In combinatorial games such aschessand Go, theminimax algorithmgives a method of selecting the next optimal move. Firstly, an evaluation functionf:\mathbb{P} \rightarrow \mathbb{R}f:P→Rfrom the set of positions to real numbers is required, representing the payoff to the first player. For ...
The results are applied to uncertain nonlinear partially observable systems, in which the nominal measure is modelled through conditional distributions, and existence of optimal minimax strategies is proved using wide-sense controls.Stochastic Processes, Finance and Control: A Festschrift in Honor of ...
Rate-Preserving Discretization Strategies for Semi-Infinite Programming and Optimal Control Control & Optimization 30 (3), 548–572.Rate-preserving discretization strategies for semi-infinite programming and optimal. Polak E,He L M. The SIAM ... E Polak,L He - 《Siam Journal on Control & Optimi...
Their well-defined rules let you explore different strategies in search of a surefire way to win. Theminimax algorithmis used to choose the optimal move at any point in a game. You’ll learn how to implement a minimax player in Python that can play the game of Nim perfectly. In this tu...
Our second contribution is to show how to use the Mirror Descentalgorithm to obtain computationally efficient strategies with minimax optimalregret bounds in specific examples. More precisely we study two canonicalaction sets: the hypercube and the Euclidean ball. In the former case, weobtain the ...
For a zero-sum differential game, an algorithm is proposed for computing the value of the game and constructing optimal control strategies with the help of stepwise minimax. It is assumed that the dynamics can be nonlinear and the cost functional of the game is the sum of an integral term ...
As opposed to other tree-exploration techniques, this new algorithm considers complete paths of a tree (strategies) where a given entropy is spread. The optimal randomized strategy is efficiently computed by means of a simple recurrence relation while keeping the same complexity as the original ...
We study the regret of optimal strategies for online convex optimization games. Using von Neumann's minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical minimization algorithm in a stochastic process setting: it is equal ...
The results of a case study indicate that the reasonable solutions generated can help decision makers understand the consequence of short-term and long-term decisions, identify optimal strategies for filter allocation and selection with minimized system-maintenance cost and system-failure risk....
minimax strategies are proposed. Also, we prove that the values of the finite-horizon problem converge to the values of the infinite-horizon problems. Moreover, for finite-horizon problems an algorithm of calculation of minimax strategies is developed and tested by using time-varying stochastic ...