arXiv subjects

Anas Mifrani

Publications and source records attributed to Anas Mifrani.

5 recordsLinked to original sources

arXiv2025

Linear programming for finite-horizon vector-valued Markov decision processes

We propose a vector linear programming formulation for a non-stationary, finite-horizon Markov decision process with vector-valued rewards. Pareto efficient policies are shown to correspond to efficient solutions of the linear program, and vector linear programming theory allows us to fully characterize deterministic efficient policies. An algorithm for enumerating all efficient deterministic policies is presented then tested numerically in an engineering application.

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arXiv2025

Proof of Soland's conjecture on the efficient solutions to a multicriteria optimization problem

This note proves Richard M. Soland's conjecture that given an efficient solution to a multicriteria optimization problem, there need not exist a continuous, strictly increasing and strictly concave criterion space function that attains its maximum at the vector of criteria values achieved by that solution. We work out an important implication of this result for multicriteria decision making.

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arXiv2024

Multiple objective linear programming over the probability simplex

This paper considers the problem of maximizing multiple linear functions over the probability simplex. A classification of feasible points is indicated. A necessary and sufficient condition for a member of each class to be an efficient solution is stated. This characterization yields a computational procedure for ascertaining whether a feasible point is efficient. The procedure does not require that candidates for efficiency be extreme points. An illustration of the procedure is offered.

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arXiv2024

Efficient points in a sum of sets of alternatives

The concept of efficiency plays a prominent role in the formal solution of decision problems that involve incomparable alternatives. This paper develops necessary and sufficient conditions for the efficient points in a sum of sets of alternatives to be identical to the efficient points in one of the summands. Some of the conditions cover both finite and infinite sets; others are shown to hold only for finite sets. Examples are provided that illustrate these results.

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arXiv2023

A Counterexample and a Corrective to the Vector Extension of the Bellman Equations of a Markov Decision Process

Under the expected total reward criterion, the optimal value of a finite-horizon Markov decision process can be determined by solving the Bellman equations. The equations were extended by D. J. White to processes with vector rewards in 1982. Using a counterexample, we show that the assumptions underlying this extension fail to guarantee its validity. Analysis of the counterexample leads us to articulate a sufficient condition for White's functional equations to be valid. The condition is shown to be true when the policy space has been refined to include a special class of non-Markovian policies, or when the dynamics of the model are deterministic, or when the decision making horizon does not exceed three time steps. The paper demonstrates that, in general, the solutions to White's equations are sets of Pareto efficient policy returns over the refined policy space. Our results are illustrated with an example.

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