We present a nearly optimal differentially private version of the well known LASSO estimator. Our algorithm provides privacy protection with respect to each training example. The excess risk of our algorithm, compared to the non-private version, is Õ(1/n), assuming all the input data has bounded `∞ norm. This is the first differentially private algorithm that achieves such a bound without the p...

The paper is concerned with a general optimization problem for a nonlinear control system, in the presence of a running cost and a terminal cost, with free terminal time. We prove the existence of a patchy feedback whose trajectories are all nearly optimal solutions, with pre-assigned accuracy.

We study algorithms for computing the convolution of a private input x with a public input h, while satisfying the guarantees of (ε, δ)-differential privacy. Convolution is a fundamental operation, intimately related to Fourier Transforms. In our setting, the private input may represent a time series of sensitive events or a histogram of a database of confidential personal information. Convolut...

This note relaxes a condition given by Demko and Hill for the existence of a uniformly nearly-optimal stationary strategy in negative dynamic programming.

in this paper, an integration of improve particle swarm optimization (ipso) incombination with successive quadratic programming (sqp) so called ipso-sqpalgorithm is proposed to solve time optimal bang-bang control problems. theprocedure is found not sensitive to the initial guess of the solution. due to randomselection in the first stage of the search process, the chance of converging to theglo...