the...

Timed-Arc Petri Nets (TAPN) is a well studied extension of the classical Petri net model where tokens are decorated with real numbers that represent their age. Unlike reachability, which is known to be undecidable for TAPN, boundedness and coverability remain decidable. The model is supported by a recent tool called TAPAAL which, among others, further extends TAPN with invariants on places in o...