We put forward a Dynamic Regularized Parametric (DRP) approach for active portfolio policies. We build upon the parametric policy framework of Brandt et al. (2009) that directly links the portfolio weights to a limited set of asset characteristics. This yields a parsimonious specification that avoids modeling the joint distribution of returns, and as such remains applicable for large asset universes. We relax the assumption that policy coefficients are constant over time, to accommodate that the relevance of specific characteristics for future asset performance may vary. Dynamic policy coefficients are obtained by maximizing the conditional expected utility for each time period, with transaction costs being limited through a trading regularization. This dual-objective optimization problem results in an elegant filter to update the policy coefficients, balancing between adapting to valuable new, yet inherently noisy, information and providing a stable strategy that avoids costly re-balancing. We demonstrate that for a mean-variance utility investor, our framework yields an intuitive analytical solution. In an empirical application using the full universe of stocks from the NYSE, AMEX and Nasdaq, we find that the DRP approach produces substantial gains in out-of-sample portfolio performance, where both incorporating dynamics and regularization are important to achieve this.