We present the results of a partially quenched lattice QCD calculation of light quark masses with $N_f=2$ degenerate dynamical flavors. Numerical simulations are carried out using the plaquette gauge action and the Wilson quark action at $beta = 5.8$ ($a^{-1} simeq 3.2gev$). The spatial extension of the $24^3 times 48$ lattice is about 1.5 fm. Configurations have been generated at four values of the sea quark masses, for which the ratio of pseudoscalar over vector meson masses is in the range $M_P/M_V simeq 0.60 div 0.75$. An important feature of the present study is the use of non-perturbative renormalization, performed with the $ri$ method. The effects of dynamical sea quarks in the determination of light quark masses have been investigated by performing a quenched calculation on a similar lattice. Our results for the average up-down and strange quark masses are $m_{ud}^{MS} (2gev) = 4.3(4) (^{+1.1}_{-0.4})mev$ and $m_s^{MS}(2gev)=101(8)(^{+25}_{-9}) mev$. These values are larger than those obtained by evaluating the quark mass renormalization constants with one-loop (boosted) perturbation theory. Our results for the light quark masses are compatible with those obtained in the quenched simulation. No significant sea quark effects are seen, at the values of sea quark masses used in the present study.
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