This paper shows that optimal set-membership filtering (SMF) is identical to minimax ( ) filtering, if optimal SMF corresponds to the smallest error bound specification that leads to a non-empty feasible solution. An adaptive minimax filtering algorithm that uses optimal quadratic approximations to the minimax cost function is proposed for adaptive implementation of optimal SMF. The proposed al...

In this chapter, the robust optimal control of linear quadratic system is considered. This problem is first formulated as a minimax optimal control problem. We prove that it admits a solution. Based on this result, we show that this infinite-dimensional minimax optimal control problem can be approximated by a sequence of finite-dimensional minimax optimal parameter selection problems. Furthermo...

A new voting procedure for electing committees, called the minimax procedure, is described. Based on approval voting (AV), it chooses the committee that minimizes the maximum “Hamming distance” to all voters (minimax outcome). Such an outcome may be diametrically opposed to the outcome obtained from aggregating votes in the usual manner, which minimizes the sum of the Hamming distances to all v...

In this paper we present a direct and simple approach to obtain bounds on the asymptotic minimax risk for the estimation of constrained binomial and multinomial proportions. Quadratic, normalized quadratic and entropy loss are considered and it is demonstrated that in all cases linear estimators are asymptotically minimax optimal. For the quadratic loss function the asymptotic minimax risk does...

In this paper, we propose a novel implementation of a minimax decision rule for continuous density hidden Markov model based robust speech recognition. By combining the idea of the minimax decision rule with a normal Viterbi search, we derive a recursive minimax search algorithm, where the minimax decision rule is repetitively applied to determine the partial paths during the search procedure. ...

This paper analyzes a connection between risk-sensitive and minimax criteria for discrete-time, nite-state Markov Decision Processes (MDPs). We synthesize optimal policies with respect to both criteria, both for nite horizon and discounted in nite horizon problems. A generalized decision-making framework is introduced, leading to stationary risk-sensitive and minimax optimal policies on the in ...