Neural networks were evolved through genetic algorithms to focus minimax search in the game of Othello. At each level of the search tree, the focus networks decide which moves are promising enough to be explored further. The networks effectively hide problem states from minimax based on the knowledge they have evolved about the limitations of minimax and the evaluation function. Focus networks ...

It is known that bounds on the minimax values of nodes in a game tree can be used to reduce the computational complexity of minimax search for two-player games. We describe a very simple method to estimate bounds on the minimax values of interior nodes of a game tree, and use the bounds to improve minimax search. The new algorithm, called forward estimation, does not require additional domain k...

The problems of predictive density estimation with Kullback-Leibler loss, optimal universal data compression for MDL model selection, and the choice of priors for Bayes factors in model selection are interrelated. Research in recent years has identified procedures which are minimax for risk in predictive density estimation and for redundancy in universal data compression. Here, after reviewing ...

Neural networks were evolved through genetic algorithms to focus minimax search in the game of Othello. At each level of the search tree, the focus networks decide which moves are promising enough to be explored further. The networks effectively hide problem states from minimax based on the knowledge they have evolved about the limitations of minimax and the evaluation function. Focus networks ...

Consider estimating the mean vector from data Nn( ; I) with lq norm loss, q 1, when is known to lie in an n-dimensional lp ball, p 2 (0;1). For large n, the ratio of minimax linear risk to minimax risk can be arbitrarily large if p < q. Obvious exceptions aside, the limiting ratio equals 1 only if p = q = 2. Our arguments are mostly indirect, involving a reduction to a univariate Bayes minimax ...

New formulas are given for the minimax linear risk in estimating a linear functional of an unknown object from indirect data contaminated with random Gaussian noise. The formulas cover a variety of loss functions, and do not require the symmetry of the convex a priori class. It is shown that affine minimax rules are within a few percent of minimax even among nonlinear rules, for a variety of lo...

Toeplitz covariance matrices are used in the analysis of stationary stochastic processes and a wide range of applications including radar imaging, target detection, speech recognition, and communications systems. In this paper, we consider optimal estimation of large Toeplitz covariance matrices and establish the minimax rate of convergence for two commonly used parameter spaces under the spect...

This article presents the results of an empirical experiment designed to gain insight into what is the effect of the minimax on the evaluation function. The experiment’s simulations were performed upon the KRK chess endgame. Main result is that dependencies between evaluations of sibling nodes in a game tree and an abundance of possibilities to commit blunders present in the KRK endgame are not...

Markov games is a framework which can be used to formalise n-agent reinforcement learning (RL). Littman (Markov games as a framework for multi-agent reinforcement learning, in: Proceedings of the 11th International Conference on Machine Learning (ICML-94), 1994.) uses this framework to model two-agent zero-sum problems and, within this context, proposes the minimax-Q algorithm. This paper revie...

We present three results on the complexity of Minimax Approval Voting. First, we study Minimax Approval Voting parameterized by the Hamming distance d from the solution to the votes. We show Minimax Approval Voting admits no algorithm running in time O(2 log ), unless the Exponential Time Hypothesis (ETH) fails. This means that the O(d) algorithm of Misra et al. [AAMAS 2015] is essentially opti...